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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.

( 3 , 1 ) , ( 2 , 1 ) , ( 0 , 0 ) , ( 2 , 1 )

To determine

To calculate: The least square regression line for the points (3,1),(2,1),(0,0)(1,1),(2,1) and also plot the points and sketch the regression line.

Explanation

Given Information:

The provided points are (3,1),(2,1),(0,0)(1,1),(2,1).

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,

(3,1),(2,1),(0,0)(1,1),(2,1)

Since, five points are given, thus n=5.

Here the points for the xi would be,

xi=3,2,0,1 and 2

And the points for the yi would be,

yi=1,1,0,1 and1

Then calculate the different values as,

xi=(3)+(2)+0+1+2=2

yi=(1)+(1)+0+1+1=0

xi2=(3)2+(2)2+(0)2+(1)2+(2)2=9+4+0+1+4=18

And,

xiyi=(3)(1)+(2)(1)+(0)(0)+(1)(1)+(2)(1)

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