Additional Statistics:
S: The standard error of the regression (S) is 0.0214408.
R-Squared (R-Sq): The R-squared value is 96.0%, indicating that 96.0% of the variation in the Cr concentration can be explained by the regression model.
Adjusted R-Squared (R-Sq(adj)): The adjusted R-squared value is 95.5%, which takes into account the number of predictor variables in the model.
The analysis of variance (ANOVA) results for the regression analysis of Cr (chromium) are as follows:
Regression: The model includes 3 degrees of freedom (DF) and the sum of squares (SS) for regression is 0.284668. The mean sum of squares (MS) is 0.094889. The F-value is 206.41, indicating that the regression model is statistically significant. The p-value is 0.000, further supporting the significance of the regression model
Residual Error: The residual error, which represents the variability not explained by the regression model, has 26 degrees of freedom. The sum of squares for the residual error is 0.011952, and the mean sum of squares is 0.000460.
Total: The total sum of squares is 0.296620, with a total of 29 degrees of freedom.
These results suggest that the regression model is a very good fit for the data and explains a significant portion of the variation in the cr concentration.
(A). IN THE REGRESSION ANALYSIS FOR VERNONIA AMYGDALINA (HC), THE EQUATION TO PREDICT THE HC CONCENTRATION IS AS FOLLOWS.
HC = 3.10 + 0.00589 Time_1 + 0.00339 Mass_1 - 0.460 * pH_1
The coefficient values for each predictor variable are as follows:
Constant: 3.0969
Time_1: 0.0058911 with a standard error (SE) of 0.0005299
Mass_1: 0.0033893 with a standard error (SE) of 0.0007112
pH_1: -0.4596 with a standard error (SE) of 0.1432
The T-values and P-values indicate the significance of each predictor variable:
Time_1: T = 11.12, P < 0.000 (highly significant)
Mass_1: T = 4.77, P < 0.000 (highly significant)
pH_1: T = -3.21, P = 0.004 (significant)
These results suggest that time and mass have a highly significant impact on the HC concentration, while pH_1 also has a significant impact.
Additional Statistics:
S: The standard error of the regression (S) is 0.0166601.
R-Squared (R-Sq): The R-squared value is 93.4%, indicating that 93.4% of the variation in the HC concentration can be explained by the regression model.
Adjusted R-Squared (R-Sq(adj)): The adjusted R-squared value is 92.7%, which takes into account the number of predictor variables in the model.
These results suggest that the regression model is a good fit for the data and explains a significant portion of the variation in the HC concentration, primarily influenced by the time, mass, and pH_1 variables.
THE ANALYSIS OF VARIANCE (ANOVA) RESULTS FOR THE REGRESSION ANALYSIS OF VERNONIA AMYGDALINA (HC) ARE AS FOLLOWS.
Regression: The model includes 3 degrees of freedom (DF) and the sum of squares (SS) for regression is 0.102634. The mean sum of squares (MS) is 0.034211. The F-value is 123.26, indicating that the regression model is statistically significant. The p-value is 0.000, further supporting the significance of the regression model.
Residual Error: The residual error, which represents the variability not explained by the regression model, has 26 degrees of freedom. The sum of squares for the residual error is 0.007217, and the mean sum of squares is 0.000278.
Total: The total sum of squares is 0.109851, with a total of 29 degrees of freedom.
These results suggest that the regression model is a good fit for the data and explains a significant portion of the variation in the HC concentration.
(B). IN THE REGRESSION ANALYSIS FOR PB_1 (LEAD), THE EQUATION TO PREDICT THE PB_1 CONCENTRATION IS AS FOLLOW.
Pb_1 = 0.73 + 0.00881 Time_1 + 0.00204 Mass_1 - 0.104 * pH_1
The coefficient values for each predictor variable are as follows:
Constant: 0.726
Time_1: 0.008814 with a standard error (SE) of 0.001413
Mass_1: 0.002037 with a standard error (SE) of 0.001897
pH_1: -0.1037 with a standard error (SE) of 0.3820
The T-values and P-values indicate the significance of each predictor variable:
Time_1: T = 6.24, P < 0.000 (highly significant)
Mass_1: T = 1.07, P = 0.293 (not significant)
pH_1: T = -0.27, P = 0.788 (not significant)
These results suggest that time has a significant impact on the Pb_1 concentration, while mass and pH_1 do not appear to be significant.
Additional Statistics:
S: The standard error of the regression (S) is 0.0444367.
R-Squared (R-Sq): The R-squared value is 87.6%, indicating that 87.6% of the variation in the Pb_1 concentration can be explained by the regression model.
Adjusted R-Squared (R-Sq(adj)): The adjusted R-squared value is 86.1%, which takes into account the number of predictor variables in the model.
THE ANALYSIS OF VARIANCE (ANOVA) RESULTS FOR THE REGRESSION ANALYSIS ARE AS FOLLOWS.
Regression: The model includes 3 degrees of freedom (DF) and the sum of squares (SS) for regression is 0.36149. The mean sum of squares (MS) is 0.12050. The F-value is 61.02, indicating that the regression model is statistically significant. The p-value is 0.000, further supporting the significance of the regression model.
Residual Error: The residual error, which represents the variability not explained by the regression model, has 26 degrees of freedom. The sum of squares for the residual error is 0.05134, and the mean sum of squares is 0.00197.
Total: The total sum of squares is 0.41283, with a total of 29 degrees of freedom.
These results suggest that the regression model is a decent fit for the data and explains a significant portion of the variation in the Pb_1 concentration, primarily influenced by the time variable.
(C) In our research on revolutionizing soil remediation, specifically exploring the frontiers of bioremediation using Vernonia galamensis and Vernonia amydalina spices in hydrocarbon-contaminated soil, we conducted a regression analysis to evaluate the performance factors. We found that the presence of zinc (Zn_1) in the soil can be predicted using the following equation: Zn_1 = 3.78 + 0.00823 Time_1 + 0.00530 Mass_1 - 0.573 pH_1.
Analyzing the predictors, we observed that time (Time_1), mass (Mass_1), and pH (pH_1) all play significant roles. Specifically, time had a positive coefficient of 0.0082314, indicating that as time increases, the presence of zinc in the soil also tends to increase. Similarly, mass showed a positive coefficient of 0.005304, implying that higher mass contributes to higher zinc levels. On the other hand, pH had a negative coefficient of -0.5733, suggesting that higher pH levels may lead to a decrease in zinc concentration.
The analysis further revealed that the regression model accounted for approximately 93.8% of the variability in zinc levels (R-Sq = 93.8%), indicating a strong relationship between the predictors and the response variable. This relationship was also supported by the adjusted R-Squared value of 93.1%. Moreover, the standard error (S) of the model was found to be 0.0239661, indicating the accuracy of the predictions.
“In our analysis of variance, we evaluated the significance of the regression model in predicting zinc levels in hydrocarbon-contaminated soil using Vernonia galamensis and Vernonia amydalina spices. The results indicate a highly significant relationship between the predictors and the response variable.
The regression model demonstrated a significant overall impact, as evidenced by the F-statistic of 131.74 with a corresponding p-value of 0.000. This indicates that the model as a whole is effective in explaining the variability in zinc concentrations.
Furthermore, we assessed the variability within the model by examining the residual error. The sum of squares (SS) for the residual error was found to be 0.014934, with degrees of freedom (DF) of 26. This translates to a mean square (MS) value of 0.000574, representing the average variation in zinc levels not accounted for by the predictors
Considering both the regression and residual error, the total sum of squares (SS) was calculated to be 0.241937, with a total of 29 degrees of freedom (DF). This provides an overview of the overall variation in zinc concentrations within the hydrocarbon-contaminate
These findings underscore the significance of the regression model in accurately predicting zinc levels, highlighting the potential of Vernonia galamensis and Vernonia amydalina spices in revolutionizing soil remediation. The low p-value and high F-statistic further emphasize the strength and reliability of the model in explaining the variations observed in the data
(D) We conducted a regression analysis to examine the relationship between chromium levels (Cr_1) and the factors of time (Time_1), mass (Mass_1), and pH (pH_1) in the context of our research on revolutionizing soil remediation. The regression equation derived from our analysis is as follows: Cr_1 = -2.36 + 0.00428 Time_1 + 0.00556 Mass_1 + 0.345 pH_1.
Analyzing the predictors, we found that each factor plays a significant role in influencing chromium levels. Time exhibited a positive coefficient of 0.0042798, indicating that an increase in time can lead to higher chromium concentrations. Similarly, mass showed a positive coefficient of 0.0055637, suggesting that higher mass contributes to increased chromium levels. pH also had a positive coefficient of 0.3454, indicating that higher pH values are associated with higher chromium concentrations.
The regression model accounted for approximately 97.7% of the variability observed in chromium levels (R-Sq = 97.7%). This indicates a strong relationship between the predictors and the response variable. The adjusted R-Squared value of 97.5% further supports the model’s effectiveness in explaining the variations in chromium concentrations.
The standard error (S) of the model was found to be 0.0169970, which represents the accuracy of the predictions made by the model.
In our analysis of variance, we examined the significance of the regression model in predicting chromium levels (Cr_1) based on the factors of time (Time_1), mass (Mass_1), and pH (pH_1) in the context of soil remediation. The results revealed a highly significant relationship between the predictors and the response variable.
The regression model showed a significant overall impact, with a calculated F-statistic of 373.21 and a corresponding p-value of 0.000. This indicates that the model as a whole is effective in explaining the variability observed in chromium concentrations.
To further assess the variability within the model, we examined the residual error. The sum of squares (SS) for the residual error was found to be 0.00751, with 26 degrees of freedom (DF). This leads to a mean square (MS) value of 0.00029, representing the average variation in chromium levels not accounted for by the predictors.
Considering both the regression and residual error, the total sum of squares (SS) was calculated to be 0.33097, with a total of 29 degrees of freedom (DF). This provides an overview of the overall variation in chromium concentrations within the context of the soil remediation study.
These findings emphasize the significant role of the regression model in accurately predicting chromium levels, highlighting the potential of the time, mass, and pH factors in revolutionizing soil remediation. The low p-value and high F-statistic further underscore the strength and reliability of the model in explaining the observed variations in the data.
(E). IN OUR STUDY ON CLAY SOIL,
we conducted a multiple regression analysis using Minitab software to model the relationship between the presence of a specific component (HC) and the factors of time, mass, and pH. The regression equation derived from our analysis is as follows: HC = -6.59 + 0.00538 Time + 0.00455 Mass + 0.970 pH.
Analyzing the predictors, we observed that each factor plays a significant role in influencing the presence of the component. Time exhibited a positive coefficient of 0.005381, indicating that an increase in time can lead to higher levels of the specific component. Similarly, mass showed a positive coefficient of 0.004554, suggesting that higher mass contributes to increased levels of the component. pH also had a positive coefficient of 0.970, indicating that higher pH values are associated with higher levels of the component.
The regression model demonstrated statistical significance, as evidenced by the t-values and p-values for each predictor. The constant term had a t-value of -3.30 and a corresponding p-value of 0.003. The coefficients for time and mass had t-values of 4.90 and 2.73, respectively, with p-values of 0.000 and 0.011. These results indicate that each predictor significantly contributes to the presence of the component in the clay soil.
In the analysis of the Vernonia Galamensis model for clay soil, we further evaluated the significance of the pH factor and the overall model performance using additional statistical measures. Here’s the paraphrased information you provided:
“The pH factor showed a coefficient of 0.9696 with a standard error of 0.3016. The corresponding t-value was 3.22, and the associated p-value was 0.003. These results indicate that pH has a significant positive effect on the presence of the specific component in the clay soil when considering the Vernonia Galamensis model.
The regression model accounted for approximately 93.5% of the variability observed in the component levels (R-Sq = 93.5%), indicating a strong relationship between the predictors and the response variable. The adjusted R-Squared value of 92.7% further supports the model’s effectiveness in explaining the observed variations.
In the analysis of variance
we assessed the significance of the regression model as a whole. The model yielded an F-statistic of 124.36 and a p-value of 0.000, indicating a highly significant impact. This suggests that the model is effective in explaining the variability in the component levels.
Examining the variability within the model, the residual error showed a sum of squares (SS) of 0.04649, with 26 degrees of freedom (DF), resulting in a mean square (MS) value of 0.00179. This represents the average variation in component levels not accounted for by the predictors.
Considering both the regression and residual error, the total sum of squares (SS) was calculated to be 0.71364, with a total of 29 degrees of freedom (DF). This provides an overview of the overall variation in component levels within the context of the Vernonia Galamensis model for clay soil.
These findings highlight the significance of pH in influencing the presence of the specific component in clay soil. The high R-Squared values and low p-value in both the regression analysis and analysis of variance further support the reliability and effectiveness of the model, underscoring the potential of Vernonia Galamensis in revolutionizing soil treatment for clay soil.”
IN OUR REGRESSION ANALYSIS FOR LEAD (PB) LEVELS,
we examined the relationship between Pb and the factors of time, mass, and pH. The regression equation derived from our analysis is Pb = 2.96 + 0.00782 Time + 0.00324 Mass - 0.443 pH.
Analyzing the predictors, we found that each factor plays a significant role in influencing Pb levels. Time exhibited a positive coefficient of 0.0078210, indicating that as time increases, Pb levels tend to increase. Similarly, mass showed a positive coefficient of 0.003239, suggesting that higher mass contributes to higher Pb levels. On the other hand, pH had a negative coefficient of -0.4431, indicating that higher pH values are associated with lower Pb levels.
The regression model accounted for approximately 91.9% of the variability observed in Pb levels (R-Sq = 91.9%). This indicates a strong relationship between the predictors and the response variable. The adjusted R-Squared value of 91.0% further supports the model’s effectiveness in explaining the variations in Pb concentrations.
The standard error (S) of the model was found to be 0.0268981, which represents the accuracy of the predictions made by the model.
IN THE ANALYSIS OF VARIANCE,
We assessed the significance of the regression model in predicting lead (Pb) levels based on the factors of time, mass, and pH. Here’s a paraphrased version of the information you provided:
The analysis of variance revealed that the regression model as a whole has a significant impact on Pb levels, as indicated by the F-statistic of 98.37 and a corresponding p-value of 0.000. This suggests that the model is effective in explaining the variability observed in Pb concentrations.
Examining the variability within the model, the residual error had a sum of squares (SS) of 0.018811, with 26 degrees of freedom (DF). This resulted in a mean square (MS) value of 0.000724, representing the average variation in Pb levels not accounted for by the predictors.
Considering both the regression and residual error, the total sum of squares (SS) was calculated to be 0.232324, with a total of 29 degrees of freedom (DF). This provides an overview of the overall variation in Pb levels within the context of the regression model.
These findings further confirm the significant impact of the regression model in explaining the variability in Pb levels. The low p-value and high F-statistic indicate the reliability and effectiveness of the model, emphasizing the potential of time, mass, and pH as predictors for Pb concentrations.
IN OUR REGRESSION ANALYSIS FOR ZINC (ZN) LEVELS
We examined the relationship between Zn and the factors of time, mass, and pH. The regression equation derived from our analysis is Zn = -2.67 + 0.00210 Time + 0.00169 Mass + 0.396 pH.
Analyzing the predictors, we found that each factor plays a significant role in influencing Zn levels. Time exhibited a positive coefficient of 0.0020999, indicating that as time increases, Zn levels tend to increase. Similarly, mass showed a positive coefficient of 0.0016856, suggesting that higher mass contributes to higher Zn levels. Additionally, pH had a positive coefficient of 0.39558, indicating that higher pH values are also associated with higher Zn levels.
The regression model accounted for approximately 98.1% of the variability observed in Zn levels (R-Sq = 98.1%). This indicates a strong relationship between the predictors and the response variable. The adjusted R-Squared value of 97.9% further supports the model’s effectiveness in explaining the variations in Zn concentrations.
The standard error (S) of the model was found to be 0.00879440, which represents the accuracy of the predictions made by the model.
IN THE ANALYSIS OF VARIANCE,
We assessed the significance of the regression model in predicting zinc (Zn) levels based on the factors of time, mass, and pH. Here’s a paraphrased version of the information you provided:
The analysis of variance revealed that the regression model as a whole has a highly significant impact on Zn levels, as indicated by the F-statistic of 445.67 and a corresponding p-value of 0.000. This suggests that the model is highly effective in explaining the variability observed in Zn concentrations.
Examining the variability within the model, the residual error had a sum of squares (SS) of 0.002011, with 26 degrees of freedom (DF). This resulted in a mean square (MS) value of 0.000077, representing the average variation in Zn levels not accounted for by the predictors.
Considering both the regression and residual error, the total sum of squares (SS) was calculated to be 0.105417, with a total of 29 degrees of freedom (DF). This provides an overview of the overall variation in Zn levels within the context of the regression model.
These findings further confirm the highly significant impact of the regression model in explaining the variability in Zn levels. The low p-value and high F-statistic indicate the reliability and effectiveness of the model, emphasizing the potential of time, mass, and pH as predictors for Zn concentrations.
IN THE REGRESSION ANALYSIS OF CR (CONTAMINANT REMOVAL) VERSUS TIME, MASS, AND PH, WE OBTAINED THE FOLLOWING RESULTS.
The regression equation is: Cr = 1.71 + 0.00830 Time + 0.00608 Mass - 0.271 * pH
The predictors, coefficients (Coef), standard errors (SE Coef), t-values (T), and p-values (P) are as follows.
Constant: 1.713, SE Coef: 1.689, T: 1.01, P: 0.320
Time: 0.0082985, SE Coef: 0.0009276, T: 8.95, P: 0.000
Mass: 0.006083, SE Coef: 0.001410, T: 4.31, P: 0.000
pH: -0.2708, SE Coef: 0.2548, T: -1.06, P: 0.298
We also calculated the standard deviation (S) as 0.0357295, indicating the variability in the data. The coefficient of determination (R-Sq) is 91.4%, suggesting that 91.4% of the variation in Cr can be explained by the predictors. The adjusted R-Square (R-Sq(adj)) is 90.4%, which accounts for the degrees of freedom in the model.
We conducted an Analysis of Variance (ANOVA) to assess the significance of the regression model in explaining the variation in Cr (Contaminant Removal). Here are the results:
REGRESSION:
● Degrees of Freedom (DF): 3
● Sum of Squares (SS): 0.35398
● Mean Square (MS): 0.11799
● F-value: 92.43
● p-value: 0.000
Residual Error
Total:
The ANOVA indicates that the regression model is highly significant, with a p-value of 0.000. This suggests that the predictors (Time, Mass, pH) collectively have a strong influence on the variation in Cr. The Residual Error represents the unexplained variation in the data, while the Total SS represents the total variation observed.
LET’S DIVE INTO THE VERNONIA AMYGDALINA MODELLING!
Specifically, we’ll focus on the regression analysis of HC_1 (Hydrocarbon Concentration) versus Time_1, Mass_1, and pH_1. Here’s what we discovered:
The regression equation we derived is: HC_1 = -13.8 + 0.00243 Time_1 - 0.00250 Mass_1 + 2.06 * pH_1
Now, let’s take a closer look at the predictors, their coefficients (Coef), standard errors (SE Coef), t-values (T), and p-values (P):
Constant: -13.772, SE Coef: 1.484, T: -9.28, P: 0.000
Time_1: 0.0024258, SE Coef: 0.0009678, T: 2.51, P: 0.019
Mass_1: -0.002502, SE Coef: 0.001491, T: -1.68, P: 0.105
pH_1: 2.0617, SE Coef: 0.2248, T: 9.17, P: 0.000
These coefficients reveal the impact of each predictor on HC_1. The constant term provides an initial starting point. Time_1 has a positive coefficient, indicating that it contributes positively to HC_1. Mass_1, on the other hand, has a negative coefficient, suggesting a decreasing effect on HC_1. pH_1 displays a significant positive coefficient, indicating a strong positive influence on HC_1.
In summary, our analysis suggests that Time_1, Mass_1, and pH_1 play crucial roles in explaining the variation in HC_1. Time_1 and pH_1 have a significant impact, while Mass_1 exhibits a relatively weaker influence.
let’s explore the statistical analysis of the Vernonia Amygdalina Modelling. We obtained the following important metrics:
Standard Deviation (S): 0.0345595
Coefficient of Determination (R-Sq): 96.8%
Adjusted R-Square (R-Sq(adj)): 96.5%
These metrics provide insights into the accuracy and goodness-of-fit of the model. The high R-Sq value suggests that 96.8% of the variance in HC_1 can be explained by the predictors (Time_1, Mass_1, pH_1). The adjusted R-Sq value takes into account the degrees of freedom in the model and provides an accurate measure of the model’s explanatory power.
Additionally, we performed an Analysis of Variance (ANOVA) to assess the significance of the regression model:
Regression
● Degrees of Freedom (DF): 3
● Sum of Squares (SS): 0.95150
● Mean Square (MS): 0.31717
● F-value: 265.55
● p-value: 0.000
Residual Error:
Total:
The ANOVA results indicate that the regression model is highly significant, with a p-value of 0.000. In other words, the predictors collectively have a significant impact on HC_1. The Residual Error represents the unexplained variation in the data, while the Total SS represents the total variation observed.
Overall, these findings provide strong evidence for the effectiveness of the Vernonia Amygdalina Modelling in predicting HC_1 and understanding the factors influencing it.
THE REGRESSION ANALYSIS OF PB_1 (LEAD CONCENTRATION) VERSUS TIME_1, MASS_1, AND PH_1
Here are the key findings:
The regression equation we derived is: Pb_1 = 3.96 + 0.00844 Time_1 + 0.00589 Mass_1 - 0.598 * pH_1
Now, let’s examine the predictors, their coefficients (Coef), standard errors (SE Coef), t-values (T), and p-values (P):
Constant: 3.962, SE Coef: 1.697, T: 2.33, P: 0.028
Time_1: 0.008439, SE Coef: 0.001107, T: 7.62, P: 0.000
Mass_1: 0.005892, SE Coef: 0.001705, T: 3.46, P: 0.002
pH_1: -0.5983, SE Coef: 0.2571, T: -2.33, P: 0.028
These coefficients represent the impact of each predictor on Pb_1. The constant term provides the starting point, while Time_1, Mass_1, and pH_1 show their respective influences on Pb_1. Time_1 has a positive coefficient, suggesting a positive relationship with Pb_1. Mass_1 also exhibits a positive coefficient, indicating its positive influence. Interestingly, pH_1 displays a negative coefficient, implying a negative association with Pb_1.
Now, let’s explore the statistical metrics of the model:
Standard Deviation (S): 0.0395213
Coefficient of Determination (R-Sq): 84.2%
Adjusted R-Square (R-Sq(adj)): 82.4%
The R-Sq value of 84.2% indicates that 84.2% of the variation in Pb_1 can be explained by the predictors. The R-Sq(adj) accounts for the degrees of freedom in the model and provides a more accurate measure of the model’s explanatory power.
In summary, the regression analysis provides insights into the relationship between Pb_1 and the predictors (Time_1, Mass_1, pH_1). The model’s statistical metrics and the significance of the individual predictors contribute to a better understanding of Pb_1 and its influencing factors.
IN ORDER TO ASSESS THE SIGNIFICANCE OF THE REGRESSION MODEL FOR PB_1, AN ANALYSIS OF VARIANCE (ANOVA) WAS CONDUCTED. HERE ARE THE RESULTS:
REGRESSION:
● Degrees of Freedom (DF): 3
● Sum of Squares (SS): 0.216307
● Mean Square (MS): 0.072102
● F-value: 46.16
● p-value: 0.000
Residual Error:
Total:
The ANOVA results indicate that the regression model is highly significant, with a p-value of 0.000. This suggests that the predictors (Time_1, Mass_1, pH_1) collectively have a significant impact on Pb_1. The Residual Error represents the unexplained variation in the data, while the Total SS represents the total variation observed.
Overall, these findings provide strong evidence for the effectiveness of the regression model in explaining the variation in Pb_1 and emphasizing the significance of the predictors.
Regression Analysis: Zn_1 and its relationship with Time_1, Mass_1, and pH_1
The regression equation shows that Zn_1 (Zinc) can be estimated based on the values of Time_1, Mass_1, and pH_1. The equation is given by Zn_1 = -1.63 + 0.00253 Time_1 + 0.00189 Mass_1 + 0.244 pH_1.
Predictor Coefficients:
The coefficients for each predictor variable are as follows:
Time_1: 0.0025315
Mass_1: 0.0018940
pH_1: 0.24446
These coefficients represent the change in Zn_1 associated with a one-unit increase in each predictor, while holding other predictors constant.
Statistical Measures:
Standard Error (SE) represents the precision of the coefficient estimates.
T-value indicates the significance of the coefficient, where larger absolute values suggest more significant relationships.
P-value shows the probability of observing a coefficient as extreme as the one obtained, assuming the null hypothesis (no relationship) is true.
Additional information:
The constant term in the regression equation is -1.6346, indicating the estimated Zn_1 value when all predictors are zero.
The Standard Error (S) of the regression is 0.00870020, which represents the average distance between the observed and predicted values.
R-squared (R-Sq) is 98.1%, indicating that the predictor variables explain 98.1% of the variability in Zn_1.
R-squared (adjusted) (R-Sq(adj)) is 97.8%, which considers the number of predictor variables and adjusts R-squared accordingly.
The Analysis of Variance (ANOVA) shows the breakdown of the sources of variation in the data:
1. Regression:
Degrees of Freedom (DF): 3
um of Squares (SS): 0.099379
Mean Square (MS): 0.033126
F-value: 437.64
P-value: 0.000
The regression analysis indicates that the predictor variables have a significant impact on the response variable.
1. Residual Error:
Degrees of Freedom (DF): 26
Sum of Squares (SS): 0.001968
Mean Square (MS): 0.000076
The residual error represents the unexplained variation in the data that is not accounted for by the regression model.
1. Total:
The total variation in the data is the sum of the variation explained by the regression model and the residual error.
The ANOVA results indicate a highly significant relationship between the predictor variables and the response variable. The variation explained by the regression model is much larger than the unexplained variation.
1. Regression Analysis: Cr_1 and its relationship with Time_1, Mass_1, and pH_1:
The regression equation shows that Cr_1 (Chromium) can be estimated based on the values of Time_1, Mass_1, and pH_1. The equation is given by Cr_1 = 1.80 + 0.00685 Time_1 + 0.00940 Mass_1 - 0.279 pH_1.
Predictor Coefficients:
The coefficients for each predictor variable are as follows:
Time_1: 0.0068464
Mass_1: 0.009396
pH_1: -0.2788
These coefficients represent the change in Cr_1 associated with a one-unit increase in each predictor, while holding other predictors constant.
Statistical Measures:
Standard Error (SE) represents the precision of the coefficient estimates.
T-value indicates the significance of the coefficient, where larger absolute values suggest more significant relationships.
P-value shows the probability of observing a coefficient as extreme as the one obtained, assuming the null hypothesis (no relationship) is true.
Additional information:
The constant term in the regression equation is 1.801, indicating the estimated Cr_1 value when all predictors are zero.
The Standard Error (S) of the regression is 0.0278546, which represents the average distance between the observed and predicted values.
R-squared (R-Sq) is 94.9%, indicating that the predictor variables explain 94.9% of the variability in Cr_1.
R-squared (adjusted) (R-Sq(adj)) is 94.3%, which considers the number of predictor variables and adjusts R-squared accordingly.
These results suggest a strong relationship between the predictor variables and the response variable. However, it’s important to note that the coefficient for pH_1 is not statistically significant at the conventional level (P = 0.136). Further investigation may be needed to determine the significance of this variable.
The Analysis of Variance (ANOVA) table shows the breakdown of the sources of variation in the data:
Regression:
Degrees of Freedom (DF): 3
Sum of Squares (SS): 0.37409
Mean Square (MS): 0.12470
F-value: 160.72
P-value: 0.000
The regression analysis indicates that the predictor variables have a highly significant impact on the response variable.
Residual Error:
Degrees of Freedom (DF): 26
Sum of Squares (SS): 0.02017
Mean Square (MS): 0.00078
The residual error represents the unexplained variation in the data that is not accounted for by the regression model.
Total:
The total variation in the data is the sum of the variation explained by the regression model and the residual error.
The ANOVA results indicate a highly significant relationship between the predictor variables and the response variable. The variation explained by the regression model is much larger than the unexplained variation.
PROCEED WITH THE ANALYSIS FOR THE SANDY-LOAMY SOIL AND THE VERNONIA GALAMENSIS MODEL
Vernonia Galamensis Modelling.
a. Regression Analysis: HC (Hydrocarbon) versus Time, Mass, and pH:
The regression equation for the Sandy-Loamy Soil and Vernonia Galamensis model is as follows:
HC = -126 - 0.0207 Time - 0.0157 Mass + 18.6 pH
This equation represents the relationship between the Hydrocarbon concentration (HC) and the factors Time, Mass, and pH.
The coefficients in the equation show the impact of each factor on the Hydrocarbon concentration. A negative coefficient indicates that as the corresponding factor increases, the Hydrocarbon concentration decreases, while a positive coefficient indicates the opposite.
Using the least squares method, this regression equation was derived to best fit the data and predict the Hydrocarbon concentration based on the given factors.
Based on the information provided, here’s a paraphrased version of the analysis for the Vernonia Galamensis model on Sandy-Loamy Soil:
Regression Coefficients:
Constant: -125.51 (P = 0.003)
Time: -0.02073 (P = 0.127)
Mass: -0.01570 (P = 0.247)
pH: 18.619 (P = 0.004)
These coefficients represent the impact of each predictor variable (Time, Mass, and pH) on the Hydrocarbon concentration (HC).
Statistical Measures:
These measures indicate the goodness of fit and the explanatory power of the model. The R-squared value suggests that 62.3% of the variability in HC can be explained by the predictor variables.
Analysis of Variance:
Regression:
● Degrees of Freedom (DF): 3
● Sum of Squares (SS): 4.6396
● Mean Square (MS): 1.5465
● F-value: 14.31 (P = 0.000)
Residual Error:
● Degrees of Freedom (DF): 26
● Sum of Squares (SS): 2.8102
● Mean Square (MS): 0.1081
Total:
The ANOVA table indicates that the regression model is statistically significant, with a significant F-value (P = 0.000). This implies that the predictors collectively have a significant impact on the variation in HC.
Overall, the Vernonia Galamensis model on Sandy-Loamy Soil shows a moderate fit to the data, with pH being the most significant predictor. Further analysis or experimentation may be needed to improve the model’s performance.
THE REGRESSION EQUATION THAT DESCRIBES THE RELATIONSHIP BETWEEN PB (LEAD) AND THE VARIABLES TIME, MASS, AND PH IS AS FOLLOWS.
Lead (Pb) = -37.7 - 0.00290 Time + 0.00340 Mass + 5.56 * pH
Now, let’s take a look at the predictor coefficients and their statistical significance:
The constant coefficient is -37.681, indicating the baseline value of Pb when all other variables are zero. It has a standard error (SE) of 6.988 and a statistically significant T-value of -5.39 (p-value of 0.000).
The coefficient for Time is -0.002902, suggesting that as Time increases, there is a slight decrease in Pb concentration. However, this coefficient is not statistically significant, with a T-value of -1.23 (p-value of 0.229).
The coefficient for Mass is 0.003397, indicating that as Mass increases, there is a slight increase in Pb concentration. However, like Time, this coefficient is not statistically significant, with a T-value of 1.43 (p-value of 0.165).
The coefficient for pH is 5.562, suggesting that as pH increases, there is a significant increase in Pb concentration. This coefficient has a SE of 1.042 and a statistically significant T-value of 5.34 (p-value of 0.000)
THE OVERALL GOODNESS OF FIT OF THE REGRESSION MODEL IS ASSESSED THROUGH THE FOLLOWING METRICS:
The standard deviation (S) of the residuals is 0.0589214, indicating the average difference between the predicted and actual Pb values..
The R-squared value (R-Sq) is 93.3%, which means that 93.3% of the variability in Pb can be explained by the variables Time, Mass, and pH in the regression model.
The adjusted R-squared value (R-Sq(adj)) is 92.5%, taking into account the number of predictors in the model.
The ANOVA table provides information about the variance and significance of the regression model:
Source: This column indicates the source of the variation in the analysis.
DF (Degrees of Freedom): This column represents the degrees of freedom associated with each source of variation.
MS (Mean Square): This column represents the mean square, which is the sum of squares divided by the degrees of freedom.
F (F-value): This column shows the F-value, which is a ratio of the mean squares between regression and residual error. It measures the significance of the regression model.
P (p-value): This column provides the p-value associated with the F-value, indicating the significance level of the regression model.
Based on the ANOVA table:
Regression: The regression model has 3 degrees of freedom (DF) and accounts for a significant amount of variance in the data. The sum of squares (SS) for regression is 1.25980, and the mean square (MS) is 0.41993. The F-value is 120.96, with a very low p-value of 0.000, suggesting that the regression model is statistically significant.
Residual Error: The residual error represents the unexplained variance in the data after considering the regression model. It has 26 degrees of freedom and a sum of squares (SS) of 0.09026. The mean square (MS) for residual error is 0.00347.
Total: The total sum of squares (SS) is 1.35007, representing the total variance in the data.
The ANOVA indicates that the regression model significantly explains the variability in the data, as evidenced by the high F-value and low p-value. This suggests that the predictors (Time, Mass, and pH) have a significant impact on the Pb concentration.
The regression equation that describes the relationship between Zn (Zinc) and the variables Time, Mass, and pH is as follows:
Zinc (Zn) = -23.3 - 0.00135 Time + 0.00122 Mass + 3.45 * pH
Now, let’s delve into the predictor coefficients and their statistical significance:
The constant coefficient is -23.321, representing the baseline value of Zn when all other variables are zero. It has a standard error (SE) of 1.407 and a highly statistically significant T-value of -16.57 (p-value of 0.000).
The coefficient for Time is -0.0013451, indicating that as Time increases, there is a slight decrease in Zn concentration. This coefficient is statistically significant, with a T-value of -2.83 (p-value of 0.009).
The coefficient for Mass is 0.0012178, suggesting that as Mass increases, there is a slight increase in Zn concentration. This coefficient is also statistically significant, with a T-value of 2.54 (p-value of 0.017).
The coefficient for pH is 3.4524, indicating that as pH increases, there is a significant increase in Zn concentration. This coefficient has a SE of 0.2098 and a highly statistically significant T-value of 16.46 (p-value of 0.000).
The goodness of fit of the regression model is assessed through the following metrics:
The standard deviation (S) of the residuals is 0.0118667, indicating the average difference between the predicted and actual Zn values.
The R-squared value (R-Sq) is 99.2%, suggesting that 99.2% of the variability in Zn can be explained by the variables Time, Mass, and pH in the regression model.
The adjusted R-squared value (R-Sq(adj)) is 99.1%, taking into account the number of predictors in the model.
Based on these findings, it appears that Time, Mass, and pH are significant predictors of Zn concentration..
The ANOVA table provides information about the variance and significance of the regression model.
Source: This column indicates the source of the variation in the analysis.
DF (Degrees of Freedom): This column represents the degrees of freedom associated with each source of variation.
SS (Sum of Squares): This column indicates the sum of squares for each source of variation.
MS (Mean Square): This column represents the mean square, which is the sum of squares divided by the degrees of freedom.
F (F-value): This column shows the F-value, which is a ratio of the mean squares between regression and residual error. It measures the significance of the regression model.
P (p-value): This column provides the p-value associated with the F-value, indicating the significance level of the regression model.
Based on the ANOVA results
Regression: The regression model has 3 degrees of freedom (DF) and accounts for a significant amount of variance in the data. The sum of squares (SS) for regression is 0.45649, and the mean square (MS) is 0.15216. The F-value is 1080.55, with a very low p-value of 0.000, suggesting that the regression model is highly statistically significant.
Residual Error: The residual error represents the unexplained variance in the data after considering the regression model. It has 26 degrees of freedom and a sum of squares (SS) of 0.00366. The mean square (MS) for residual error is 0.00014.
Total: The total sum of squares (SS) is 0.46015, representing the total variance in the data.
The ANOVA indicates that the regression model significantly explains the variability in the data, as evidenced by the high F-value and low p-value. This suggests that the predictors (Time, Mass, and pH) have a strong and significant impact on the Zn concentration.
The regression equation that describes the relationship between Cr (Chromium) and the variables Time, Mass, and pH is as follows:
Chromium (Cr) = -18.6 + 0.00396 Time + 0.00195 Mass + 2.76 * pH
Now, let’s take a look at the predictor coefficients and their statistical significance:
The constant coefficient is -18.648, indicating the baseline value of Cr when all other variables are zero. It has a standard error (SE) of 1.941 and a highly statistically significant T-value of -9.61 (p-value of 0.000).
The coefficient for Time is 0.0039635, suggesting that as Time increases, there is a slight increase in Cr concentration. This coefficient is statistically significant, with a T-value of 6.05 (p-value of 0.000).
The coefficient for Mass is 0.0019489, indicating that as Mass increases, there is a slight increase in Cr concentration. This coefficient is also statistically significant, with a T-value of 2.95 (p-value of 0.007).
The coefficient for pH is 2.7577, indicating that as pH increases, there is a significant increase in Cr concentration. This coefficient has a SE of 0.2893 and a highly statistically significant T-value of 9.53 (p-value of 0.000).
The goodness of fit of the regression model is assessed through the following metrics:
The standard deviation (S) of the residuals is 0.0163666, indicating the average difference between the predicted and actual Cr values.
The R-squared value (R-Sq) is 99.0%, informing us that 99.0% of the variability in Cr can be explained by the variables Time, Mass, and pH in the regression model.
The adjusted r-squared value (r-sq(adj)) is 98.9%, taking into account the number of predictors in the model..
Based on these findings, it appears that Time, Mass, and pH are significant predictors of Cr concentration.
Vernonia amygdalina modeling refers to the process of developing a statistical or mathematical model to understand and predict the behavior, characteristics, or effects of Vernonia amygdalina, which is a plant species known for its medicinal properties. The modeling process involves analyzing data, identifying relevant variables, and fitting the data to a mathematical or statistical model. This allows researchers to gain insights into the various factors that influence Vernonia amygdalina and make predictions about its behavior, growth patterns, or potential applications. By using modeling techniques, researchers can enhance their understanding of Vernonia amygdalina and explore its potential uses in different fields such as medicine, agriculture, or environmental studies.
A. In the regression analysis conducted, the response variable “HC_1” was analyzed in relation to the predictor variables “Time_1,” “Mass_1,” and “pH_1.” The objective of this analysis was to examine the relationship between the predictor variables and their potential impact on the response variable. Through regression analysis, the model identifies the coefficients that best fit the data and allows for predictions or inferences to be made based on the values of the predictor variables. By studying the relationship between “HC_1” and “Time_1,” “Mass_1,” and “pH_1,” valuable insights can be gained regarding the influence of these factors on hydrocarbon levels
.R
The regression equation is
HC_1 = - 145 - 0.0395 Time_1 - 0.0217 Mass_1 + 21.5 pH_1
Predictor Coef SE Coef T P
Constant -144.86 22.10 -6.55 0.000
Time_1 -0.03950 0.01004 -3.93 0.001
Mass_1 -0.021669 0.008885 -2.44 0.022
pH_1 21.498 3.297 6.52 0.000
S = 0.208392 R-Sq = 87.5% R-Sq(adj) = 86.1%
Analysis of Variance
Source DF SS MS F P
Regression 3 7.9029 2.6343 60.66 0.000
Residual Error 26 1.1291 0.0434
Total 29 9.0320
.B….In the regression analysis performed, the response variable “Pb_1” was examined in relation to the predictor variables “Time_1,” “Mass_1,” and “pH_1.” The main objective of this analysis was to assess the relationship between the predictor variables and their potential impact on the response variable. By running regression analysis, the model determines the coefficients that best fit the data and enables predictions or inferences to be made based on the values of the predictor variables. By studying the relationship between “Pb_1” and “Time_1,” “Mass_1,” and “pH_1,” valuable insights can be gained concerning the influence of these factors on lead levels.
The regression equation is
Pb_1 = - 23.7 + 0.00058 Time_1 + 0.0130 Mass_1 + 3.48 pH_1
Predictor Coef SE Coef T P
Constant -23.74 10.01 -2.37 0.025
Time_1 0.000577 0.004546 0.13 0.900
Mass_1 0.012987 0.004024 3.23 0.003
pH_1 3.484 1.493 2.33 0.028
S = 0.0943675 R-Sq = 90.6% R-Sq(adj) = 89.5%
Analysis of Variance
Source DF SS MS F P
Regression 3 2.23640 0.74547 83.71 0.000
Residual Error 26 0.23154 0.00891
Total 29 2.46794
C. In the regression analysis conducted, the response variable “Zn_1, was analyzed in relation to the predictor variables “Time_1,” “Mass_1,” and “pH_1.” The purpose of this analysis was to assess the relationship and potential influence of these predictor variables on the response variable. Through regression analysis, the model determines the coefficients that best fit the data and enables predictions or inferences to be made based on the values of the predictor variables. By examining the relationship between “Zn_1” and “Time_1,” “Mass_1,” and “pH_1,” valuable insights can be gained regarding the impact of these factors on zinc levels.
The regression equation is
Zn_1 = - 4.66 + 0.00585 Time_1 + 0.0124 Mass_1 + 0.669 pH_1
Predictor Coef SE Coef T P
Constant -4.662 3.611 -1.29 0.208
Time_1 0.005848 0.001641 3.56 0.001
Mass_1 0.012441 0.001452 8.57 0.000
pH_1 0.6695 0.5388 1.24 0.225
S = 0.0340525 R-Sq = 97.1% R-Sq(adj) = 96.7%
Analysis of Variance
Source DF SS MS F P
Regression 3 0.99199 0.33066 285.16 0.000
Residual Error 26 0.03015 0.00116
Total 29 1.02214
D. In the regression analysis conducted, the response variable “Cr”.was analyzed in relation to the predictor variables “Time_1,” “Mass_1,” and “pH_1.” The aim of this analysis was to determine the relationship and potential influence of these predictor variables on the response variable. Through regression analysis, the statistical model identifies the coefficients that best fit the data and allows for predictions or inferences to be made based on the values of the predictor variables.
The regression equation is a mathematical representation of the relationship between a dependent variable and one or more independent variables. It is used to predict or estimate the value of the dependent variable based on the values of the independent variables.
Cr = - 16.8 + 0.00258 Time_1 + 0.00153 Mass_1 + 2.48 pH_1
Predictor Coef SE Coef T P
Constant -16.768 1.707 -9.82 0.000
Time_1 0.0025843 0.0007755 3.33 0.003
Mass_1 0.0015306 0.0006863 2.23 0.035
pH_1 2.4798 0.2547 9.74 0.000
S = 0.0160963 R-Sq = 99.0% R-Sq(adj) = 98.9%
Analysis of Variance: (ANOVA) is a statistical technique used to compare the means of multiple groups or factors to determine if there are significant differences among them. It helps in understanding the variability within and between groups and assesses the impact of different factors on the observed variations. ANOVA provides insights into whether the differences observed in the data are statistically significant or simply due to chance. By calculating the F-statistic and corresponding p-value, ANOVA helps researchers make informed decisions and draw meaningful conclusions from their data analysis.
Source DF SS MS F P
Regression 3 0.70075 0.23358 901.55 0.000
Residual Error 26 0.00674 0.00026
Total 29 0.70749
Based on the various models developed, the primary focus lies on two key statistical indicators: the p-value and the R2 value. The p-value, or probability value, plays a crucial role in determining the significance of a model. A model is considered to be statistically significant if the overall p-value is less than 0.05, indicating a high level of confidence in its accuracy. On the other hand, the R2 value represents the coefficient of determination, which measures the relationship between variables. A higher R2 value, closer to 100%, indicates a stronger correlation between the variables, making it a desirable outcome in model evaluation.
CONCLUSION AND RECOMMENDATION .
CONCLUSION.
In conclusion, this research study has demonstrated the effectiveness of Vernonia Galamensis and Vernonia Amygdalina, commonly known as bitter leaf, in remediating hydrocarbon and metal-contaminated soils. The study focused on sandy-loamy soil, clay soil, and swamp soil as representative soil types. The contamination involved the presence of hydrocarbons and metals in the soil. Through the application of bitter leaf extracts, the microorganisms present in the extracts, such as Pseudomonas aeruginosa, Staphylococcus aureus, and Escherichia coli, along with the phytochemicals present in the leaves, played a crucial role in the degradation of the metals present in the contaminated soil. These findings highlight the potential of bitter leaf as a natural and eco-friendly solution for soil remediation. By utilizing the bio-remedial properties of bitter leaf, the study offers a promising approach to mitigate the environmental impacts of hydrocarbon and metal contamination in various soil types. This research contributes to the field of environmental sustainability and aligns with the global efforts towards achieving the Sustainable Development Goals, particularly SDG 15 (Life on Land) and SDG 12 (Responsible Consumption and Production). The study’s findings provide valuable insights for further research and implementation of bitter leaf-based remediation strategies, ultimately leading to the restoration and preservation of contaminated soils and ecosystems,”After applying approximately 40g of both Vernonia extracts, a remarkable reduction of over 50% in contaminant concentration was observed across all soil samples within a span of 40 days. These promising findings establish the efficacy of both Vernonia extracts as highly effective bio-remediating agents suitable for the remediation of polluted soils.
RECOMMENDATION
It is recommended that to get the best remediating effect, depending on the vernonia extracts available. It should be applied wet and blended into the polluted soil. This is because the micro-organisms present to perform the bio-remediating activity is still active and numerous in the leaf as well as the area of contact between the micro-organisms and the pollutants are well increased. The increase in surface contact is due to the blending into the soil substrate. Applying the room dry is better in few approaches as it helps the remediation of more Pb in clay soil than using the wet blended extracts. Thus it is advised that the wet blended is used clinically with a more neutral PH to enable the micro-organisms function properly.
Limitation of Study
The first limitation to this study is the lack of financial support from the institution, to get more results like other metals and the constituents of the hydrocarbon like the PONA (paraffin, olefin, Naphthenes and aromatic) analysis requires more finance which cannot be handled by one person alone. Secondly, the non-availability of quality labs around to aid in carrying our environmental analysis is of a concern. This limits the type of projects and studies that should be carried out to aid knowledge contribution.
Contribution to Knowledge
In this thesis, I have been able to establish that the vernonia Galamensis and Vernonia Amygdalina can be used for bio-remediation and have developed regression models to know and predict the extent of materials and time required to perform remediation activities in the three types of soil for the required contaminants.