In the printout from question #4, we were given the regression equation = 282 + 0.634x . The t -test
for H 0 : β = 0 yielded a P -value of 0.000. What is the conclusion you would arrive at based on these
data?
Answer: Because P is very small, we would reject the null hypothesis that the slope of the regression line
is 0. We have strong evidence of a predictive linear relationship between x and y .
Suppose the computer output for regression reports P = 0.036. What is the P -value for H (^) A : β > 0
(assuming the test was in the correct direction for the data)?
Answer: 0.018. Computer output for regression assumes the alternative is two sided (H (^) A : β ≠ 0). Hence
the P -value reported assumes the finding could have been in either tail of the t -distribution. The correct
P -value for the one-sided test is one-half of this value.
Practice Problems
Multiple-Choice
Which of the following statements is (are) true?
I. In the computer output for regression, s is the estimator of σ , the standard deviation of the
residuals.
II. The t -test statistic for the H 0 : β = 0 has the same value as the t -test statistic for H 0 : ρ = 0.
III. The t -test for the slope of a regression line is always two sided (H (^) A : β ≠ 0).
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
Use the following output in answering questions 2–4:
A study attempted to establish a linear relationship between IQ score and musical aptitude. The following
table is a partial printout of the regression analysis and is based on a sample of 20 individuals.
The value of the t -test statistic for H 0 : β = 0 is
a. 4.05