HW3SOL

leaves), x1=mean temperature (centigrate), x2=mean relative humidity. Run JMP to answer the following questions. (1) Fit the linear model with both independent variables. (a) What are the coefficients of the regression model y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2? β 0 = 20 . 002552 , β 1 = − 0 . 290153 , β 2 = 1 . 4009541. (b) Is the model significant? Be 95% confident. Yes. (c) Now look at the individual parameters. i. Is x 1 a significant predictor? No. ii. Is x 2 a significant predictor? Yes. iii. Is there a collinearity problem according to VIF? No. (2) Fit the following new model, y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + β 3 ∗ x 1 2 + β 4 ∗ x 2 2 + β 5 ∗ x 1 ∗ x 2 + ε to the aphid data. Compare the linear model (reduced model) with the new model (complete model). (a) What is the value of the test statistics and p value? The test statistics = 1.64179003770589, the pvalue = 0.20137. (b) Did you reject H 0 ? Be 95% confident. No. (c) Which model has a higher adjusted R square? y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + β 3 ∗ x 1 2 + β 4 ∗ x 2 2 + β 5 ∗ x 1 ∗ x 2 + ε . (4) Calculate a new response variable ty = log ( y ), the natural logarithm of the aphid count. Fit the new model, ty = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + ε to the aphid data. Compare the fit in this log model to the previous new model. (a) Which has the highest Adjusted R square? • y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + ε • y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + β 3 ∗ x 12 + β 4 ∗ x 2 2 + β 5 ∗ x 1 ∗ x 2 + ε • ty = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + ε y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + β 3 ∗ x 12 + β 4 ∗ x 2 2 + β 5 ∗ x 1 ∗ x 2 + ε . (b) Which has a lowest RMSE? • y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + ε • y = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + β 3 ∗ x 12 + β 4 ∗ x 2 2 + β 5 ∗ x 1 ∗ x 2 + ε • ty = β 0 + β 1 ∗ x 1 + β 2 ∗ x 2 + ε 3