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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 Least Squares Regression Line In Exercises 5-8, find the least squares regression line for the given points. Then plot the points and sketch the regression line. See

(-3, 0), (- 1, 1),(1, 1),(3, 2)

To determine

To calculate: The least square regression Line for the points (3,0),(1,1),(1,1),(3,2). And also plot the regression line obtained.

Explanation

Given Information:

The points are given as (3,0),(1,1),(1,1),(3,2)

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

Here, the regression function is f(x)=ax+b.

And take derivative with respect a and b and put derivative equal to solve equation.

Calculation:

Consider the given points, (3,0),(1,1),(1,1),(3,2)

Now, make the table for point to find the value of f(x),

x 3 1 1 3
yactual 0 1 1 2
f(x) 3a+b a+b a+b 3a+b

Now, find the squared errors of model,

S=[3a+b0]2+[a+b1]2+[a+b1]2+[3a+b2]2

Now, find the derivative with respect a and put equal to zero,

dSda=dda([3a+b0]2+[a+b1]

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