A set of data is available on 392 vehicles. The goal is to find a model to predict the variable logmpg = the log of miles per gallon. The possible independent variables are: cylinders = Number of cylinders between 4 and 8, displacement = Engine displacement (cu. inches), horsepower = Engine horsepower, weight = Vehicle weight (lbs.), acceleration = Time to accelerate from 0 to 60 mph (sec.), and year = Model year (modulo 100).

An analyst fits two models. The output for these two models is provided below, use that output for this problem.

Model 1: logmpg=0+1cylinders+2displacement+3horsepower+4weight+5acceleration+6year

The regression equation is

logmpg = 1.83 - 0.0233 cylinders + 0.000287 displacement - 0.00100 horsepower - 0.000264 weight - 0.00121 acceleration + 0.0296 year

Predictor	Coef	SE Coef	T	P
Constant	1.8275	0.1685	10.85	0.000
Cylinders	-0.02328	0.01175	-1.98	0.048
Displacement	0.0002874	0.0002603	1.10	0.270
Horsepower	-0.0010020	0.0004894	-2.05	0.041
Weight	-0.00026427	0.00002370	-11.15	0.000
Acceleration	-0.001214	0.003609	-0.34	0.737
Year	0.029649	0.001861	15.93	0.000

S = 0.121512

R-Sq = 87.4%

R-Sq(adj) = 87.2%

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	6	39.5254	6.5876	446.16	0.000
Residual Error	385	5.6845	0.0148
Total	391	45.2100

Model 2: logmpg=0+1cylinders+2horsepower+3weight+4year

The regression equation is

logmpg = 1.77 - 0.0139 cylinders - 0.000724 horsepower - 0.000258 weight + 0.0296 year

Predictor	Coef	SE Coef	T	P
Constant	1.7709	0.1486	11.92	0.000
Cylinders	-0.013908	0.008589	-1.62	0.106
Horsepower	-0.0007236	0.0003469	-2.09	0.038
Weight	-0.00025751	0.00001858	-13.86	0.000
Year	0.029559	0.001850	15.98	0.000

S = 0.121422

R-Sq = 87.4%

R-Sq(adj) = 87.2%

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	4	39.5043	9.8761	669.86	0.000
Residual Error	387	5.7057	0.0147
Total	391	45.2100

1. For model 1, test the null hypothesis that all the coefficients for all the variables are all equal to 0 in other words that 1=...=6=0

2. For model 1, test the null hypothesis that the coefficient corresponding to the variable horsepower = 0 versus the alternative hypothesis that this coefficient is not equal to 0. Write a short sentence that explains your result in a simple manner.

3. Which of the two models are a better fit for this data? Justify your answer.

4. Predict the logmpg for a car with the following inputs: cylinders = 8, displacement = 305, horsepower = 135, weight = 3.5, acceleration = 11.5, and year = 70.