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AGENDA

AGENDA. MULTIPLE REGRESSION REVIEW Overall Model Test (F Test for Regression) Test of Model Parameters Test of β i = β i * Coefficient of Multiple Determination (R 2 ) Formula Confidence Interval CORRELATION BASICS Hypothesis Test on Correlation. Multiple Regression Basics.

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AGENDA

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  1. AGENDA MULTIPLE REGRESSION REVIEW • Overall Model Test (F Test for Regression) • Test of Model Parameters • Test of βi = βi* • Coefficient of Multiple Determination (R2) Formula • Confidence Interval CORRELATION BASICS • Hypothesis Test on Correlation

  2. Multiple Regression Basics Y=b0 + b1X1 + b2X2 +…bkXk • Where Y is the predicted value of Y, the value lying on the estimated regression surface. The terms b0,…,k are the least squares estimates of the population regression parameters ßi

  3. I. ANOVA Table for Regression Analysis

  4. II. Test of Model Parameters H0: β1= 0 No Relationship H1: β1 ≠ 0 Relationship t-calc = n = sample size t-critical:

  5. III. Test of βi = βi* H0: β1= βi* H1: β1≠ βi* t-calc = n = sample size t-critical:

  6. IV. Coefficient of Multiple Determination (R2) Formula R2 = or Adjusted R2 =

  7. V. Confidence Interval Range of numbers believed to include an unknown population parameter.

  8. Multiple Regression Review Great rebounding is going to offer your team more opportunities to score, and give the opposing team less opportunities to score. Think about it: just one rebound could add a 6 point swing to your team’s score! Good rebounding is going to give your team more possessions, which means more scoring. -powerbasketball.com Players play — tough players win," was the motto made famous Michigan State University men's basketball coach Tom Izzo — who built rebuilt the MSU program during the mid-1990s around toughness and rebounding, taking the Spartans to five Finals 4s in the last 15 years. Much of the success Izzo's Spartans have attained is attributed to their brutal practices and the now signature "war drill" that places a special emphasis on rebounding, toughness, getting after loose balls and accountability to your teammates. -newburyportnews.com

  9. Determinants of Points Scored (X1) = Field Goal Percentage (X2) = Number of Assists (X3) = Number of Total Rebounds N = 20 Games

  10. Output from Computer

  11. Multiple Regression Example Conduct the following tests: • What is the R2? the adjusted R2? • Overall Model F test • Test whether β1 = 0 • Test whether one more assist leads to 2 more points • Construct a 95% confidence interval for β3

  12. Correlation Review • Measures the strength of the linear relationship between two variables • Ranges from -1 to 1 • Positive = direct relationship • Negative = inverse relationship • Near 0 = no strong linear relationship • Does NOT imply causality

  13. Y Y r=1 r=-1 X X Y Y Y r=-.8 r=0 r=.8 X X X Illustrations of correlation Y r=0 X

  14. VI. Hypothesis Test on Correlation • To test the significance of the linear relationship between two random variables: H0: =0 no linear relationship H1: 0linear relationship • This is a t-test with (n-2) degrees of freedom:

  15. VI. Hypothesis Test on Correlation (cont.) • Is the number rebounds related to the number of points scored Sxy = 8.958 Sx = 4.160 Sy = 10.639

  16. r = .670 (0.001) r = .635 (0.003) r = .202 (0.392)

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