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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Least Squares Regression Line In Exercises 81 and 82, find the least squares regression line for the given points. Then plot the points and sketch the regression line.

( 2 , 4 ) , ( 1 , 2 ) , ( 1 , 1 ) , ( 2 , 2 )

To determine

To calculate: The least square regression line for the points (2,4),(1,2),(1,1),(2,2) and also plot the points and sketch the regression line.

Explanation

Given Information:

The provided points are (2,4),(1,2),(1,1),(2,2).

Formula used:

The least square regression for the points (x1,y1),(x2,y2)(xn,yn) is given by the function f(x)=ax+b, where,

a=ni=1nxiyii=1nxii=1nyini=1nxi2(i=1nxi)2 and b=1n(i=1nyiai=1nxi)

Calculation:

Consider the points,

(2,4),(1,2),(1,1),(2,2)

Since four points are given, thus n=4.

Here the points for the xi would be,

xi=2,1,1 and 2

And the points for the yi would be,

yi=4,2,1 and2

Then, calculate the different values as,

xi=(2)+(1)+1+2=0

yi=4+2+(1)+(2)=3

xi2=(2)2+(1)2+(1)2+(2)2=4+1+1+4=10

And,

xiyi=(2)4+(1)2+(1)1+2(2)=8214=15

Now substitute

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