Question

A group of researchers at a media consulting firm are interested in understanding the factors that shape TV viewing behavior. The researchers collect data from a random sample of 699 adult respondents over age 40 in the United States. The research consultants hypothesize that individuals' income levels influence how much television they watch per day. The dataset includes a variable capturing each person's annual income in thousands of dollars (i.e. one unit = $1000). Their dataset also includes a measure of daily television watching hours. The SPSS regression output they obtained was transformed into Table 1. The table includes the relevant information from the SPSS output. For this problem, you should focus only on equation #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 1 can also be written as: $LaTeX: \hat{Y}$ Y^ = 8.69 -.116 (X)

1. Please identify the value of the slope (using equation 1) and

2. interpret what it means, referencing the variables involved (using Equation 1).

Answer 1

Answer

(A) Given that the regression equation is

y = 8.69 - 0.116x

Using the given regression equation, we can write

slope coefficient is b = -0.116

so, required value of slope is -0.116

(B) We know that slope tells us about the expected change in value of dependent variable y based on the unit change in the independent variable x

Here dependent variable is number of hours of TV watched per day and independent variable is annual income of respodent

slope coefficient is -0.116

so, we can interpret it as

For every $1000 increase in annual income of respondent, number of hours of TV watched per day decreases by 0.116 hours