1. Inferences Concerning Regression Parameters
Section 4
Inferences Concerning
Regression Parameters

2. Testing the Correlation Coefficient
Steps
1. Hypotheses
Ho : = 0 (no linear correlation)
H1 : > 0 (positive linear correlation)
H1 : < 0 (negative linear correlation)
H1 : (linear correlation)
2. Test Statistic

3. Steps Continued t-value df = n – 2 Critical Value
Use level of significance,
t-value
df = n – 2
4. Decision

4. Years of Experience (x)
Example
Years of Experience (x)
Salary (y) 12 29 16 31 6 23 34 27 38 8 24 5 22 19 36 13 33
Use a 1% level of significance to test that (Given r = )

5. Testing the Slope Steps Hypotheses Ho : = 0 H1 : > 0 H1 : < 0
2. Test Statistic

6. Steps Continued 3. Critical Value Use level of significance, t-value
df = n – 2
4. Decision

7. Example x y
9.9
37.1
11.4 43
8.1
33.4
14.7
47.1
8.5
26.5
12.6
40.2
Se = 3.78
SSx = 32.17
b = 2.55
Use a 1% level of significance to test that

8. Confidence Interval for
b - E <
< b + E
E =
df = n – 2

9. Example
Plate tectonics and the spread of the ocean floor are very important in modern studies of earthquakes and earth science. The following data give
x = age of volcanic islands in Indian Ocean
y = distance of the island from the center of
the midoceanic ridge

10. Example Continued Construct a 75% confidence interval for x y 120 3083 16 60
15.5 50
14.5 35 22 18 20 12 17
Construct a 75% confidence interval for