   Chapter 7.7, Problem 1CP ### 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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# Find the sum of the squared errors for the linear model f ( x ) = 2.9 x − 6 Linear model and the quadratic model g ( x ) = 0.20 x 2 + 0.5 x − 1 Quadratic model with respect to the points ( 2 , 1 ) , ( 4 , 5 ) , ( 6 , 9 ) , ( 8 , 16 ) , ( 10 , 24 ) .Then decide which model is a better fit.

To determine

To calculate: The sum of squared error for the given linear model f(x)=2.9x6 and the quadratic model q(x)=0.20x2+0.5x1 with respect to the points then decide which model is a better fit.

Explanation

Given Information:

The linear model f(x)=2.9x6 and the quadratic model q(x)=0.20x2+0.5x1.

The points are (2,1),(4,5),(6,9),(8,16),(10,24).

Formula used:

The sum of squared error for the model y=f(x) with respect points (x1,y1),(x2,y2)....(xn,yn) is given by,

S=[f1(y)y1]2+[f2(x)y2]2+...[fn(x)yn]2

Here sum of squared error will less that model will be a better fit.

Calculation:

Consider the provided model,

Linear model f(x)=2.9x6

Being by evaluating each model at the given x values as shown in the table.

 x 2 4 6 8 10 Actual y values 1 5 9 16 24 Linear model f(x)=2.9x−6 0

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