- 1 -
Example:
For a certain statistics course, data for student’s scores on Exam 1 are used to try to predict student’s scores
on Exam 2.
1. What is the estimated least squares regression line?
y_hat = -4.85586 + 0.96325x
2. Is there a linear relationship between Exam 1 and Exam 2?
State your hypotheses, test statistic, p-value,
and conclusion in terms of the problem.
Yes.
H
0
: β = 0 H
a
: β ≠ 0.
t = 6.39, P-value < 0.0001.
Reject the null, we have a significant linear
relationship between Exam 1 and Exam 2 scores.
3. What is the percent of variation in Exam 2 explained by Exam 1.
R-square = 0.2943, so 29.43%.
4. What is the estimate for the standard deviation of the error, s
e
?
Root MSE = 14.05383
5. Give the 95% confidence interval for the regression coefficient for Exam 1.
df = n – 2 = 98, use 60 from the table
b ± (t crit) s
b
= 0.96325 ± 2.000(0.15068) = (0.66189, 1.26461)
6. A student received an 82% on Exam 1.
What is this student’s predicted score on Exam 2?
y_hat = -4.85586 + 0.96325(82) = 74.13064

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