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.

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 α = .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 in the model?

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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0.5 0.3 1.2 0.8 1.8 2.5 3.4 0.1 2 3 5 Regression Analysis: y versus x, x-sq The regression equation is y = 0.196 - 0.100 x + 0.0619 x-sq SE Coef 0.07395 Predictor Coef т Constant 0.19643 2.66 0.045 -0.10000 0.061905 0.03770 -2.65 0.045 x-sq2 0.004089 15.14 0.000 S = 0.0530049 R-Sq = 99.9% R-Sq (adj) = 99.8% Analysis of Variance Source DF MS Regression Residual Error 9.4210 4.7105 1676.61 0.000 0.0140 0.0028 Total 9.4350 Seq ss 8.7771 Source DF X-sq 0.6438