Question 1:
Which of the variables (age or number of bidders) appears to have the strongest linear relationship with price (and hence should be
selected as the explanatory variable for your model)?
a. Age
b. Number of Bidders
c. Neither variable has a linear relationship with price
Now, suppose that you use Excel to fit a linear regression model with price as the response variable and age as the explanatory variable.
The output from the regression analysis is shown on the next page.
Use this output to answer the remaining questions.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7302
R Square 0.5332
Adjusted R Square 0.5177
Standard Error 273.0284
Observations 32
ANOVA
df SS MS F Significance F
Regression 1 2554859.011 2554859 34.27 0.0000021
Residual 30 2236335.207 74544.51
Total 31 4791194.219
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -191.66 263.89 -0.7263 0.4733 -730.59 347.27 -730.59 347.27
Age 10.48 1.79 5.8543 0.0000021 6.82 14.13 6.82 14.13
Question 2:
What percentage of the variability in price of clocks can be explained by the age of the clocks (e.g., what percentage of the variability
in clocks is explained by this regression model)?
a. 53.32%
b. 10.48%
c. 73.02%
Question 3:
What is the form of the regression equation for this model?
a. y = 263.89 + 1.79x
b. y = -191.66 + 10.48x
c. y = 10.48 - 191.66x
Question 4:
What is the p-value that you would use to test the hypothesis that age is a useful predictor of the price of antique grandfather clocks?
a. 0.4733
b. 5.8543
c. 0.0000021
Question 5:
Continuing with question 4, at the 5% significance level, can you conclude that age is a useful predictor of the price of antique
grandfather clocks?
a. Yes. You would reject the null hypothesis and conclude that age is a useful predictor.
b. No. You would fail to reject the null hypothesis and conclude that age is not a useful predictor.
Question 6:
How much would you expect the price of an antique grandfather clock to increase if its age increased by 1 year?
a. $10.48
b. $191.66
c. We can't tell from the information given.
Question 7:
Suppose that you've got your eye on a clock that is 125 years old. How much would you expect (predict) the price of this clock to be?
a. $1118.34
b. $1310
c. $1250
Question 8:
Suppose that you're also interested in buying an antique grandfather clock that is only 50 years old.
Should you use this model to predict the price of that clock?
a. Yes - You would predict the price of the clock to be $332.34
b. No - This would be extrapolation.
Question 9:
Would it be correct to say that increasing age causes the price of antique grandfather clocks to increase?
a. Yes - The slope is positive which indicates an increasing trend.
b. No - Correlation does not imply causation.
Question 10:
Based on the following residual plots, which of the following statements is true?
a. None of the assumptions appear to be violated.
b. The normality assumption appears to be violated.
c. The constant variance assumption appears to be violated.