Stat 112 Notes 6 Today: –Chapters 4.2 (Inferences from a Multiple Regression Analysis)
Stat 1301 The Regression Line
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Stat 1301 Stat 1301 The Regression Line The Regression Line
description
Stat 1301 The Regression Line. Recall: SD Line --. goes through point of averages passes through “heart” of elliptical shaped cloud. Selling price (Y). Used Car data: AVGx = 6.4 SDx = 3 (Age) AVGy = 11,290SDy = 6,044 (Price) r = - 0.82. Age in years (X). - PowerPoint PPT Presentation
Transcript of Stat 1301 The Regression Line
Stat 1301Stat 1301
The Regression LineThe Regression Line
Recall: SD Line --Recall: SD Line --
goes through point of averages
passes through “heart” of elliptical shaped cloud
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
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0 5 10 15Age in years (X)
Selling price
(Y)
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
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0 5 10 15Age in years (X)
Selling price
(Y)
SD Line
The Regression LineThe Regression Line
A “smoothed” graph of averages
Used to predict Y (the dependent variable) from knowing X (the independent variable)
The Regression LineThe Regression Line(continued)(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
Regression Line
SD Line
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
Regression Line
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
SD Line
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
NOTE: The regression line has smaller slope than SD line i.e regression line is not as steep
Easier Way to Predict - Easier Way to Predict - Use Regression LineUse Regression Line
(Chapter 12)(Chapter 12)Equation:
y = mx + b m = slopeb = y-intercept
whererSDy
m = SDx
b = AVGy - mAVGx
Predicting Y whenPredicting Y whenyou know Xyou know X
Put value for X into regression equation and solve for Ysolve for Y
What height would you predict for a son whose father is:
(a) 72” tall
(b) 64” tall
(c) 68” tall
ˆ .5 35Y X
Used Car data:
AVGx = 6.4 SDx = 3 (Age)
AVGy = 11,290 SDy = 6,044 (Price)
r = - 0.82
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
Regression Line
Used Car Data
Price AVG = 11,290 SD = 6044Age 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
