4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

Concept explainers

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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Question

Chapter 7.3, Problem 70E

To determine

Tocalculate:the least squares regression parabola by evaluating the values of a, b, and c.

Expert Solution

Answer to Problem 70E

1y1y3

y=−9800x2+437200x−31310

Explanation of Solution

Given information:

The system of equation,

4c+520b+69600a=228520c+69600b+9568000a=2816069600c+9568000b+1346880000a=3575200

Calculation:

Writ the matrix equation for the given system.

[4520696005206960095680006960095680001346880000][cba]=[228281603575200]

The solution of this equation can be found as shown below.

Now, solve for a, b, and c by finding the inverse of the 3×3 matrix.

[cba]=[4520696005206960095680006960095680001346880000]−1[228281603575200]=(857920−2691400411600−26914008498000−1332000411600−13320001640000)(228281603575200)=(−31310437200−9800)

Therefore, c=−31310,b=437200,a=−9800 .

So, the least squares regression parabola is y=−9800x2+437200x−31310 .

To determine

To graph: The model found in part (a) by using graphing utility and then plot the given data in the same viewing window.

Expert Solution

Explanation of Solution

Given information:

The data set as shown below.

Number, x100120140160Percent, y75685530

Graph:

The graph of the model and the data set can be drawn as shown below.

EBK PRECALCULUS W/LIMITS, Chapter 7.3, Problem 70E

It can be observed that each data point lies on the graph of the model. This shows that the least squares regression parabola fits the data set.

To determine

To estimate: the percentage of females that had offspring when there were 170 females.

Expert Solution

Answer to Problem 70E

15.025%

Explanation of Solution

Given information:

The number of females is 170.

Calculation:

Substitute x=170 in the model found in part (a) to estimate the percentage of females that had offspring.

y=−9800x2+437200x−31310=−9800(170)2+437200(170)−31310=60140=15.025

To determine

To estimate: the number of females when there were 40% of the females had offspring.

Expert Solution

Answer to Problem 70E

153

Explanation of Solution

Given information:

The percent of females having offspring, 40%.

Calculation:

Substitute y=40 in the model found in part (a) and solve for x to estimate the number of females.

40=−9800x2+437200x−3131040⋅ 800=−9800x2⋅ 800+437200x⋅ 800−31310⋅ 80032000=−9x2+1748x−25040−9x2+1748x−25040=32000−9x2+1748x−25040−32000=32000−32000x=−1748±17482−4(−9)(−57040)2(−9)=−1748±1002064−2⋅ 9x=−1748+1002064−18,x=−1748−1002064−18x=1748−100206418,x=1748+100206418x=41.49825, x=152.72397x≈41, x≈153

Out of these two values, only x=153 is relevant to the data set. So, the number of females was 153.

Chapter 7.3, Problem 69E

Chapter 7.3, Problem 71E

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

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - Prob. 28E Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.6 - Prob. 35E Ch. 7.6 - Prob. 36E Ch. 7.6 - Prob. 37E Ch. 7.6 - Prob. 38E Ch. 7.6 - Prob. 39E Ch. 7.6 - Prob. 40E Ch. 7.6 - Prob. 41E Ch. 7.6 - Prob. 42E Ch. 7.6 - Prob. 43E Ch. 7.6 - Prob. 44E Ch. 7.6 - Prob. 45E Ch. 7.6 - Prob. 46E Ch. 7.6 - Prob. 47E Ch. 7.6 - Prob. 48E Ch. 7.6 - Prob. 49E Ch. 7.6 - Prob. 50E Ch. 7.6 - Prob. 51E Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - 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Tocalculate :the least squares regression parabola by evaluating the values of a, b, and c.

Concept explainers

Videos

Tocalculate:the least squares regression parabola by evaluating the values of a, b, and c.

Answer to Problem 70E

Explanation of Solution

To graph: The model found in part (a) by using graphing utility and then plot the given data in the same viewing window.

Explanation of Solution

To estimate: the percentage of females that had offspring when there were 170 females.

Answer to Problem 70E

Explanation of Solution

To estimate: the number of females when there were 40% of the females had offspring.

Answer to Problem 70E

Explanation of Solution

Chapter 7 Solutions