In an investigation to determine the relationship between the degree of metal corrosion and the length of time the metal is exposed to the action of soil acids, the percentage of corrosion and exposure time were measured weekly.

The data were fitted using the quadratic model,
E(y) = β0 + β1x + β2x2, with the following results.
Excel output for Exercise 13.35

a. What percentage of the total variation is explained by the quadratic regression of y on x?
b. Is the regression on x and x2 significant at the a = .05 level of significance?
c. Is the linear regression coefficient significant when x2 is in the model?
d. Is the quadratic regression coefficient significant when x is in the model?
e. The data were fitted to a linear model without the quadratic term with the results that follow. What can you say about the contribution of the quadratic term when it is included i n the model?
Excel output for Exercise 13.35

f. The plot of the residuals from the linear regression model in part e shows a specific pattern. What is the term in the model that seems to be missing?

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y 0.1 03 0.5 0.8 5 1.8 2.5 3.4 6 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.9993 0.9985 0.9979 0.0530 ANOVA df SS MS 9.421 4.710 1676.610 0.014 0.003 9.435 F Significance F 0.000 Regression Residual Total Coefficients Standard Error tStat P-value Intercept 0.196 0.100 0.062 0.074 2.656 0.045 0.038 -2.652 0.045 0.004 15.138 0.000 x-sq SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.9645 0.9303 0.9187 0.3311 ANOVA df 1 8.777 8.777 80.052 6 7 MS Significance F Regression Residual Tota 0.000 0.658 9.435 0.110 Standar Coefficients 0.732 0.457 t Stat 2.838 8.947 P-value 0.030 0.000 Error Intercept 0.258 0.051 Residuals versus the Fitted Values response is y) 0.5 0.4 0.3 0.2 0.1 9 0.0 -0.1 -0.2 -0.3 -0.4 0.0 0.5 1.0 1.5 2.0 25 3.0 Fitted Value