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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 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 )   =   0.7 x +   2 ,   g ( x )   =   0.06 x 2 0.7 x   +   1

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

To determine

To calculate: The sum of the squared errors for the linear model f(x)=0.7x+2  and the quadratic model g(x)=0.06x20.7x+1 using the points (3,4),(1,2),(1,1),(3,0)  and decide which model is better.

Explanation

Given Information:

The linear model is f(x)=0.7x+2  and the quadratic model is g(x)=0.06x20.7x+1.

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

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 1 1 3
yactual 4 2 1 0
f(x) 4.1 2.7 1.3 -0.1
g(x) 3.64 1

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