Chapter 14, Partial Correlation and Multiple Regression and Correlation Video Solutions, The Essentials of Statistics: A Tool for Social Research

Problem 1

In problem $13.1$, data regarding voter turnout in five cities was presented. For the sake of convenience, the data for three of the variables are presented again here along with descriptive statistics and zero-order correlations.
a. Compute the partial correlation coefficient for the relationship between turnout $(\underline{Y})$ and unemployment $(X)$ while controlling for the effect of negative advertising $(Z) .$ What effect does this control variable have on the bivariate relationship? Is the relationship between turnout and unemployment direct? (HINT: Use Formula $14.1$ and see "Types of Relationships" in the section on partial correlation.)
b. Compute the partial correlation coefficient for the relationship between turnout $(Y)$ and negative advertising $(X)$ while controlling for the effect of unemployment $(Z) .$ What effect does this have on the bivariate relationship? Is the relationship between turnout and negative advertising direct? (Hint: Use Formula $14.1$ and see "Types of Relationships" in the section on partial correlation. You will need this partial correlation to compute the multiple correlation coefficient.)
c. Find the unstandardized multiple regression equation with unemployment $\left(X_{1}\right)$ and negative ads $\left(X_{2}\right)$ as the independent variables. What turnout would be expected in a city in which the unemployment rate was $10 \%$ and $75 \%$ of the campaign ads were negative? (Hint: Use Formulas $14.4$ and $14.5$ to compute the partial slopes and then use Formula $14.6$ to find $a$, the $Y$ intercept. The regression line is stated in Formula 14.3. Substitute 10 for $X_{1}$ and 75 for $X_{2}$ to com pute predicted $Y .)$
d. Compute beta-weights for each independent variable. Which has the stronger impact on turnout? (Hint: Use Formulas $14.7$ and $14.8$ to calculate the beta-weights.)
e. Compute the multiple correlation coefficient $(R)$ and the coefficient of multiple determination $\left(R^{2}\right)$. How much of the variance in voter turnout is explained by the two independent variables? (Hint:
Use Formula 14.11. You calculated $r_{y 2.1}^{2}$ in part b. of this problem.)
f. Write a paragraph summarizing your conclusions about the relationships among these three variables.

James Kiss

Numerade Educator

11:26

Problem 2

A scale measuring support for increases in the national defense budget has been administered to a sample. The respondents have also been asked to indicate how many years of school they have completed and how many years, if any, they served in the military. Take "support" as the dependent variable. Compute the zero-order correlations among the three variables.
a. Compute the partial correlation coefficient for the relationship between support $(Y)$ and years of school $(X)$ while controlling for the effect of years of service $(Z)$. What effect does this have on the bivariate relationship? Is the relationship between support and years of school direct?
b. Compute the partial correlation coefficient for the relationship between support $(Y)$ and years of service $(X)$ while controlling for the effect of years of school (Z). What effect does this have on the bivariate relationship? Is the relationship between support and years of service direct? (Hint: You will need this partial correlation to compute the multiple correlation coefficient.)
c. Find the unstandardized multiple regression equation with school $\left(X_{1}\right)$ and service $\left(X_{2}\right)$ as the independent variables. What level of support would be expected in a person with 13 years of school and 15 years of service?
d. Compute beta-weights for each independent variable. Which has the stronger impact on support?
e. Compute the multiple correlation coefficient $(R)$ and the coefficient of multiple determination $\left(R^{2}\right) .$ How much of the variance in support is explained by the two independent variables? (Hint: You calculated $r^{2}{ }_{y 2.1}$ in part $\bar{b}$ of this problem. $)$
f. Write a paragraph summarizing your conclusions about the relationships among these three variables.

Heather Duong

Numerade Educator

01:07

Problem 3

Data on civil strife (number of incidents), unemployment, and urbanization have been gathered for 10 nations. Take civil strife as the dependent variable.
a. Compute the partial correlation coefficient for the relationship between strife $(Y)$ and unemployment $(X)$ while controlling for the effect of urbanization
(Z). What effect does this have on the bivariate relationship? Is the relationship between strife and unemployment direct?
b. Compute the partial correlation coefficient for the relationship between strife $(Y)$ and urbanization $(X)$ while controlling for the effect of unemployment $(Z)$. What effect does this have on the bivariate relationship? Is the relationship between strife and urbanization direct? (Hint: You will need this partial correlation to compute the multiple correlation coefficient.)
c. Find the unstandardized multiple regression equation with unemployment $\left(X_{1}\right)$ and urbanization $\left(X_{2}\right)$ as the independent variables. What level of strife would be expected in a nation in which the unemployment rate was $10 \%$ and where $90 \%$ of the population lived in urban areas?
d. Compute beta-weights for each independent variable. Which has the stronger impact on civil strife?
e. Compute the multiple correlation coefficient $(R)$ and the coefficient of multiple determination $\left(R^{2}\right)$. How much of the variance in strife is explained by the two independent variables?
f. Write a paragraph summarizing your conclusions about the relationships among these three variables.

James Kiss

Numerade Educator

02:16

Problem 4

In problem 13.5, three measures of crime and three other variables were presented for each of 10 states. The data are reproduced on the next page.
a. Find the multiple regression equations (unstandardized) with each crime variable (one at a time) and poverty and education as independent variables.
b. Make a prediction for each crime variable for a state with a $5 \%$ poverty rate and a score of 75 for the percent of high school graduates.
c. Compute beta-weights for each of the independent variables (poverty and education) in each equation and then compare their relative effect on each dependent variable.
d. Compute $R$ and $R^{2}$ for each crime variable. Write a paragraph summarizing your findings.

James Kiss

Numerade Educator

02:38

Problem 5

Problem $13.4$ presented data on 10 precincts. The information is reproduced here.
Take voter turnout as the dependent variable and do the following:
a. Find the multiple regression equations (unstandardized).
b. What turnout would you expect for a precinct in which 0\% of the voters were Democrats and $5 \%$ were minorities?
c. Compute beta-weights for each independent variable and then compare their relative effect on turnout. Which was the more important factor?
d. Compute $R$ and $R^{2}$.
e. Write a paragraph summarizing your findings.

Sheryl Ezze

Numerade Educator

02:17

Problem 6

Twelve families have been referred to a counselor, and she has rated each of them on a cohesiveness scale. Also, she has information on family income and the number of children currently living at home. Take family cohesion as the dependent variable.
a. Find the multiple regression equations (unstandardized).
b. What level of cohesion would be expected in a family with an income of $\$ 20,000$ and 6 children?
c. Compute beta-weights for each independent variable and then compare their relative effect on cohesion. Which was the more important factor?
d. Compute $R$ and $R^{2}$.
e. Write a paragraph summarizing your findings.

Victor Salazar

Numerade Educator

09:23

Problem 7

Problem $13.8$ presented per capita expenditures on education for 15 states, along with rank on income per capita and the percentage of the population that has graduated from high school. The data are reproduced here.
Take per capita expenditures as the dependent variable:
a. Compute beta-weights for each independent variable and then compare their relative effect on expenditures. Which was the more important factor?
b. Compute $R$ and $R^{2}$.
c. Write a paragraph summarizing your findings.

Phumlani Ngcobo

Numerade Educator

02:39

Problem 8

The scores on four variables for 20 individuals are reported here: hours of TV (average number of hours of TV viewing each day), occupational prestige (higher scores indicate greater prestige), number of children, and age. Take TV viewing as the dependent variable and then select two of the remaining variables as independent variables.
a. Compute beta-weights for each of the independent variables you selected and then compare their relative effect on the hours of television watching. Which was the more important factor?
b. Compute $R$ and $R^{2}$.
c. Write a paragraph summarizing your findings.

Akhil Choudhary

Numerade Educator

01:58

Problem 9

Problem $13.6$ presented data on three variables for 15 nations. The scores are reproduced below.
Take fertility as the dependent variable:
a. Compute beta-weights for each independent variable and then compare their relative effect on fertility. Which was the more important factor? Interpret the direction of each relationship with fertility.
b. Compute $R$ and $R^{2}$.
c. Write a paragraph summarizing your findings.

James Kiss

Numerade Educator