Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.881644384
R Square	0.77729682
Adjusted R Square	0.767919844
Standard Error	2.046234994
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	4	1388.337623	347.0844058	82.89418891	3.94359E-30
Residual	95	397.7723769	4.187077651
Total	99	1786.11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	30.46621607	3.539611332	8.607220742	1.55786E-13	23.43919912	37.49323302	23.43919912	37.49323302
Engine size	-0.026439837	0.008914999	-2.965769936	0.003818268	-0.044138349	-0.008741326	-0.044138349	-0.008741326
Compression Ratio	0.364901894	0.056081385	6.506649162	3.58903E-09	0.253566269	0.476237519	0.253566269	0.476237519
Horsepower	-0.051842045	0.011121451	-4.661446094	1.02351E-05	-0.073920917	-0.029763173	-0.073920917	-0.029763173
Peak RPM	-0.000491152	0.00061553	-0.797933319	0.426899263	-0.001713133	0.000730829	-0.001713133	0.000730829

Answer the following questions using the above Liner Regression Analysis:

Dependent Variable: City MPG

Independent Varaibles: Engine Size, Compression Ratio, Horsepower, Peak RPM

1: Based on your regression output, what is the equation we would use to generate a point estimate for the city MPG using the four predictor variables?

2: Which of the predictor variables are statistically significant at the 5% significance level?

3: What is the 95% confidence interval for the effect that an increase of 1cc in engine size will have on the city MPG? (i.e., what is our 95% confidence interval for the increase or decrease in city MPG if we increase engine size by 1cc?)

4: Are you confident that increasing the engine size will really increase or decrease the city MPG in the direction that your confidence interval says it will? Why or why not?

5: Given your regression output, what effect do you think the peak RPM has on the city MPG, and why?

Answer 1

Solution:

a. The regression equation is

Y = 30.4662 - 0.0264 Engine size + 0.3649 Compression ratio - 0.0518 Horsepower - 0.00049 Peak RPM

b. Since p-value of engine size, compression ratio and horsepower are less than 0.05 significance level, we can conclude that the predictor variables engine size, compression ratio and horsepower are statistically significant.

c. 95% confidence interval for the effect that an increase of 1cc in engine size will have on the city MPG is -0.0441to -0.0087.

d. yes, increasing the engine size by 1 cc will decrease the city MPG because the confidence interval is negative.

e. Peak RPM is negatively related to city MPG as city MPG increases, peak RPM decreases and vice versa.