1. True or False The correlation coefficient r has the same sign as the slope b
ID: 3301166 • Letter: 1
Question
1. True or False The correlation coefficient r has the same sign as the slope b1 in the least squares fit Y = b0 + b1X.
2. True or False In simple linear regression, if the 95% confidence interval for the slope includes 0 then the regression equation’s F-stat will have a p-value larger than .05.
3. True or False In multiple regression, if the F-test has a p-value less than .05 then all of the slopes will also have p-values less than .05.
4. True or False In regression, R-square is the proportion of the variance in the dependent variable that is explained using the set of independent variables.
5. Which of the following statements is most nearly correct, other things being equal?
a. Using Student's t instead of z makes a confidence interval narrower.
b. The table values of z and t are about the same when the mean is large.
c. For a given confidence level, the z value is always smaller than the t value.
d. Student's t is rarely used because it is more conservative to use z.
6. If when hypothesis testing we are testing at the conventional level of .05 and the p-value is 0.2333, then we should:
a. Accept the null hypothesis.
b. Accept the alternative hypothesis.
c. Decide that the result is statistically significant.
d. Cannot be determined from the information given.
Explanation / Answer
(1) True, b=r*sd(y)/sd(x) so b and r will have same sign
(2) True
(3)False
(4)True
(5)c. For a given confidence level, the z value is always smaller than the t value.
(6) a. Accept the null hypothesis.
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