Data on the gasoline mileage performance of 32 different automobiles were collected. The dataset contains two...

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Data on the gasoline mileage performance of 32 different automobiles were collected. The dataset contains two variables: (1) gasoline mileage (miles per gallon), y, and (2) engine displacement (cubic inches), x. Below are some summary statistics of the data: x=285.0437 32 i=1 32 32 (xx)2=426103 (x - x)y = -20180.07 i=1 = 20.22312 (vi - y) = 1237.544 i=1 Below is the output given by R (note: some original outputs are removed and replaced by XXX): Residual standard error: 3.065 on XXX degrees of freedom Multiple R-squared: XXX, Adjusted R-squared: F-statistic: XXX on XXX and XXX DF, p-value: XXX XXX (a) Fit a simple linear regression model relating gasoline mileage (miles per gallon), y, to engine displacement (cubic inches), x. Report the fitted regression line. (b) Construct the analysis-of-variance table. (c) Test for the significance of regression at the 5% level of significance. Use t test. (d) Test for the significance of regression at the 5% level of significance. Use F test. (e) Find a 95% confidence interval on the mean gasoline mileage if the engine displacement is 275 inch. (f) Find a 95% prediction interval on the gasoline mileage if the engine displacement is 275 inch. (g) What percent of the total variability in gasoline mileage is accounted for by the linear relationship with engine displacement? Data on the gasoline mileage performance of 32 different automobiles were collected. The dataset contains two variables: (1) gasoline mileage (miles per gallon), y, and (2) engine displacement (cubic inches), x. Below are some summary statistics of the data: x=285.0437 32 i=1 32 32 (xx)2=426103 (x - x)y = -20180.07 i=1 = 20.22312 (vi - y) = 1237.544 i=1 Below is the output given by R (note: some original outputs are removed and replaced by XXX): Residual standard error: 3.065 on XXX degrees of freedom Multiple R-squared: XXX, Adjusted R-squared: F-statistic: XXX on XXX and XXX DF, p-value: XXX XXX (a) Fit a simple linear regression model relating gasoline mileage (miles per gallon), y, to engine displacement (cubic inches), x. Report the fitted regression line. (b) Construct the analysis-of-variance table. (c) Test for the significance of regression at the 5% level of significance. Use t test. (d) Test for the significance of regression at the 5% level of significance. Use F test. (e) Find a 95% confidence interval on the mean gasoline mileage if the engine displacement is 275 inch. (f) Find a 95% prediction interval on the gasoline mileage if the engine displacement is 275 inch. (g) What percent of the total variability in gasoline mileage is accounted for by the linear relationship with engine displacement?