1. Introduction to Linear Regression

2. Wake Forest Men’s BBall HeightWeightHeightWeight 74”17579”205 74”19584”235 78”20084”230 73”18577”210 79”20572”170 80”25072”175 80”21578”195 77”235 Height (in inches) Weight (in pounds)

3. Correlation vs. Causation What type of correlation is there between height and weight? Does that mean causation? Turn Diagnostics On and Find the Linear Regression for the data. Pearson’s Correlation Coefficient: “r- value” -1 0 +1 Strong negative No Strong Positive Correlation Correlation Correlation

4. Graph and Residuals Residual – The distance from the data points to the line. Which points have positive residual? Which points have negative residual? To find the “Least Squares Regression” statisticians try to minimize the distance between the residuals and the line of best fit. (Tomorrow’s activity)

5. Interpolation vs. Extrapolation If another basketball player joined the team and he was 69 inches tall, how much would he weigh according to the linear regression line? –Approximately 163 pounds This is EXTRAPOLATION because we are using a value outside of the data’s range. May or may not be a good prediction.

6. Interpolation vs. Extrapolation What if a player weighed 225 pounds, how tall would he be? Then according to the data he would be around 81 inches tall. This is INTERPOLATION, because the value is within the ranges of the data. The answer would be more likely to be correct for a prediction.

7. NFL Avg Points per Game and Yards/Completion TeamPoints per Game Yards per Completion New England Patriots32.411.62 Atlanta Falcons25.99.88 Pittsburgh Steelers23.412.8 Green Bay Packers24.311.72 Chicago Bears20.910.92 Buffalo Bills17.710.64 Dallas Cowboys24.610.66 Philadelphia Eagles27.411.21 Minnesota Vikings17.610.15 New York Jets22.911.26

8. Pearson’s Correlation Coefficient How strong is the correlation? Is there one? Would this be a good model for prediction? Why or why not?

9. GPA and TV Hours per week # of hours of TV per week GPA 143.1 102.4 202.0 73.8 252.2 93.4 152.9 133.2 43.7 213.5

10. Predict What would someone’s GPA be if he/she watched 5 hours of TV. Is this a good model to use for this prediction? If someone’s GPA was a 3.1, what would this data say about the number of hours he/she watched TV?