Question

For Questions 4-11, use the swiss dataset, which is built into R.

Fit a multiple linear regression model with Fertility as the response and the remaining variables as predictors. You should use ?swiss to learn about the background of this dataset.

9. 1 Run Reset Report the value of the F statistic for the significance of regression test. Enter answer here point 10. 1 Run Reset 0.01. What decision do Carry out the significance of regression test using a you make? 11 1 Run Reset Consider a model that only uses the predictors Education, Catholic, and Infant.Mortality. Use an F test to compare this with the model that uses all predictors. Report the p-value of this test. Enter answer here

Answer 1

The following R code can be used to obtain the required results.

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##question 9 : F statistic value

> summary(lm(Fertility~.,data=swiss))$fstatistic[1]
   value 
19.76106

##question 10 : Carry out the significance of the regression test at 0.01 level of significance

> summary(1m(Fertility~. ,data-swiss)) call 1m (formula Fertility ., data = swiss) Residuals Min Median 1Q -5, 2617 30 Max 4.1198 15, 3213 -15.2743 0, 5032 Coefficients: Estimate Std. Error t value Pr (>t|) (Intercept) Agriculture Examination 66.91518 10.70604 6. 250 1.91e-07 -0.17211 0.07030 -2.448 -1.016 0.01873 -0. 25801 0.25388 0.31546 Education catholic -0.87094 0.18303 -4.758 2.43e-05 0.10412 2.953 0.03526 0.00519 Infant.Mortality 1.07705 0.00734 0.38172 2.822 (Intercept) Agriculture Examination ** Education catholic Infant.Mortality signif. codes: *' 0.001 0.01 0 0.05 0.1 1 Residual standard error: 7.165 on 41 degrees of freedom 0.7067, Adjusted R-squared: Multiple R-squared: 0.671 F-statistic: 19.76 on 5 and 41 DF, p-value 5.594 e-10

# as we can see the p - value of the F - Statistic is 5.594*10^-10 which is less than 0.01> Thus our decision is that the regression model is significant,

## Question 11 : F-statistic value and p-value for the new model

> summary(1m(Fertility-Education+Catholic+Infant.Mortality , data-swiss)) call: 1mformula Fertility Education Catholic Infant.Mor tality, data swiss) Residuals: мin Median 1Q 3Q 4.1568 15.1187 Маx -14.4781 -5.4403 -0.5143 coefficients: Estimate Std. Error t value Pr t|) (Intercept) Education 48. 67707 7.91908 6.147 2.24e-07 -0.75925 0.11680 -6. 501 6.83e-08 catholic 0.09607 0.02722 3. 530 0.00101 Infant. Mortality 1.29615 0.38699 3.349 0.00169 (Intercept) Education catholic Infant. Mortality signif. codes 0 0.001 1 0.05 .'0.1 0.01 Residual standard error: 7.505 on 43 degrees of freedom Adjusted R-squar ed: 0.639 Multiple R-squared: 0.6625 F-statistic: 28.14 on 3 and 43 DF, p-value: 3.15e-10

# as you may notice the f-statistic value is 28.14 and the p-value of the test for regression significance is 3.15*10^-10

Answer 2

res<-cor(swiss)