Question 1

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income.  Which is the dependent variable?

Accepted Answer

A

Question 2

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, percent of population in the community holding a bachelor's degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest level of education attained.[Adapted from 1^stCanadian Lind text 14-14] Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%) How many dependent variables are there in this regression?

Accepted Answer

D

Question 3

i. A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation.
Ii) Autocorrelation often happens when data has been collected over periods of time.
Iii) Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different values of Y'.

Accepted Answer

Statement (i) is correct as a multiple regression equation indeed defines the relationship between the dependent and independent variables. Statement (ii) is correct because autocorrelation is common in time series data. Statement (iii) is incorrect because homoscedasticity refers to the condition where the variance of the residuals is constant across all levels of the independent variable, not different.

Question 4

i. Multiple regression analysis examines the relationship of several dependent variables on the independent variable.
Ii) A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation.
Iii) Autocorrelation often happens when data has been collected over periods of time.

Accepted Answer

Multiple regression analysis examines the relationship of one dependent variable with several independent variables, not several dependent variables. Statement (ii) correctly describes the multiple regression equation, and statement (iii) correctly describes autocorrelation.

Question 5

i. Multiple regression is used when two or more independent variables are used to predict a value of a single dependent variable.
Ii) The values of b1, b2 and b3 in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant.
Iii) Autocorrelation often happens when data has been collected over periods of time.

Accepted Answer

Multiple regression involves multiple independent variables predicting a dependent variable. The coefficients (b1, b2, b3) represent changes in the dependent variable for unit changes in independent variables, holding others constant. Autocorrelation is common in time series data.

Question 6

i. The values of b1, b2 and b3 in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant. 
ii. Multiple regression analysis examines the relationship of several dependent variables on the independent variable.
Iii) A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation.

Accepted Answer

Statement (i) and (iii) are correct. Statement (ii) is incorrect because multiple regression analysis examines the relationship of several independent variables on a single dependent variable, not several dependent variables on an independent variable.

Question 7

Multiple regression analysis is applied when analyzing the relationship between

Accepted Answer

Multiple regression analysis is used to examine the relationship between one dependent variable and multiple independent variables.

Question 8

i. Violating the need for successive observations of the dependent variable to be uncorrelated is called autocorrelation.
Ii) If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are negative.
Iii) Given a multiple linear equation Y' = 5.1 + 2.2X1 - 3.5X2, assuming other things are held constant, an increase in one unit of the second independent variable will cause a -3.5 unit change in Y.

Accepted Answer

Autocorrelation refers to the correlation of a signal with a delayed copy of itself, which is a violation in regression analysis. An inverse relationship between dependent and independent variables results in negative regression coefficients. In the given equation, a unit increase in X2 results in a -3.5 change in Y, as indicated by the coefficient of X2.

Question 9

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, and percent of population in the community holding a bachelor's degree as their highest level of education attained.  Determine the regression equation.

Accepted Answer

The answer of Angela Chou has been asked to investigate...

Question 10

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, and percent of population in the community holding a bachelor's degree as their highest
Of education attained.  Determine the regression equation.

Accepted Answer

The answer of Angela Chou has been asked to investigate...

Question 11

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:  In the regression model, which of the following are dummy variables?

Accepted Answer

The answer of A manager at a local bank analyzed...

Question 12

How is the Y intercept in the multiple regression equation represented?

Accepted Answer

In a multiple regression equation, the Y-intercept is typically represented by b0, not any of the options provided.

Question 13

For a unit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y' = 5.2 + 6.3X1 - 7.1X2?

Accepted Answer

The coefficient of X1 in the regression equation is 6.3, indicating that for a unit increase in X1, the dependent variable Y' is expected to increase by 6.3 units, holding other variables constant.

Question 14

i. The values of b1, b2 and b3 in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant. 
ii. A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation.
Iii) If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are positive.

Accepted Answer

Statement (i) and (ii) are correct. Statement (iii) is incorrect because if an inverse relationship exists, the regression coefficients would be negative, not positive.

Question 15

i. Multiple regression is used when two or more independent variables are used to predict a value of a single dependent variable. 
ii. The values of b1, b2 and b3 in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant.
Iii) Multiple regression analysis examines the relationship of several dependent variables on the
Independent variable.

Accepted Answer

Statement (i) and (ii) are correct as multiple regression involves multiple independent variables predicting a single dependent variable, and the coefficients represent the change in the dependent variable for a unit change in an independent variable while holding others constant. Statement (iii) is incorrect because multiple regression does not involve several dependent variables.

Question 16

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, percent of population in the community holding a bachelor's degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest levelof education attained. [Adapted from 1^stCanadian Lind text 14-14] Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%) What is the estimated percentage of poor persons living below the poverty line in a community with 5% of the community as single-families, a 5% unemployment rate, only 5% holding a Bachelor's Degree and 25% having High School as their highest attained educational level?

Accepted Answer

The estimated percentage of poor persons living below the poverty line in a community with 5% of the community as single-families, a 5% unemployment rate, only 5% holding a Bachelor's Degree and 25% having High School as their highest attained educational level is 2.375%.Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)Poor (%) = -3.81 + 0.798 (5) + 0.624 (5) - 0.170 (5) - 0.003 (25)Poor (%) = -3.81 + 3.99 + 3.12 - 0.85 - 0.075Poor (%) = 2.375

Question 17

i. If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are positive.
Ii) Given a multiple linear equation Y' = 5.1 + 2.2X1 - 3.5X2, assuming other things are held constant, an increase of one unit in the second independent variable will cause a -3.5 unit change in Y.
Iii) When the variance of the differences between the actual and the predicted values of the dependent variable are approximately the same, the variables are said to exhibit homoscedasticity.

Accepted Answer

An inverse relationship means the regression coefficient is negative, so (i) is false. Statement (ii) correctly describes the effect of X2 on Y. Statement (iii) correctly defines homoscedasticity.

Question 18

If there are four independent variables in a multiple regression equation, there are also four

Accepted Answer

In a multiple regression equation, each independent variable has its own regression coefficient, so with four independent variables, there are four regression coefficients.

Question 19

The information above is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA. Predict the number of wins for a team with:
BATAVG = 0.260 HOMERUNS = 150 ERA = 3
STOLENBASE = 100 ERROR = 100
PAYROLL = 25(million) ATTENDANCE = 3(million)

Accepted Answer

The answer of  The information above is from the...

Question 20

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The independent variables selected are percent of single families in each community, the unemployment rate in each community, percent of population in the community holding a bachelor's degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest level of education attained. [Adapted from 1st Canadian Lind text 14-14]

Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
Which single event would have the strongest effect in reducing the % poor in Ontario?

Accepted Answer

The answer of Angela Chou has been asked to investigate...

Quiz 13: Multiple Regression and Correlation Analysis

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which is the dependent variable?

Multiple regression analysis is applied when analyzing the relationship between

How is the Y intercept in the multiple regression equation represented?

For a unit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y' = 5.2 + 6.3X1 - 7.1X2?

If there are four independent variables in a multiple regression equation, there are also four