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 yˆ  10  2 x . 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 e  y  yˆ  11  [10  2(1)]  11  12  1
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 ˆ 2  SS E /(n  2)  18 /(20  2)  1 .
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 H 0 : 1  0 in simple linear regression. The form
of this statistic is
ˆ1
T0 
se( ˆ1 )
True False
True
11. If the null hypothesis of significance of regression H 0 :   0 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 H 0 :   0 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 t02  F0 .
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 di  ei / ˆ 2 ,
where ˆ 2 is the error or residual mean square. Standardized residuals are effective as in
looking for outliers.
True False
True
19. If SST  100 and SSE  15 , the value of R2 is:
a. 0.75
b. 0.90
c. 0.85
d None of the above.
Answer – c. R 2  1 
SS E
15
 1
 0.85.
SST
100
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 H 0 :   0 is rejected, then H 0 :   0 will also be rejected, provided that the
significance levels are the same.
True False
True