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3.2 - Residuals and Least Squares Regression Line

3.2 - Residuals and Least Squares Regression Line. Residuals. the difference between an observed value of the response variable and the value predicted by the regression line. residual = y -.

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3.2 - Residuals and Least Squares Regression Line

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  1. 3.2 - Residuals and Least Squares Regression Line

  2. Residuals • the difference between an observed value of the response variable and the value predicted by the regression line. • residual = y -

  3. predicted long jump distance = 304.56 - 27.63(sprint time)Find and interpret the residual for a sprint time of 8.09 seconds.(FYI - the data gathered showed a long jump distance of 151 in for a sprint time of 8.09 seconds) First, find the predicted value Second, find the residual. Third, determine if it is above or below the predicted value. Fourth, write an interpretive sentence!

  4. Least Squares Regression Line • the line that makes the sum of the square of the residuals as small as possible. Web Applet #1: http://hspm.sph.sc.edu/courses/J716/demos/LeastSquares/LeastSquaresDemo.html Web Applet #2: http://bcs.whfreeman.com/tps4e/#628644__666392__

  5. Calculating the Least-Squares Regression Line* These are on your formula sheet, just with different notation instead of a and b*

  6. What does the slope of the least-squares regression line tell us? • a change in 1 standard deviation in x corresponds to a change of r standard deviations in y. • There is a close relationship between correlation and slope!

  7. The number of miles (in thousands) for 11 used Hondas has a mean of 50.5 and a standard deviation of 19.3. The advertised prices had a mean of $14,425 and a standard deviation of $1899. The correlation for these variables is r = -0.874. Find the equation of the least-squares regression line and explain what the slope represents. Slope: Intercept: LSRL: For each additional 19.3 thousand miles we expect the cost to decrease $1660.

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