   Chapter 7.7, Problem 3E ### 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 ) = 1.4 x + 8 , g ( x ) = 0.14 x 2 − 1.6 x + 7 ( − 2 , 11 ) , ( − 1 , 10 ) , ( 0 , 7 ) , ( 3 , 4 )

To determine

The better fit for the given points between the two models and sum of the squared error of the given f(x) and g(x).

Explanation

Given Information:

Among the two given models, one is line f(x)=1.4x+8 and the other is the quadratic model g(x)=0.14x21.6x+7. The given points for the fit are (2,11),(1,10),(0,7),(3,4)

The sum of square of a model f(x) at points (x1,y1),(x2,y2),(x3,y3),.........(xx,yy)

S={(f(x1)y1)2+(f(x2)y2)2+...+(f(xx)yy)2}

The function which has the least value among the given model is the better fit for the points.

Now, given f(x) is linear model and g(x) is quadratic model

f(x)=1.4x+8  g(x)=0.14x21.6x+7

Calculating the value of models f(x) and g(x) at given points:

At x1=2 f(x1)=10.8  g(x1)=10

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