Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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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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Question

Chapter 1.1, Problem 46E

(a)

To determine

To find:The linear regression equation for the given data.

(a)

Expert Solution

Answer to Problem 46E

The linear regression equation for the given data is y=0.680027x+9.012539 .

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

To find the linear regression equation of the given data, use graphing calculator.

Step 1: Press STAT1 keys to enter the given data.

Step 2: List the input values 19, 21, 24, 27, 29, 31, 34, 38 and 43 in the L1 column.

Step 3: List the input values 22, 23, 25, 28, 31, 28, 32, 34 and 39 in the L2 column.

Step 4: Press the keystrokes STAT⇒4ENTER to find line of regression and again press ENTER key. So, the linear regression equation for the given data is:

y=0.680027x+9.012539

Therefore, thelinear regression equation for the given data is y=0.680027x+9.012539 .

(b)

To determine

To find: The slope of the regression line for the given data and describe the representation of the slope.

(b)

Expert Solution

Answer to Problem 46E

The slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

From part (a), the linear regression equation for the given data is y=0.680027x+9.012539 .

It is known that slope-form of a line is y=mx+c . Compare the above equation with this equation.

m≈0.68

Therefore, the slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.

(c)

To determine

To plot: The graph of the linear regression equation on a scatter plot for the given data.

(c)

Expert Solution

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Graph:

To make the scatter plot enter the data, then follow the stepsusing graphing calculator.

Step 1: Press 2ndY= and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press GRAPH key. Set the window at [15, 45] with scale 5 by [20, 40] with scale 2.

Step 3: Press the keystrokes STAT⇒42nd1,2nd2,VARS⇒11ENTER . Now, press GRAPH and TRACE key to plot the graph as shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.1, Problem 46E

Figure (1)

Interpretation:From the graph it can be interpreted that the weight of girls is increasing as there is increasing.

(d)

To determine

To find: The weight of 30 month old girl by using the regression equation.

(d)

Expert Solution

Answer to Problem 46E

The approximate weight of 30 month old girl is 29.4 pounds.

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

From part (a), the linear regression equation for the given data is y=0.680027x+9.012539 .

To find the weight of 30 month old girl, substitute 30 for x in the above equation.

y=0.680027(30)+9.012539=20.40081+9.012539≈29.4

Therefore, the approximate weight of 30 month old girl is 29.4 pounds.

Chapter 1.1, Problem 45E

Chapter 1.1, Problem 47E

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Prob. 61E Ch. 1.6 - Prob. 62E Ch. 1.6 - Prob. 1QQ Ch. 1.6 - Prob. 2QQ Ch. 1.6 - Prob. 3QQ Ch. 1.6 - Prob. 4QQ Ch. 1 - Prob. 1RE Ch. 1 - Prob. 2RE Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - 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