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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 ) = 2.0 x 3 , ( x ) = 0.14 x 2 + 1.3 x 3 ( 1 , 4 ) , ( 1 , 3 ) , ( 4 , 5 ) , ( 6 , 9 )

To determine

The sum of the squared error of the given models f(x) and g(x) by doing so determine the both fit for the given points between the 2 models.

Explanation

Given Information:

Two given models, one is linear f(x)=2.0x3 and the other is the quadratic model g(x)=0.14x2+1.3x3. The given points for the better fit are (1,4),(1,3),(2,0),(4,5),(6,9).

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)=2.0x3  g(x)=0.14x21.3x+3

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

At x1=1f(x1)=5    g(x1)=4.16

And

x2=1      f(x2)=1      g(x2)=1

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