   Chapter 7.7, Problem 1E ### 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 Sum of the Squared Errors In Exercises 1-4, find the sum of the squared errors for the linear model f(x) and the quadratic model g(x) using the given points. Then decide which model is a better fit. See Example 1. f ( x ) = 1.6 x + 6 , g ( x ) = 0.29 x 2 + 2.2 x + 6 ( − 3 , 2 ) , ( − 2 , 2 ) , ( − 1 , 4 ) , ( 0 , 6 ) , ( 1 , 8 )

To determine

To calculate: The sum of the squared errors for the linear model f(x)=1.6x+6 and the quadratic model g(x)=0.29x2+2.2x+6 using the points (3,2),(2,2),(1,4),(0,6),(1,8) and decide which model is better

Explanation

Given Information:

The linear model is f(x)=1.6x+6 and the quadratic model is g(x)=0.29x2+2.2x+6.

And the given points are (3,2),(2,2),(1,4),(0,6),(1,8).

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

Use the formula for calculation of sum of squared errors for each model individually and

compare them.

Calculation:

Consider the provided information:

Now make the table to evaluate each model at the given x-values,

 x −3 −2 −1 0 1 y−actual 2 2 4 6 8 f(x) 1.2 2.8 4.4 6 7.6 g(x) 2

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