Using the correlation homework, you will conduct a regression instead of a corre

Question

Using the correlation homework, you will conduct a regression instead of a correlation for the word problems only! This will be due next Wednesday, May 3rd.

For those problems follow and answer each step.

[1] Create a linear equation that best describes the data.

[2] Discuss if the model is better than chance.

[3] Discuss significant predictors.

[4] Tell me about the R-Square.

[5] Describe the output of the regression.

15.129 Corvette Prices. Following are the age and price data for Corvettes from Exercise 15.23. 6 6 6 2 2 5 4 5 1 4 y 290 280 295 425 384 315 355 328 425 325 At the 5% level of significance, do the data provide sufficient evidence to conclude that age and price of Corvettes are negatively linearly cor- related? 15.130 Custom Homes. Following are the size and price data for custom homes from Exercise 15.24. x 26 27 33 29 29 34 30 40 22 y 540 555 575 577 606 661 738 804 496

Explanation / Answer

1)

y=456.6-27.90x

2)

It is better than chance because it is significant (p-value is less than 0.05)

3)

Age is a significant predictor of price because it has a p-value less than 0.05.

4)

r^2 is 0.93677540582113 which means 93.68 % of the variation in y is accounted for by independent variable x.

5)

SUMMARY OUTPUT Regression Statistics Multiple R 0.967871585 R Square 0.936775406 Adjusted R Square 0.928872332 Standard Error 14.24652913 Observations 10 ANOVA df SS MS F Significance F Regression 1 24057.89126 24057.89126 118.5330384 4.48427E-06 Residual 8 1623.708738 202.9635922 Total 9 25681.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 456.6019417 11.43289905 39.93754687 1.69959E-10 430.2376293 482.9662542 x -27.90291262 2.562889198 -10.88728792 4.48427E-06 -33.81294571 -21.99287953

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