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. =

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Presentation transcript:

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 percentile of weight correspond the 80 th percentile in height?

Ch. 11 R.M.S Error for Regression error = actual – predicted = residual When we make a prediction we usually have some error in our prediction. RMS(error) for regression describes how far points typically are above/below the regression line.

Baggage handout. y = x = 1.What are the cases? 2.What is the relationship between the 2 variables? 3.Is this a positive or negative association? 4.Average x = Average y = 5. Plots of deviations and residuals.

If the residual plot has a pattern to it, the linear regression was probably not well fit to the data. The residual plot should have the points evenly spread above and below the horizontal axis.

Calculating RMS(error)=square root(sum of the square errors divided by the total number of values). The RMS(error) has the same units as y (the variable being predicted. 68% of the points should be 1 RMS(error) from the regression line 95% of the points should be 2 RMS(error)s from the regression line Examples (Ch.11 Set A #4, 5, 7 p. 184)

RMS(error) for regression line of y on x is (Use the SD of the variable being predicted.)

Special cases of RMS(error) for different values of r. r = 0.3, 0.6, 0.8, 0.9, 0.95, 0.99 What happens to RMS(error) as r increases? Homoscedasticity (football-shaped scatter diagram) Heteroscedasticity: different scatter around the regression line Examples #11 p. 200, p. 192 figure

Example (Ch.11 Set D #3 p.193) In order to use the normal approximation, the scatter diagram should be football-shaped with points thickly scattered in the center and fading at the edges. If a scatter diagram is football-shaped, take the points in a narrow vertical strip and they will be away from the regression line by amounts similar to the RMS(error). –The new average is estimated from the regression method –The new SD is approximately equal to the RMS(error) of the regression line. Example set E #1 p. 197