   Chapter 7.7, Problem 7E ### 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( -2, 4), (-1, 1), (0,-1), (1,-3)

To determine

To calculate: The least square regression Line for the points (2,4),(1,1),(0,1),(1,3) . And also plot the regression line obtained.

Explanation

Given Information:

The points are:

(2,4),(1,1),(0,1),(1,3)

Formula used:

The sum of squared errors of model y=f(x)

S=[f(x1)y1]2+[f(x2)y2]2++[f(xn)yn]2

Here, the regression equation is f(x)=ax+b.

And take derivative with respect a and b and put derivative equal to solve equation.

Calculation:

Consider the given points, (2,4),(1,1),(0,1),(1,3)

Now, make the table for point to find the value of f(x),

 x −2 −1 0 1 y−actual 4 1 −1 −3 f(x) −2a+b −a+b b a+b

Now, find the squared errors of model,

S=[2a+b4]2+[a+b1]2+[b+1]2+[a+b+3]2

Now, find the derivative with respect a and put equal to zero,

dSda=dda([2a+b4]2+[a+b1]2+[b+1]2+[a+b+3]2)

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