Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
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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Chapter 7.2, Problem 57E

a.

To determine

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

a.

Expert Solution
Check Mark

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.

  Precalculus with 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 .

b.

To determine

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

b.

Expert Solution
Check Mark

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.

  Precalculus with 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 .

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Chapter 7.2, Problem 56E
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Chapter 7.2, Problem 58E

Chapter 7 Solutions

Precalculus with Limits

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