Stat 1301 The Regression Line

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Stat 1301The Regression Line
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Recall SD Line --

• goes through point of averages
• passes through heart of elliptical shaped cloud

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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
Age in years (X)
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
SD Line
Age in years (X)
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The Regression Line

• A smoothed graph of averages
• Used to predict Y (the dependent variable) from
  knowing X (the independent variable)

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The Regression Line(continued)

• Passes through the point of averages (AVGx,
  AVGy) r SDy
• Has slope m
• SDx
• i.e. a change of 1SDx for independent
  variable is associated with r SDy change in
  dependent variable

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SD Line
Regression Line
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
Age in years (X)
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
Regression Line
Age in years (X)
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
SD Line
Age in years (X)
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
Age in years (X)
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• NOTE The regression line has smaller slope than
  SD line
• i.e regression line is not as steep

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Easier Way to Predict - Use Regression
Line(Chapter 12)

• Equation
• y mx b m slope
• b y-intercept
• where
• rSDy m SDx b
  AVGy - mAVGx

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Predicting Y whenyou know X

• Put value for X into regression equation and
  solve for Y

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What height would you predict for a son whose
father is (a) 72 tall (b) 64 tall (c)
68 tall
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• Used Car data
• AVGx 6.4 SDx 3 (Age)
• AVGy 11,290 SDy 6,044 (Price)
• r - 0.82

Selling price (Y)
Regression Line
Age in years (X)
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Used Car Data
Price AVG 11,290 SD 6044 Age AVG 6
yrs SD 3 yrs r -.82
1. Find the equation of the regression line for
predicting Price from Age
2. Predict Price if car is (a) 3 years old
(b) 10 years old
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