Exercise 2 The following regression output is the result of a multiple regressio

Question

Exercise 2 The following regression output is the result of a multiple regression application using curb weight, cylinders, and horsepower as the three independent variables to explain the variation in the highway miles. A number of the output fields are missing. SUMMARY OUTPUT Regression Statistics 0817375723 Multiple R R Square Adjusted R Square Standard Error Observations 30 ANOVA MS F Signficance F Regression Residual Total 26 167.9951613 29 506.1686667 Lower 99% Upper 99% Coefficients Standard Error Stat Pyalue Intercept Curb Weight cylinders Horse Power 47.22301432 3.421673506 13.80114562 1.786-13 0.004930366 0.001308628 0.20096439 0.760908438 0 016090908 0.012343873 From the given information answer the following questions: a) What is the coefficient of determination? What does this statistic tell you? b) What is the adjusted coefficient of determination? What does this statistic tell you? C) can we conclude at the 5% significance level that the model is useful in predicting the variation in highway miles? d) Can we conclude at the 5% significance level that curb weight and the highway miles are linearly related? e) Does this data provide enough evidence at the 5% significance level to conclude that the cylinders and the highway miles have negative linear relationship? 1 Interpret the coefficient bl. g) Interpret the coefficient b2.

Explanation / Answer

From the given data

a) R - Square = 338.1715057/ = 0.668
b) Adjusted R-Square = 0.62981
SE = 2.5419

c) P-value = .000 which is less than alpha = 5%

Yes, the model is useful in predicting the variation in hight way miles.

d) From the given data

P-value of curb weight is 0.0008 < alpha (0.05) so Curb weight is significant

i.e. We conclude that the curb weight and the highway miles are linearly related

e) P-value of cylinders weight is 0.0023 < alpha (0.05) so cylinders weight is significant

i.e. We conclude that the cylinders and the highway miles are linearly related

f) b1 = -0.00493 which is < 0 it is negative correlation

i.e. As curb weight increase 1 unit or kg then highway miles decrease 0.00493 miles

g) b2 = -0.20096 <0 it is negative correlation

i.e. As cyclinders increase 1 unit or kg then highway miles decrease 0.20096 miles

ANOVA Table Source Sum of Square df Mean Square F-ratio F-critical P-value Regression 338.1715057 3 112.7238352 17.4457 4.6366 0.0000 Residuals 167.9951613 26 6.4614 Total 506.166667 29 119.1852352

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