introduction to linear regression. wake forest men’s bball heightweightheightweight...
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Introduction to Linear Regression
Wake Forest Men’s BBall Height Weight Height Weight
74” 175 79” 205
74” 195 84” 235
78” 200 84” 230
73” 185 77” 210
79” 205 72” 170
80” 250 72” 175
80” 215 78” 195
77” 235
Height (in inches)
Wei
ght
(in p
ound
s)
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
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)
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.
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, becausethe value is within the ranges of the data.
The answer would be more likely to be correct for a prediction.
NFL Avg Points per Game and Yards/Completion
Team Points
per Game
Yards
per Completion
New England Patriots
32.4 11.62
Atlanta Falcons 25.9 9.88
Pittsburgh Steelers 23.4 12.8
Green Bay Packers 24.3 11.72
Chicago Bears 20.9 10.92
Buffalo Bills 17.7 10.64
Dallas Cowboys 24.6 10.66
Philadelphia Eagles 27.4 11.21
Minnesota Vikings 17.6 10.15
New York Jets 22.9 11.26
Pearson’s Correlation Coefficient
• How strong is the correlation? Is there one?
• Would this be a good model for prediction? Why or why not?
GPA and TV Hours per week# of hours
of TV per week
GPA
14 3.1
10 2.4
20 2.0
7 3.8
25 2.2
9 3.4
15 2.9
13 3.2
4 3.7
21 3.5
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?