Question

# SUMMARY OUTPUT Regression Statistics Multiple R 0.881644384 R Square 0.77729682 Adjusted R Square 0.767919844 Standard Error...

 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?

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.

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