The below data below is a subset of data obtained in an experiment to study the relationship between x (soil pH) and y(A1 Concentration). Run an analysis to determine the best fit model that has the highest coefficient of determination between the following models (Exponential, Linear, Logarithmic, Polynomial 2, Polynomial 3 and Power). Use either excel and SPSS to conduct the analysis.

a. Which model provides the best fit and why?

i. What is the R squared Exponential?

ii. What is the R squared Linear?

iii. What is the R squared Logarithmic?

iv. What is the R squared Polynomial 2?

v. What is the R squared Polynomial 3?

vi. What is the R squared Power?

vii. What is the Best fit model?

b. What is the linear or nonlinear equation associated with this best fit model?

c. Using the best fit model equation, what is the predicted value of A1 Concentration for a pH value of 4.5 and the corresponding residual.

i. What is the Predicted y at x = 4.5?

ii. What is the Residual for x = 4.5

d. Provide an ANOVA table for this best fit model. (use SPSS. Load the data into SPSS then go to Analyze/Regression Curve Estimation and select ANOVA table for the best fit model you are looking for)

e. From the ANOVA table, is there a relationship between the independent and dependent variable. Test at alpha equal to .05.

i. What is the Calculated F value?

ii. What is the Critical F Value?

iv. What is the P-Value?

v. Is there a relationship between x and y (explain)

f. Conduct a utility test at the alpha equal .05 level to determine if the x variable contributes to model relationship. Does the x variable contribute to the relationship of x and y? Why or why not?

g. Conduct a utility test at the alpha equal .05 level to determine if the constant value contributes to model relationship. Does the constant value contribute of x and y? Why or why not?

h. What is the critical T value from parts f and g?

x (Soil pH)	y (A1 conc)
4.01	1.20
4.07	0.78
4.08	0.83
4.10	0.98
4.18	0.65
4.20	0.76
4.23	0.40
4.27	0.45
4.30	0.39
4.41	0.30
4.45	0.20
4.50	0.24
4.58	0.10
4.68	0.13
4.70	0.07
4.77	0.04