   Chapter 14.4, Problem 17E Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

In Problems 17 and 18, use the points given in the tables to write the equation of the line that is the best fit for the points. X 3 4 5 6 y 15 22 28 32

To determine

To calculate: The equation of the line that is the best fit for the points given in the table

 x 3 4 5 6 y 15 22 28 32
Explanation

Given Information:

The provided table is,

 x 3 4 5 6 y 15 22 28 32

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),......,(xn,yn) is y^=a+bx, where b=i=1nxii=1nyini=1nxiyi(i=1nxi)2ni=1nxi2, and a=i=1nyibi=1nxin.

Calculation:

Consider the table,

 x 3 4 5 6 y 15 22 28 32

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

That is, x1=3,x2=4,x3=5,x4=6.

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

That is, y1=15,y2=22,y3=28,y4=32.

Thus, the points are (3,15),(4,22),(5,28),(6,32).

Recall that, 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=i=1nxii=1nyini=1nxiyi(i=1nxi)2ni=1nxi2, and a=i=1nyibi=1nxin.

Since, the number of data points is 4. Thus, n=4.

Calculate the value of b.

Substitute 4 for n in b=i=1nxii=1nyini=1nxiyi(i=1nxi)2ni=1nxi2,

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