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Multiple Regression

Multiple Regression. Using Additional Explanatory Variables. Try this …. Look at the relationship between average driving distance & scoring average for 146 LPGA golfers in 2009. The least-squares regression line is ŷ = 87.95 – 0.0609x. Interpret the slope :.

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Multiple Regression

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  1. Multiple Regression Using Additional Explanatory Variables

  2. Try this … Look at the relationship between average driving distance & scoring average for 146 LPGA golfers in 2009. The least-squares regression line is ŷ = 87.95 – 0.0609x. Interpret the slope: The standard deviation of the residuals is s = 1.01. Interpret the standard deviation of the residuals:

  3. Another Variable? Recently, we compared explanatory variables to see which had a bigger influence on the response variable. Let’s examine a ___________of explanatory variables to see if we can get the standard deviation of residuals even lower.

  4. Model A model showing multiple regression: ŷ = 100.62 – 0.0844x1 – 0.097412x2 when x1 = average driving distance x2 = driving accuracy We find out that in 2009, Lorena Ochoa had a average driving distance of 265.2 yards and a driving accuracy of 71.8%. Predict her scoring average for the year.

  5. Standard Deviationof the Residuals x1 = average driving distance x2= driving accuracy x3 = putting average

  6. Interpret the Coefficients As long as all but one explanatory variables are known, the coefficient of the unknown explanatory variable can be interpreted. ŷ = 77.35 – 0.0901x1 – 0.098499x2 + 0.8246x3 Interpret the coefficient of x1.

  7. Sum it Up • A _________________ model uses more than one explanatory variable to predict the value of a numerical response variable. • The _________ of a numerical explanatory variable describes how much the predicted value of the response variable will change for each one-unit increase in the explanatory variable, assuming that the values of the other explanatory variables stay the same.

  8. Example What attracts fans to hockey game? Data from 2010-2011 regular season was gathered and the following model was created to predict attendance: ŷ = 10,146 + 161.6x1 + 0.603x2 where x1 = number of wins x2 = number of power play opportunities • Calculate the residual for the Toronto Maple Leafs, who had 37 wins, 601 power play opportunities, and an average attendance of 19,534. • Which seems to be the bigger attraction, winning games or rough play?

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