1. Chapter 6 (cont.) Difference Estimation

2. Recall the Regression Estimation Procedure 2

3. The Model n The first order linear model y = response variable x = explanatory variable b 0 = y-intercept b 1 = slope of the line e = error variable 3 x y 00 Run Rise   = Rise/Run  0 and  1 are unknown population parameters, therefore are estimated from the data.

4. The Least Squares (Regression) Line 4

5. 5 3 3     4 1 1 4 (1,2) 2 2 (2,4) (3,1.5) Sum of squared differences =(2 - 1) 2 +(4 - 2) 2 +(1.5 - 3) 2 + (4,3.2) (3.2 - 4) 2 = 6.89 The smaller the sum of squared differences the better the fit of the line to the data.

6. The Estimated Coefficients 6 To calculate the estimates of the slope and intercept of the least squares line, use the formulas: The least squares prediction equation that estimates the mean value of y for a particular value of x is:

7. Regression estimator of a population mean  y

8. Difference Estimation In difference estimation, b 1 is not calculated.

9. Works well when x and y are highly correlated and measured on the same scale. Difference Estimation

10. Estimated Variance of Difference Estimator

11. Diff. Est. - example AchievementFinal calculus Studenttest score, xgrade, y 13965 24378 32152 46482 55792 64789 72873 87598 93456 105275 A math achievement test was given to 486 students prior to entering college. A SRS of n=10 students was selected and their course grades in calculus were obtained. Estimate u y for this population.