1. William used a sample of 68 U.S. cities to estimate the relationship between Crime
(annual property crimes per 100,000 persons) and Income (median income per capita).
His estimated regression equation was Crime = 428 + .050 Income. Assuming that b1 is
significant, if Income decreases by 1000 we would predict that Crime will A) increase by
428 B) increase by 50 C) increase by 500 D) none of the above are correct
Answer: D) none of the above are correct
Explanation: If Income decreases by 1000, Crime will be decreased by 50
2. Bivariate prediction intervals for Y are narrowest when A) the mean of X is near the
mean of Y. B) the value of X is near the mean of X. C) the mean of X differs greatly
from the mean of Y. D) the mean of X is small
Answer: B) the value of X is near the mean of X.
3. When comparing the 90% prediction and confidence intervals for a given regression
analysis A) the prediction interval is wider than the confidence interval. B) the prediction
interval is narrower than the confidence interval C) there is no difference between the
size of the prediction and confidence intervals D) None of the above
Answer: A) the prediction interval is wider than the confidence interval.
4. Which is not true of the coefficient of determination? A) It is the square of the
coefficient of correlation. B) It is negative when there is an inverse relationship between
X and Y. C) It reports the percent of the variation in Y explained by X. D) It is based on
sum of squares (SSR, SSE, and SS total).
Answer: B) It is negative when there is an inverse relationship between X and Y.
5. If X2 is a binary predictor in Y = b0 + b1 X1 + b2 X2 then which statement is most
nearly correct? A) X2 = 1 should represent the most desirable condition. B) if b2 =
423.72 then X2 is a key predictor. C) X2 may shift the estimated equation by a constant
amount b2. D) None of the above.
Answer: C) X2 may shift the estimated equation by a constant amount b2.
6. Using a sample of 63 observations, two variables X1 and X2 are regressed against a
dependent variable Y yielding the fitted regression equation = 76.40 ? 6.388x1 + .870x2.
The standard error of b1 is 2.453. In a two-tailed test of the hypothesis that b1 = 0 at a =
.05, we would conclude that A) there is a significant direct relationship between X1 and
Y. B) there is a significant inverse relationship between X1 and Y. C) there is insufficient
statistical evidence to say that a relationship exists between X1 and Y D) there is too
much Type II error risk to conclude anything about the relationship.
Answer: Here the sign of the coefficient of x1 is missing. Here the answer depends on the
sign of b1.
If b1 = 6.388, then the correct answer is
A) there is a significant direct relationship between X1 and Y.
If b1 = -6.388, then the correct answer is
B) there is a significant inverse relationship between X1 and Y.
7. A multiple regression analysis involving two independent variables yielded the
following information: n = 12, SS(Total) = 798.011, SS(Regression Model) = 738.00.
The multiple correlation coefficient is: A) 60.011 B) 55.3389 C) 0.925 D) 0.962
Answer: D) 0.962
Explanation:
The multiple correlation coefficient = Sqrt[SS(Regression Model)/SS(Total)] =0.962
8. Based on the following regression ANOVA table, the R2 is ANOVA TABLE
Source
df
SS
MS
F
Regression
4
1793.236
448.3089 7.485401
Residual
45
2695.1
59.8911
Total
49
4488.335
A) 0.6005 B) 0.1336 C) 0.3995 D) Insufficient information to answer.
Answer: C) 0.3995
Expalnation: R2 = SS(Regression)/SS(Total) = 1793.236/4488.335 = 0.3995