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Regression Analysis for Predicting Height and Weight

This article explains the concept of regression analysis and how it can be used to predict weight based on height and vice versa. It also covers calculating RMS error, interpreting residual plots, and understanding the relationship between variables. Examples and special cases are included.

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Regression Analysis for Predicting Height and Weight

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  1. Example: set E #1 p. 175 average ht. = 70 inches SD = 3 inches average wt. = 162 lbs. SD = 30 lbs. r = 0.47 • If ht. = 73 inches, predict wt. • If wt. = 176 lbs., predict ht. • Suppose we know the 80th percentile height. What percentile of weight correspond the 80th percentile in height?

  2. 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.

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

  4. 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.

  5. 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)

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

  7. 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

  8. 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

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