Linear regression (continued) In a test-retest situation, almost always the bottom group on the 1 st test will on average show some improvement on the.

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Presentation transcript:

Linear regression (continued) In a test-retest situation, almost always the bottom group on the 1 st test will on average show some improvement on the 2 nd test. The top group will on average fall back. This is known as the regression effect. The regression effect pulls values closer to the average. So if they were above average on the 1 st test, they will be pulled down closer to the average on the 2 nd test.

When we make a scatterplot of these situations it will be “football” shaped.

Using the height of fathers and sons example from the book, we see that for larger x values, there are more points below the SD line. Therefore, on average taller fathers have shorter sons. For the shorter fathers, more points are above the SD line. Therefore, on average, shorter fathers have taller sons.

Examples: Ch. 10 set D #1-3 p. 174 We can compensate for the regression effect by using linear regression to make predictions.

Using the data from the fathers versus sons situation: average ht. of fathers = 68 inchesSD = 2.7” average ht. of sons = 69 inchesSD = 2.7” r = 0.5 How tall would the son of a 62 inch father be?

Example: set E #1 p. 175 average ht. = 70 inchesSD = 3 inches average wt. = 162 lbs.SD = 30 lbs. r = 0.47 a)If ht. = 73 inches, predict wt. b)If wt. = 176 lbs., predict ht. c)Suppose we know the 80 th percentile height. What is the 80 th percentile weight?