Chapter 14.4, Problem 4CP

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Use linear regression to write the equation of the line that is the best fit for the following points. X 50 25 10 5 y 2 4 10 20

To determine

To calculate: The equation of the line that is the best fit for the points by use of linear regression.

 x 50 25 10 5 y 2 4 10 20
Explanation

Given Information:

The provided table is,

 x 50 25 10 5 y 2 4 10 20

Formula used:

According to linear regression equation, the equation of the line that is the best fit for the given data points (x1,y1),(x2,y2),â€¦,(xn,yn) is y^=a+bx, where b=âˆ‘i=1nxiâˆ‘i=1nyiâˆ’nâˆ‘i=1nxiyi(âˆ‘i=1nxi)2âˆ’nâˆ‘i=1nxi2 and a=âˆ‘i=1nyiâˆ’bâˆ‘i=1nxin.

Calculation:

Consider the table,

 x 50 25 10 5 y 2 4 10 20

Let xi denote the values of x for 1<i<4.

That is, x1=50,x2=25,x3=10,x4=5.

Let yi denote the values of y for 1<i<4.

That is, y1=2,y2=4,y3=10,y4=20.

Thus, the points are (50,2),(25,4),(10,10),(5,20).

The equation of the line that is the best fit for the given data points (x1,y1),(x2,y2),......,(xn,yn) is y^=a+bx, where b=âˆ‘i=1nxiâˆ‘i=1nyiâˆ’nâˆ‘i=1nxiyi(âˆ‘i=1nxi)2âˆ’nâˆ‘i=1nxi2, and a=âˆ‘i=1nyiâˆ’bâˆ‘i=1nxin.

Since, the number of data points is 4.

Thus, n=4.

Calculate the value of b.

Substitute 4 for n in b=âˆ‘i=1nxiâˆ‘i=1nyiâˆ’nâˆ‘i=1nxiyi(âˆ‘i=1nxi)2âˆ’nâˆ‘i=1nxi2

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