stat 1301 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 PresentationTRANSCRIPT
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Stat 1301Stat 1301
The Regression LineThe Regression Line
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Recall: SD Line --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
0
5000
10000
15000
20000
25000
30000
0 5 10 15Age in years (X)
Selling price
(Y)
![Page 6: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/6.jpg)
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
![Page 7: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/7.jpg)
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The Regression LineThe 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 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
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Regression Line
SD Line
![Page 14: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/14.jpg)
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)
![Page 15: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/15.jpg)
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
![Page 16: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/16.jpg)
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
![Page 17: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/17.jpg)
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)
![Page 18: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/18.jpg)
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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 - 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
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Predicting Y whenPredicting Y whenyou know Xyou know X
Put value for X into regression equation and solve for Ysolve 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
ˆ .5 35Y X
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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
![Page 26: Stat 1301 The Regression Line](https://reader034.vdocument.in/reader034/viewer/2022051517/56815873550346895dc5d202/html5/thumbnails/26.jpg)
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
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