Question

b. Calculate the slope and​ y-intercept for the regression equation, SST, and Partition the SST into the SSR and the SSE.

​(Round to three decimal places as​ needed.)

c. Provide an interpretation for the value of the slope.

Suppose an environmental agency would like to investigate the relationship between the engine size of sedans and the miles per gallon (MPG) they get. The accompanying table shows the engine size in cubic liters and rated miles per gallon for a selection of sedans. Use this information to complete parts a through f. Click to view the table showing engine size and MPG for 9 car models. a. Construct a scatter plot for these data. Choose the correct graph below. CA. 0 Table of Engine Size and MPG- X Engine size Engine size MPG Engine Size MPG 2.5 19 MPG MPG 2.4 Engine Size Car Model A Model B Model C Model D Model E Model F Model G Model H Modell 3.7 b. Calculate the slope and y-intercept for the regression equation. 2.1 23 The slope is b,= (Round to three decimal places as needed.) 3.8 Print Done

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable: Independent Variable: y x= 36.238477-4.0541344 y Sample size: 9 R (correlation coefficient) = -0.84713308 R-sq = 0.71763445 Estimate of error standard deviation: 1.8577229 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 36.258477 2.6888151 0 7 13.484928 <0.0001 Slope -4.0541344 0.96117694 0 7-4.2178857 0.0039 Analysis of variance table for regression model: Source DF SS MS F-stat Model 1 61.397614 61.397614 17.790559 Error 7 24.157942 3.4511345 Total 8 85.555556 P-value 0.0039

Intercept $\beta$ ₀ = 36.258

Slope $\beta$ ₁ = -4.054

SST = 85.556

SSR = 61.398

SSE = 24.158