Reading and Comprehension Questions for Chapter 11
1. A scatter diagram is a convenient way to display graphically the relationship between two variables.
True False
True
2. A scatter diagram can be helpful in choosing the form of an empirical model.
True False
True
3. Regression analysis can be used to establish cause-and-effect relationships between variables.
True False
False
4. It can be dangerous to extrapolate with regression models.
True False
True
5. The standard method for estimating the parameters in a simple linear regression model is the method of least squares.
True False
True
6. a fitted linear regression model is . If x = 1 and the corresponding observed value of y = 11, the residual at this observation is:
a. +1
b. -1.
c. 0.
d. -2.
Answer – b. The residual is
7. If the error or residual sum of squares from fitting a simple linear regression model to 20 observations is 18, the estimate of the variance of the model errors is
a. 1.5
b. 1.0
c. 2.0
None of the above
Answer – b. The estimate of the error variance is .
8. The method of least squares results in unbiased estimator of the slope and intercept in a simple linear regression model.
True False
True
9. The standard error of the slope is a measure of how precisely the slope of the regression model has been estimated.
True False
True
10. A t-statistic can be used for testing in simple linear regression. The form of this statistic is
True False
True
11. If the null hypothesis of significance of regression is rejected we can be comfortable in concluding that the regression model is an adequate fit to the data.
True False
False
12. An analysis of variance test can be used for testing significance of regression and this procedure is equivalent to the t-test.
True False
True
13. In testing the null hypothesis of significance of regression with a t-statistic we find that t0 = 4. The value of the F-statistic in the ANOVA procedure would be
a. 4
b. 16
c. 12
d. None of the above.
Answer – b. In simple linear regression .
14. A confidence interval on the mean response in simple linear regression is always shorter at the center of the regressor or predictor variable data and longer at the extremes.
True False
True
15. A confidence interval on the mean response in simple linear regression is always longer than the corresponding prediction interval on a single future observation at the same x-value.
True False
False
16. The residuals from a linear regression model can be used to check the underlying assumptions and to investigate model adequacy.
True False
True
17. A normal probability plot of the residuals is typically used to investigate the assumption of normality in simple linear regression.
True False
True
18. A standardized residual in simple linear regression is computed as , where is the error or residual mean square. Standardized residuals are effective as in looking for outliers.
True False
True
19. If , the value of R2 is:
a. 0.75
b. 0.90
c. 0.85
d None of the above.
Answer – c.
20. If both the response and regressor variables are random variables, we can calculate a correlation coefficient that reflects the linear relationship between these two variables.
True False
True
21. The correlation coefficient and the slope provide equivalent information in simple linear regression.
True False
False – the correlation coefficient reflects the linear relationship between x and y, while the slope measure the predicted change in the response variable y for a unit change in the regressor variable x.
22. If is rejected, then will also be rejected, provided that the significance levels are the same.
True False
True