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Name #1 ______________________________ UBIT #1 _____________________________

 

MGE 302 Assignment #3- Due Monday, Oct. 17 @ 8:00 AM

 

Submit your assignment as a single page, showing all work that you would like to be graded on the

 

answer sheet provided below. Remember, only this answer sheet page should be uploaded.

 

1.

 

a. b. c. d. 2.

 

a.(circle/mark answer A B C D b.(circle/mark answer) A B C D c.(circle/mark answer) A B C D 1 2 3 4 3.

 

a. b.(circle/mark answer)

 

c. 5 1. The data for this question can be found in HW3Data.xls on UBLearns.

 

A sociology graduate student wants to model a city's death rate using the following equation:

 

Deathrate = a + b(DoctorAvail) + c(HospitalAvail) + d(Income) + e(Population) Using the data in the RawData tab of file HW2Data.xls, estimate a multivariate linear regression

 

of the model described above.

 

a. What is the equation of the sample regression line? b. Interpret the p-values for the parameter estimates. Which variables are statistically

 

significant? Explain how you determined your answer. c. Explain in words the interpretation of the coefficient for annual per capita income. If per

 

capita income increases by $1,000/year, what happens to city's death rate? d. Estimate the death rate per 1,000 residents for a city that has 85 doctor availability per

 

100,000 residents, 198 hospital availability per 100,000 residents, an annual per captia

 

income of $9,000 and a population density of 130 residents per square mile. 2. The linear regression equation, Y = a + bX, was estimated. The following computer printout was

 

obtained:

 

DEPENDENT VARIABLE:

 

OBSERVATIONS: VARIABLE

 

INTERCEPT

 

X Y

 

18 RSQUARE

 

0.3066 FRATIO

 

7.076 PVALUE ON F

 

0.0171 PARAMETER

 

ESTIMATE

 

15.48

 

21.36 STANDARD

 

ERROR

 

5.09

 

8.03 TRATIO

 

3.04

 

2.66 PVALUE

 

0.0008

 

0.0171 a. Given the above information, the parameter estimate of b indicates

 

A. X increases by 8.03 units when Y increases by one unit.

 

B. X decreases by 21.36 units when Y increases by one unit.

 

C. Y decreases by 2.66 units when X increases by one unit.

 

D. a 10-unit decrease in X results in a 213.6 unit increase in Y. b. Given the above information, if X equals 20, what is the predicted value of Y?

 

A. 186.42

 

B. 165.69

 

C. 186.42

 

D. 411.72 c. Given the above information, which of the following statements is correct at the 1% level of

 

significance? 3. a^ and A. Both B. Neither b^ are statistically significant. a^ nor b^ is statistically significant. C. a^ is statistically significant, but b^ is not. D. b^ is statistically significant, but a^ is not. 3. A forecaster used the regression equation Qt a bt c1 D1 c2 D2 c3 D3

 

and quarterly sales data for Q1 1993 through Q4 2008 (t = 1, ..., 64) for an appliance

 

manufacturer to obtain the results shown below. Q is quarterly sales, and

 

and are

 

D1 , D2

 

D3

 

dummy variables for quarters I, II, and III.

 

DEPENDENT VARIABLE: QT RSQUARE FRATIO PVALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR TRATIO PVALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 a. Is there an upward or downward trend in sales over time? Is this trend statistically

 

significant? Justify your answer using regression statistics. b. In any given year, which ranking of quarterly sales tends to be true (mark the # of

 

your choice on the answer sheet): 1.

 

2.

 

3.

 

4.

 

5. QI > QII > QIII > QIV

 

QI > QII > QIV > QIII

 

QII > QIII > QIV > QI

 

QIII > QII > QI > QIV

 

QIII > QIV > QII > QI c. Calculate the estimated sales forecasts for the 1 st, 2nd, 3rd and 4th quarter of 2009.

 


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