probs-multreg2-dummy-sols

probs-multreg2-dummy-sols - (The next 4 questions are based...

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(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 P-Value Intercept -255 130.2 -1.96 0.052 pop 2.3 0.043 53.5 0.000 east -36 174.7 -0.21 0.836 central -327 164.1 -1.99 0.048 south -83 152.8 -0.54 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 Answer: (c) predicted doctors = -255 + 2.3 * 500 – 36*0 – 327*0 –83*0 = 895 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 Answer: (a) Predicted Doctors = -255 + 2.3 pop - 36*0 - 327*0 - 83*1 = -338 + 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.
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The slope for the variable “pop” is the same for all four regions – this is a central assumption of a model with a continuous predictor and a set of dummy variables. Only if we add interaction terms can the slope be different in each region. 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 0 (b) test statistic: t = 53.5 approximate critical value: t* = 1.98 Conclusion: Reject H 0 (c) test statistic: F = 2862 approximate critical value: F* = 3.92 Conclusion: Don't Reject H 0 (d) test statistic: t = -0.54 approximate critical value: t* = 1.98 Conclusion: Don't Reject H 0 Answer: (a) Test statistic F = (R 2 / k) / [(1-R 2 ) / (n-k-1)] = (.9551 / 4) / (.0449 / (141- 4 –1)) = 723 Want critical F from F-table , using 4 and 136 df: closest is F(4,60120) = 2.447 Because the test statistic is larger than the critical value we reject the null hypothesis. (btw, you won’t need to use the F table on the exams)
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probs-multreg2-dummy-sols - (The next 4 questions are based...

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