2.6. EXERCISES 81
Exercises
iConceptual Exercises
2.1- 2.7 True or False? Each of the statements in Exercises 2.1- 2.7 is either true or false.
For each statement, indicate whether it is true or false and, if it is false, give a reason.
2.1 If dataset A has a larger correlation between Y and X than dataset B, then the slope between
Y and X for dataset A will be larger than the slope between Y and X for dataset B?
2.2 The degrees of freedom for the model is always 1 for a simple linear regression model.
, 2.3 The magnitude of the critical value (t*) used to compute a confidence interval for the slope
of a regression model decreases as the sample size increases.
2.4 The variability due to error (SSE) is always smaller than the variation explained by the
model (SSA1odel).
2.5 If the size of the typical error increases, then the prediction interval for a new observation
becomes narrower.
2.6 For the same value of the predictor, the 95% prediction interval for a new observation is
always wider than the 95% confidence interval for the mean response.
2. 7 If the correlation between X 1 and Y is greater (in magnitude) than the correlation between X2
and Y , t hen the coefficient of determination for regressing Y on X 1 is greater than the coefficient
of determination for regressing Yon X2.
2.8 Using correlation. A regression equation was fit to a set of data for which the correlation,
r. between X and Y was 0.6. Which of the following must be true?
a. The slope of the regression line is 0.6.
b. The regression model explains 60% of the variability in Y.
c. The regression model explains 36% of the variability in Y.
d. At least half of the residuals are smaller than 0.6 in absolute value.
2.9 Interpreting the size of r 2 •
a . Does a high value of r 2, say, 0.90 or 0.95, indicate that a linear relationship is the best possible
model for the data? Explain.
b. Does a low value of r 2, say, 0.20 or 0.30, indicate that some relationship other than linear
would be the best model for the data? Explain.
3.9. EXERCISES 14!)
3.9 Exercises
Conceptual Exercises
3.1 Predicting a statistics final exam grade. A st.at.i:;tics professor assigned various grades
during the scmestff indudi11g a midtl'rm exam (out of 100 points) and a logistic regrcssiou project
(out of 30 points). The prcdictiou equation below was lit, using da tn fr0111 24 students in the clru;s,
to predict t he fiual exam score (out of 100 poillts) bm;cd Oil t.hl' midterm aud project gra