Question

Problem 1. Dummy Variable Regression. The U.S. government has been interested in pushing auto manufacturers to increase the MPG of their fleet. One goal set in 2006 was to have an average (combined city and highway) Miles Per Gallon (MPG) for SUV vehicles of 22 by 2011 A sample of 100 SUVs from 2018 and several variables were measured. The key variables are given below, along with basic Univariate statistics for each one: MPGavg A weighted average of miles per gallon, 60% highway and 40% city .MPGcity The estimated miles per gallon for city driving .MPGhwy The estimated miles per gallon for city driving Eng Size Thesize of the engine in liters Cyl 4Dum Adummy varlable coded as one if the engine is 4 cylinders, zero for 6 or 8 cylinder SUVs Cyl 6Dum Adummy variable coded as one if the engine is 6 cylinders, zero for 4 or 8 cylinder SUVs Cyl.8Dum Adummy variable coded as one if the engine is 8 cylinders, zero for 4 or 6 cylinder SUVs The following is the dummy variable regression results of MPGavg on Cyl 4Dum and Cyl 6Dum. Summary of Fit RSquare 0.7507 RSquare Adj 0.7456 Root Mean Square 1.7024 Error Mean of Response 21.2300 Observations (or Sum Wgts) 100 Analysis of Variance Sum of Mean ares Square Ratio 846.5858 423.293 146.0543 Source DF Squares Model 97 2811242 2.898 Prob >F 0001 rror C. Total 99 1127.7100 Parameter Estimates Estimate Std Error t Ratio Prob>t Term Intercept 16.9545 0.363 46.7126 <.0001 16.36 .0001 .5641 ,0001 Cyl 4Dum 7.2455 0.4429 Cyl.6Dum 3.0758 0.4686 Based on the regression results, solve for the predicted MPGavg for 4 cylinder cars. I just want the numerical answer. Use 4 decimal places and use the proper rules of rounding.

Also:

Based on the regression results, solve for the predicted MPGavg for 8 cylinder cars.

and

Based on the regression results, what is the best answer concerning average MPG for 4 cylinder SUVs.

a. 4 cylinder SUVs have statistically higher average MPG when compared to 8 cylinder SUVs.

b. The number of cylinders does not help explain average MPG.

c. 6 cylinder SUVs do not have statistically higher average MPG when compared to 8 cylinder SUVs.

d. 4 cylinder SUVs have statistically higher average MPG when compared to 6 cylinder SUVs.

Answer 1

y^ = 16.9545 + 7.2455 Cyl_4Dum + 3.0758 Cyl_6Dum

For 8Ccyliner cars
y^ = 16.9545

for 4 cylinder
y^ = 16.9545 + 7.2455
= 24.2

option A) is correct

a. 4 cylinder SUVs have statistically higher average MPG when compared to 8 cylinder SUVs.