Question

1. A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (n = 51), he collects data on the poverty rate (y, in %), the percent of the population with at least a high school education (x1), median income (x2, in $1000s), and the mortality rate per 1,000 residents (x3). He estimates the following model as y = β0 + β1 Education + β2 Income + β3 Mortality + ε. The following ANOVA table shows a portion of the regression results.

	df	SS	MS	F
Regression	3	417.3	139.1	94.6
Residual	47	69.1	1.47
Total	50	486.4
	Coefficients	Standard Error	t-stat	p-value
Intercept	60.3	4.8	12.47	1.65E-16
Education	−0.43	0.05	−7.78	5.45E-10
Income	−0.20	0.03	−7.75	6.02E-10
Morality	0.08	0.17	0.47	0.6438

The coefficient of determination indicates that ________.

2. A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the model:

Sales = β₀ +β₁Advertising + ε. The following ANOVA table shows a portion of the regression results.

	df	SS	MS	F
Regression	1	78.53	78.53	3.58
Residual	23	504.02	21.91
Total	24	582.55
	Coefficients	Standard Error	t-stat	p-value
Intercept	40.10	14.08	2.848	0.0052
Advertising	2.88	1.52	-1.895	0.0608

Which of the following is true?

Multiple Choice

• If Sales go up by $100, then we predict Advertising to go up by $2,880.

• If Advertising goes up by $100, then we predict Sales to go up by $2,880.

• If Sales go up by $100, then we predict Advertising to go up by $4,298.

• If Advertising goes up by $100, then we predict Sales to go up by $4,298.

Answer 1

Answer

(1) R square = SS(regression)/SS(total)

setitng the values from the given table, we get

R square = 417.3/486.4= 0.8579 or 85.79%

R square suggest that 85.79% variation in the poverty rate can be explained by the regression line

(2) Independent variable is advertising with slope coefficient $2.88(in thousands) or $2880

slope is positive, this means that the every unit in advertising will increase the sales by $2880

option B is correct