Statistics
Statistics
4th Edition
ISBN: 9780393929720
Author: David Freedman, Robert Pisani, Roger Purves
Publisher: Norton, W. W. & Company, Inc.
Question
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Chapter 29.8, Problem 8SRE
To determine

Obtain the regression equation for predicting y from x.

Expert Solution & Answer
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Answer to Problem 8SRE

The regression equation for predicting y from x is y^=1.6667+0.5333x_.

Explanation of Solution

The general equation of the regression line is given below:

y^=Intercept+Slope×x

The value of Intercept is given below:

y-intercept=y¯Slope×x¯

Where,

x¯sample average of xy¯sample average of ySlope=r×sysxr=(xix¯)(yiy¯)(n1)sxsysx=(xix¯)2nx1sy=(yiy¯)2ny1

The sample average of x is shown below:

x¯=xin=1+8+10+10+14+176=606=10

The sample average of y is shown below:

x¯=xin=1+4+6+12+12+76=426=7

The table below represents the values that help to find the regression equation:

xy(xix¯)(yiy¯)(xix¯)(yiy¯)(xix¯)2(yiy¯)2
11-9-6548136
84-2-3649
1060-1001
1012050025
141245201625
177700490
Total8015096

The value of sx is given below:

sx=(xix¯)2nx1=15061=1505=5.4772

The value of sy is given below:

sx=(yiy¯)2ny1=9661=965=4.3818

The value of r is given below:

r=80(61)(5.4772)(4.3818)=80119.9999=0.6667

The slope of the regression line is given below:

Slope=r×sysx=0.6667×4.38185.4772=0.5333

The value of Intercept is given below:

y-intercept=y¯Slope×x¯=70.5333×10=1.6667

Substitute the corresponding values in the regression equation.

The regression equation for predicting y from x is y^=1.6667+0.5333x_.

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