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) 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
1. A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the...
19. 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 + β1Education + β2Income + β3Mortality + ε. The...
A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (5) he collects data on the poverty rately, in the percent of the population with at least a high school education (4), median incomex.in $1000s), and the mortality rate per 1.000 residents) He estimates the following model as - PoEducation income Mortality. The following ANOVA table shows a portion of the regression results SS MS 1391 F 946...
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Question 13 Not yet answered Points out of 1.00 P Flag question A Realtor examines the factors that influence the price of a house in Arlington, Massachusetts. He collects data on recent house sales (Price, in $1000s) and notes each house's square footage (Sqft) and the number of bedrooms (Beds). Using the following regression analysis output, at 0.05 level of significance, which of the following predictors is significant in explaining the price (Y) of a house? ANOVA df MS F...
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QUESTION 27 Q27. A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: Salary = Bo + B1 Service + ε. The following ANOVA table below shows a portion of the regression results. df SS M S F Regression 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2 ,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02...
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is as follows. [You may find it useful to reference the t table.) F 0.05 ANOVA Regression Residual Total M S 229.2 4,464.56 Significance F 0.950 df SS 2 458.3 17 75,897.54 1976,355.9 Intercept Poverty Income Coefficients 754.4596...
A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: Salary = β0 + β1 Service + ε. The following ANOVA table summarizes a portion of the regression results. df SS MS F Regression 1 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02 Service 9.19 3.20 2.87 0.01...
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4. ANOVA df SS MS F Significance F Regression 2 2,517.3 1,258.6 7.49E-01 Residual 17 72,837.53 4,284.56 Total 19 75,354.80 Coefficients...
Simple Linear regression
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