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Section 4

Learn how to test the correlation coefficient and slope in regression analysis, with step-by-step instructions, critical values, test statistics, and decision-making examples.

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Section 4

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  1. 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 : 0 (linear correlation) 2. Test Statistic

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

  4. Example Use a 1% level of significance to test that (Given r = 0.9677) 0

  5. Testing the Slope Steps • Hypotheses Ho : = 0 H1 : > 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 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

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