MBA60: ADVANCED QUANTITATIVE METHODS FOR MANAGERS

 Assignment 4

2008/9

 

HELLENIC OPEN UNIVERSITY

MBA PROGRAMM

MBA60: ADVANCED QUANTITATIVE METHODS FOR MANAGERS

Advanced Quantitative Analysis – 4th Assignment

A real estate developer in northern Greece wants to predict heating oil consumption based on atmospheric temperature, the amount of insulation used and the type of house (detached house or otherwise). From a sample of 15 houses selected randomly (of the same more or less area), he collected the following data:

Dependent variable (Y)                                     = Monthly heating oil consumption in liters

X1: Temperature                                                                      = Mean atmospheric temperature (in C degrees)

X2:       Insulation                                                                                  =          Insulation used (in cubic meters)

D (dummy: Detached House)    =          1                     if it is a detached house

                                                                                                                                                            =          0                      otherwise

House	Y (liters)	X1 (C degrees)	X2 (cubic meters)	D (dummy)
1	1101.2	4.4	3	1
2	1455.2	-2.8	3	0
3	657.2	4.4	10	0
4	163.2	22.8	6	1
5	377.2	17.8	6	0
6	923.6	1.1	6	1
7	1466.8	-12.8	6	1
8	1202.4	-13.3	10	1
9	951.2	-5.0	10	0
10	485.6	17.2	3	1
11	125.6	18.3	10	0
12	814.0	5.0	6	1
13	1764.4	-6.1	3	0
14	1292.0	3.3	3	0
15	210.0	14.4	10	0

Assume that you want to build a regression model that explains the monthly heating oil consumption.

1. Use the least squares method to estimate the following model

Y = b₀ + b₁ X1 + b₂ X2 + b₃ D + U        

2. State the estimated regression equation.

3. Comment the significance of the regression coefficients.

4. Give the interpretation of the regression coefficients.

5. Determine the coefficient of determination and explain its meaning.

6. Perform a residual analysis (i.e. plot the residuals versus the Observation). Is there any evidence of a pattern in the residuals? Explain.

7. Using the above model estimate the predicted monthly heating oil consumption for a detached house with 8 cubic meters of insulation and an average atmospheric temperature of 5 C degrees.

8. What should be the monthly heating oil consumption, for a non detached house (with 8 cubic meters of insulation and an average temperature of 5 C degrees)?

9. Do you trust the above predictions? Explain.

10. If you were a journalist specializing in house construction, prepare a short article that explains how a house heating oil consumption is determined.

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