The same media consultants decided to continue their investigation of the focal relationship between income and TV viewing habits. In order to confirm the existence of the focal relationship, they decided to control for immigration status by adding a variable measuring the number of each survey respondent's grandparents who were born outside the U.S. The researchers wonder if immigration background could influence both income and TV watching (but they hope this is not true, because it could invalidate the focal relationship). The researchers conduct a multivariate regression by adding a measure of number of grandparents born outside the U.S. to the regression equation presented in Equation 2 of Table 1. The results of the second regression equation are presented in Equation 2 of Table 1. Table 1. OLS Regression Coefficients Representing Influence of Income and Control Variables on Number of Hours of TV Watched per Day Equation 1 Equation 2 Equation 3 Annual Income of respondent (x 1000) -.116 (.003) -.115 (.004) -.063 (.103) Number of respondent's grandparents born outside US -.067 (.123) -.048 (.254) Average weekly hours of employment -.131 (.000) Y-intercept (Constant) 8.69 8.07 10.32 R2 .034 .038 .070 (Significance level in parentheses) Equation 2 can also be written as: Y^ = 8.07 -.115 (X) - .067 (Z1) 1. Write out the equation for the line from the bivariate regression in a way that clearly identifies all independent and dependent variables (only using Equation 2).
The same media consultants decided to continue their investigation of the focal relationship between income and TV viewing habits. In order to confirm the existence of the focal relationship, they decided to control for immigration status by adding a variable measuring the number of each survey respondent's grandparents who were born outside the U.S. The researchers wonder if immigration background could influence both income and TV watching (but they hope this is not true, because it could invalidate the focal relationship). The researchers conduct a multivariate regression by adding a measure of number of grandparents born outside the U.S. to the regression equation presented in Equation 2 of Table 1. The results of the second regression equation are presented in Equation 2 of Table 1.
Table 1. OLS Regression Coefficients Representing Influence of Income and Control Variables on Number of Hours of TV Watched per Day
|
Equation 1 |
Equation 2 |
Equation 3 |
|
|
Annual Income of respondent (x 1000) |
-.116 (.003) |
-.115 (.004) |
-.063 (.103) |
|
Number of respondent's grandparents born outside US |
-.067 (.123) |
-.048 (.254) |
|
|
Average weekly hours of employment |
-.131 (.000) |
||
|
Y-intercept (Constant) |
8.69 |
8.07 |
10.32 |
|
R2 |
.034 |
.038 |
.070 |
(Significance level in parentheses)
Equation 2 can also be written as: Y^ = 8.07 -.115 (X) - .067 (Z1)
1. Write out the equation for the line from the bivariate regression in a way that clearly identifies all independent and dependent variables (only using Equation 2).
Regression analysis:
Regression analysis estimates the relationship among variables. That is, it estimates the relationship between one dependent variable and one or more independent variables.
The general form of first-order regression model is y-cap = β 0 + β 1 x + ε, Where, the variable y is the dependent variable that is to be modelled or predicted, the variable x is the independent variable that is used to predict the dependent variable, and ε is the error term.
Equation for line which clearly identifies all independent and dependent variables:
Given regression analysis investigates the relationship between income and TV viewing habits. The researcher conducts a multivariate regression by adding a measure of number of grandparents born outside U.S. to the regression analysis. Given regression equation is Y-cap = 8.07–0.115(X) –0.067(Z1). From the study it is clear that, the dependent variable is ‘the number of hours of TV watched per day’, the independent variables are ‘annual income of respondent’ and ‘the number of respondent’s grandparents born outside US’.
Therefore, the required regression equation is,
Number of hours of TV watched per day =8.07–0.115(Annual income of the respondent) –0.067(Number of respondent’s grandparents born outside US).
Step by step
Solved in 3 steps
