Question

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Regression Coefficients Estimates Model formula: mpg - cyl + disp + hp + am Term Coefficient Estimate Standard Error t Value (Intercept) 30.476 2.8655 10.636 cyl -0.8345 0.75709 -1.1022 disp -0.0077447 0.010716 -0.72272 Pr > It! 3.7246e-11 0.28008 0.47607 hp -0.032962 0.015614 -2.1111 0.044166 am 3.4453 1.4539 2.3697 0.025205 Model Summary: Coefficient of Determination (R-Squared) Model formula: mpg - cyl + disp + hp + am Residual Standard Error DF R-Squared Adjusted R-Squared 2.8308 27 0.80785 0.77939 Analysis of Variance Model formula: mpg - cyl + disp + hp + am Source DF Sum of Squares Mean Square Regression 909.68 227.42 Residual 27 216.37 8.0136 Total 31 1126 Pr>F F Value 28.379 4 2.54e-09 (c) [10 points] Is this model overall statistically significant? Perform the 4-method hypothesis method.

Answer 1

(c). The null and alternative hypothesis of the model adequacy.

Null Hypothesis:

$H_{0}:$ The linear model $y=\beta _{0}+\beta _{1}*Cyl+\beta _{2}*disp+\beta _{3}*hp+\beta _{4}*am$ does not fit the data .

:The model fits the data well.

Level of significance:

g= 0,05

Test statistic: F test for the regression using ratio of mean squares due to regression and Mean square due to Error.

From the ANOVA table, we shall get the F-ratio and the p-value

Decision rule: Reject $H_{0$ if the p-value <0.05.

Conclusion: The p-value for regression term in ANOVA table is 0.0000<0.05, we reject the null hypothesis. Hence, we conclude that the linear model as stated fits the data well.

(d). The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. . Here, the R-squared for the model is 0.8078 and the dusted R-square is 0.7794. We have there are 3 predictors and the adjusted R-square is after taking care of 3 predictors.