1. AGENDA I.Homework 3 II.Parameter Estimates Equations III.Coefficient of Determination (R 2 ) Formula IV.Overall Model Test (F Test for Regression)

2. I. Homework 3 1) 10-22(Note that the solutions to 10.11 and 10.21 are in the back of the book and contain the information needed to solve the problem) 2) 10.34 3) 10.38 (Note that the solutions to 10.11 and 10.21 are in the back of the book and contain the information needed to solve the problem) 4) 10.44 Due Friday, March 19.

3. What is Regression? Statistical technique for developing a mathematical equation that explains the relationship between a dependent variable (y) and one or more independent variables (x). Types of regression in MKT 317: Simple Linear Regression:Only one X Multiple Regression:More than one X

4. Simple Linear Regression Model Population Regression Model: Sample Regression Model: Y = dependent variable X = independent variable β 0 =intercept of the straight line on the Y axis β 1 =slope of the straight line ε = random error term Y = predicted value of Y b 0 =sample estimate of β 0 b 1 =sample estimate of β 1

5. Regression Scenario One generally held belief in the business world is that taller men earn more money than shorter men. In a University of Pittsburgh study, 30 MBA graduates, all approximately the same age were polled and asked to report their annual incomes and heights.

6. Scatter Plot

7. II. Parameter Estimates Equations

8. II. Parameter Estimates Example Given: SS xy = 2451.925 = 69.6 SS x = 257.2 = 108.23 SS y = 30156.32 Find the sample regression line

9. II. Parameter Estimates Example 2 Given: Find the sample regression line = 228,437.91 = 145,582 = 30 = 69.6 = 108.23

10. R 2 = or III. Coefficient of Determination (R 2 ) Formula The amount of variance explained by the model

11. III. Coefficient of Determination (R 2 ) Example From the regression output, tell the proportion of variation in salary that is explained by height. Given SSR=23,374.56 SSE=6,781.76 SST=30,156.32

12. IV. Overall Model Test (F Test for Regression) H 0 :β 1 = 0, no linear relationship between the variables H 1 : β 1 ≠ 0, linear relationship between the variables Fcalc = F critical df numerator = k df denominator = n-k-1 n = sample size k = number of independent variables

13. IV. Overall Model F Test Source of Variation Sum of Squaresdf Mean SquareF-ratioFcrit RegressionSSR1 or kMSR MSR/ MSE F (k, n-k-1) ErrorSSEn-k-1MSE TOTALSSTn-1 ANOVA Table for Regression

14. III. Overall Model Test Example (cont.) Source of Variation Sum of Squaresdf Mean SquareF-ratioFcrit Regression23,374.56 Error TOTAL30,156.32 Given SSR and SST, conduct an overall model test