Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page. d) Is the variable from your best simple linear regression model (from part a) included in the model with the lowest overall MSE (part b)? Briefly explain why it could happen that the best single variable is not in the best overall model. e) Following the best subsets regression results, the sums of squares for regression and error (also called residual) are displayed for several models. Using the regression sums of squares information for the full model containing all four x variables, calculate i) the R2 value for the full model, ii) the F statistic for the test of the H0: b1 = b2 = b3 = b4 = 0, and iii) the standard deviation of the residuals for the full model. f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model. (Calculate an F statistic, obtain a tabled F value, and report the conclusion of your test, use a = .05). g) Using the regression sums of squares information, for the model containing the terms x1, x2 and x4, calculate the t statistic for the hypothesis H0: b1 = 0, where b1 is the coefficient of x1. (Hint: first calculate an F statistic for H0 and then take its square root to obtain the t value. Assume all regression coefficients are positive.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page.

d) Is the variable from your best simple linear regression model (from part a) included in the model with the lowest overall MSE (part b)? Briefly explain why it could happen that the best single variable is not in the best overall model.

e) Following the best subsets regression results, the sums of squares for regression and error (also called residual) are displayed for several models. Using the regression sums of squares information for the full model containing all four x variables, calculate i) the R2 value for the full model, ii) the F statistic for the test of the H0: b1 = b2 = b3 = b4 = 0, and iii) the standard deviation of the residuals for the full model.

f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model. (Calculate an F statistic, obtain a tabled F value, and report the conclusion of your test, use a = .05).

g) Using the regression sums of squares information, for the model containing the terms x1, x2 and x4, calculate the t statistic for the hypothesis H0: b1 = 0, where b1 is the coefficient of x1. (Hint: first calculate an F statistic for H0 and then take its square root to obtain the t value. Assume all regression coefficients are positive.)