EBK PRECALCULUS W/LIMITS

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Question

Chapter 7.2, Problem 57E

To determine

The solution of the least square regression line for the data.

Expert Solution

Answer to Problem 57E

y=14x+19 .

Explanation of Solution

Given information:

An agriculture scientist used four test plot to determine the relationship between wheat yield y and the amount of fertiliser x . The table shows the result.

EBK PRECALCULUS W/LIMITS, Chapter 7.2, Problem 57E , additional homework tip 1

(a) Find the least squares regression line y=ax+b for the data by solving the system for a and b .

{4b+7.0a=1747b+13.5a=322

Calculation:

The system of the equations are:

{4b+7.0a=1747b+13.5a=322

To find the least squares regression line y=ax+b for the given points:

(1.0,32),(1.5,41),(2.0,48),(2.5,53)

Multiplying the first equation by −7 and the second equation by 4 and add them to eliminate b to get the value of a :

−28b−49a=−121828b+54a=1288−28b+28b−49a+54a=1218+12885a=70a=14

Find the value of b by replacing the value of a in the first equation:

4b+7.14=1744b+98=1744b=76b=19

Substitute the value of a and b in the least regression line y=ax+b :

y=ax+by=x(14)+19y=14x+19

Thus, the solution is y=14x+19 .

To determine

The demand by using the linear model from part (a).

Expert Solution

Answer to Problem 57E

y=56.338 .

Explanation of Solution

Given information:

An agriculture scientist used four test plot to determine the relationship between wheat yield y and the amount of fertiliser x . The table shows the result.

EBK PRECALCULUS W/LIMITS, Chapter 7.2, Problem 57E , additional homework tip 2

(b) Use the linear model from part (a) to estimate the yield for a fertilizer application of 160 pounds per acre.

Calculation:

By using the linear model from the part (a) to find the value of y by substituting the value of x=160 pounds/acre:

Firstly convert the pounds to bushels:

60 pounds..............1 bushel160 pounds...........z

z=16060=83≈2.667y=14x+19y=14(2.667)+19y=56.338

Therefore, the solution is y=56.338 .

Chapter 7.2, Problem 56E

Chapter 7.2, Problem 58E

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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