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Unformatted text preview: (The next 4 questions are based on the following information.) In this problem we consider an analysis of the number of active physicians in a city as a function of the city's population and the region of the United States that the city is in. The sample consists of data on 141 cities in the United States, and the variables are defined as follows • pop = city population (in thousands) • doctors = number of professionally active physicians in the city • region dummy variables are defined for 4 regions: East, Central, South, and West. east = 1 if city in the East region, 0 otherwise central = 1 if city in the Central region, 0 otherwise south = 1 if city in the South region, 0 otherwise R 2 = .9551 R 2 (Adjusted) = .9538 SSE=56,950,000 Residual SD = 647.1 Coefficients Standard Error t Stat PValue Intercept255 130.21.96 0.052 pop 2.3 0.043 53.5 0.000 east36 174.70.21 0.836 central327 164.11.99 0.048 south83 152.80.54 0.590 1. What is the predicted number of doctors in a city with a population of 500,000 in the West region? (a) 568 (b) 823 (c) 895 (d) 1150 2. What is the equation for the regression line predicting number of doctors from population for the South region? (a) Doctors = 338 + 2.3 pop (b) Doctors = 255 + 83 pop (c) Doctors = 172 + 2.3 pop (d) Doctors = 255 + 2.3 pop 3. Based on this model, in which region is the slope of the regression line relating doctors to population the steepest ? (a) The West region has the steepest regression line. (b) The Central region has the steepest regression line. (c) The East region has the steepest regression line. (d) The regression line has the same slope in all four regions. 4. To test whether the whole model is at all useful, we perform a hypothesis test of whether the population coefficients for the four independent variables (pop, east, central, and south) are all equal to 0 . What is the test statistic, approximate critical value, and conclusion for this hypothesis test? (Use alpha=.05) (a) test statistic: F = 723 approximate critical value: F* = 2.45 Conclusion: Reject H (b) test statistic: t = 53.5 approximate critical value: t* = 1.98 Conclusion: Reject H (c) test statistic: F = 2862 approximate critical value: F* = 3.92 Conclusion: Don't Reject H (d) test statistic: t = 0.54 approximate critical value: t* = 1.98 Conclusion: Don't Reject H (The next 4 questions deal with the following information.) Below. we predict hourly wages ( Wage, measured in dollars per hour) based on type of job (Professional, Clerical, or Service) and amount of education ( Educ, measured in years) for n=378 workers interviewed in a 1985 Population Survey. The type of job is coded with two dummy variables, Pro and Clerk : • Pro =1 if type of job is Professional, and Pro=0 otherwise • Clerk =1 if type of job is Clerical, and Clerk=0 otherwise....
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 Spring '09
 Regression Analysis, Northeast, average mpg

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