Mathematics 143 A
Reading Linear Regression Output
Spring 2007
Predicting Exam Score from Test Score
1. Model
(Mean Exam Score) = α + β(Test 1 Score)
2. Estimates
Parameter
σ
α
β
Estimate
s
a
b
Value
18.86
23.97
1.60
3. Inferences about β
(a) A 95% confidence interval for β is (using a critical value from t(30) of 2.042
1.604 ± 2.042 ∗ .273 = (1.047, 2.161)
(b) The p value for a test of H0 : β = 0 against the two-sided alternative is < 0.0001
which is based on a t-statistic of 1.604/2.73 = 5.880.
4. Inferences about Prediction of y for a fixed x
(a) A 95% confidence interval for µExam for the fixed value of Test1 = 80 is
152.32 ± 2.042 ∗ 3.41 = (145.35, 159.29)
(b) A 95% prediction interval for a single Exam score for a test score of 80 is
p
152.32 ± 2.042 ∗ 1 + .3.412 = (113.17, 191.47)
Mathematics 143 A
Reading Linear Regression Output
5. Checking Hypotheses
Spring 2007