   Chapter 7.7, Problem 8E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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 5-8, find the least squares regression line for the given points. Then plot the points and sketch the regression line. See(-5, -3), (-4, -2), (-2, - 1), (- 1, 1)

To determine

To calculate: The least square regression line for the points (5,3),(4,2),(2,1),(1,1) and sketch the graph.

Explanation

Given Information:

The provided points are (5,3),(4,2),(2,1),(1,1).

Calculation:

The least square regression line for the points:

(x1,y1),(x2,y2),...(x3,y3) is f(x)=ax+b

Where n is the number of points.

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

Here,

i=1nxiyi=x1y1+x2y2+x3y3...+xnyni=1nyi=y1+y2+y3...+yni=1nxi=x1+x2+x3...+xni=1nxi2=x12+x22+...+xn2

Now, substitute the values of the given points (5,3),(4,2),(2,1),(1,1) in above equations and here n=4, i=1nxiyi=15+8+21=24i=1nyi=321+1=5

And,

i=1nxi

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