   # The following variables were collected for a sample of ten precincts during the last national election. Compute r and r 2 for each combination of variables and write a paragraph interpreting the relationship between these variables. Take voter turnout as the dependent variable. Precinct Percentage Democrat Percentage Minority Percentage Voter Turnout A 33 9 36 B 78 15 60 C 62 18 64 D 50 10 56 E 45 12 55 F 56 8 52 G 85 20 25 H 25 0 42 I 13 5 89 J 33 9 88 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 12, Problem 12.4P
Textbook Problem
9 views

## The following variables were collected for a sample of ten precincts during the last national election. Compute r and r 2 for each combination of variables and write a paragraph interpreting the relationship between these variables. Take voter turnout as the dependent variable. Precinct PercentageDemocrat Percentage Minority Percentage Voter Turnout A 33 9 36 B 78 15 60 C 62 18 64 D 50 10 56 E 45 12 55 F 56 8 52 G 85 20 25 H 25 0 42 I 13 5 89 J 33 9 88

To determine

To find:

The coefficients r and r2.

### Explanation of Solution

Given:

The given statement is,

The following variables were collected for a sample of ten precincts during the last national election. The voter turnout is the dependent variable.

The given table of information is,

 Precinct PercentageDemocrat Percentage Minority Percentage Voter Turnout A 33 9 36 B 78 15 60 C 62 18 64 D 50 10 56 E 45 12 55 F 56 8 52 G 85 20 25 H 25 0 42 I 13 5 89 J 33 9 88

Approach:

The Y intercept (a) is the point of intersection of the regression line and the y axis.

The slope (b) of the regression line is the amount of change in the dependent variable (Y) by a unit change in the independent variable (X).

If the two variables are unrelated, the regression line would be parallel to the x axis.

Formula used:

The model for the least square regression line is defined as,

Y=a+bX

Where Y is the dependent variable,

X is the independent variable,

a is the Y intercept of the regression line

and, b is the slope of the regression line.

The formula for calculating the correlation coefficient r is given as,

r=(XX¯)(YY¯)[(XX¯)2][(YY¯)2]

Where X and Y are the two variables

And X¯ and Y¯ are their respective means.

Calculation:

From the given information,

The voter turnout is the dependent variable. Thus, it is represented as Y.

The rest of the variables, i.e. democrat and minority are the independent variables and are represented as X1 and X2 respectively.

Consider the following table of sum of squares of democrat and voter turnout.

 Precinct Democrat (X1) (X1−X¯) (X1−X¯)2 Voters Turnout (Y) (Y−Y¯) (Y−Y¯)2 (X1−X¯)(Y−Y¯) A 33 −15 225 36 −20.7 428.49 310.5 B 78 30 900 60 3.3 10.89 99 C 62 14 196 64 7.3 53.29 102.2 D 50 2 4 56 −0.7 0.49 −1.4 E 45 −3 9 55 −1.7 2.89 5.1 F 56 8 64 52 −4.7 22.09 −37.6 G 85 37 1369 25 −31.7 1004.89 −1172.9 H 25 −23 529 42 −14.7 216.09 338.1 I 13 −35 1225 89 32.3 1043.29 −1130.5 J 33 −15 225 88 31.3 979.69 −469.5 Totals 480 ∑(X1−X¯)2=4746 567 ∑(Y−Y¯)2=3762.1 ∑(X−X¯)(Y−Y¯)=−1957

From above table, substitute 33 for X1 and 48 for X¯ in (X1X¯).

(X1X¯)=(3348)(X1X¯)=15

Square the both sides of the equation.

(X1X¯)2=(15)2(X1X¯)2=225

Proceed in the same manner to calculate (X1X¯)2 for all the 1iN for the rest data and refer table for the rest of the (X1X¯)2 values calculated. Then the value of (X1X¯)2 is calculated as,

(X1X¯)2=225++900+196+4+9+64+1369+529+1225+225=4746

Substitute 1957 for (XX¯)(YY¯), 4746 for (X1X¯)2 and 3762

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Solving an Equation In Exercises11-26, solve for x. e2x=e5

Calculus: Early Transcendental Functions

23-42 Find f. f(t)=46/t4,f(1)=6,f(2)=9,t0

Calculus (MindTap Course List)

A Doomsday Situation The population of a certain breed of rabbits introduced onto an isolated island is given b...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Combine the like terms: 5m2m

Elementary Technical Mathematics

29. Find what value of c is the function a probability density function.

Mathematical Applications for the Management, Life, and Social Sciences

The area of the region at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

5. The USA Today reports that the average expenditure on Valentine’s Day is \$100.89. Do male and female consume...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Population Growth There are originally 255 foxes and 104 rabbits on a particular game reserve. The fox populati...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Population Model In one model of the changing population P(t) of a community, it is assumed that dPdt=dBdtdDdt....

A First Course in Differential Equations with Modeling Applications (MindTap Course List) 