Inferences Concerning Regression Parameters Section 4 Inferences Concerning Regression Parameters

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

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

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 = 0.9677)

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

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

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

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

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

Example Continued Construct a 75% confidence interval for x y 120 30 83 16 60 15.5 50 14.5 35 22 18 20 12 17 Construct a 75% confidence interval for