Question

Price (thousands of $)	Size (sq. ft.)	# of Bedrooms	# of Baths	Distance to Town Center	Garage Dummy (1=garage; 0=no garage)	Pool Dummy (1=pool; 0=no pool)
271.8	2100	2	2.5	9	1	0
221.1	2300	3	1.5	18	0	1
266.6	2400	4	2	13	1	0
292.4	2100	4	2	14	1	0
209	1700	2	1.5	8	1	0
270.8	2500	6	2	7	1	0
246.1	2100	4	2	18	1	0
194.4	2300	2	2	11	0	0
281.3	2100	3	2	16	1	0
172.7	2200	4	2	16	0	1
207.5	2300	5	2.5	21	0	1
198.9	2200	3	2	10	1	1
209.3	1900	6	2	15	1	1
252.3	2600	4	2	8	1	0
192.9	1900	4	2.5	14	1	1
209.3	2100	5	1.5	20	0	0
345.3	2600	8	2	9	1	0
326.3	2100	6	3	11	1	0
173.1	2200	2	1.5	21	1	1
187	1900	2	2	26	0	0
257.2	2100	2	2	9	1	0
233	2200	3	1.5	14	1	0
180.4	2000	2	2	11	0	0
234	1700	2	2	19	1	0
207.1	2000	2	2	11	1	0
247.7	2400	5	2	16	1	0
166.2	2000	3	2	16	1	1
177.1	1900	2	2	10	1	0
182.7	2000	4	2.5	14	0	1
216	2300	4	2	19	0	0
312.1	2600	6	2.5	7	1	0
199.8	2100	3	2	19	1	0
273.2	2200	5	3	16	1	0
206	2100	3	1.5	9	0	1
232.2	1900	3	1.5	16	1	1
198.3	2100	4	1.5	19	1	1
205.1	2000	3	2	20	0	1
207.5	2100	3	2	10	0	1
209.7	2200	4	2	19	1	1
294	2100	2	2.5	13	1	0
176.3	2000	2	2	17	0	1
294.3	2400	7	2	8	1	0
224	1900	3	2	6	1	1
125	1900	2	1.5	18	0	0
236.8	2600	4	2	17	1	1
164.1	2300	4	2	19	0	0
217.8	2500	3	2	12	0	0
192.2	2400	2	2.5	16	0	0
125.9	2400	2	1.5	28	0	0
220.9	2300	2	2	12	1	1
294.5	2700	6	2	15	1	0
244.6	2300	2	2.5	9	1	0
199	2500	3	1.5	18	0	1
240	2600	4	2	13	1	0
263.2	2300	4	2	14	1	0
188.1	1900	2	1.5	8	1	0
243.7	2700	6	2	7	1	0
221.5	2300	4	2	18	1	0
175	2500	2	2	11	0	0
253.2	2300	3	2	16	1	0
155.4	2400	4	2	16	0	1
186.7	2500	5	2.5	21	0	1
179	2400	3	2	10	1	1
188.3	2100	6	2	15	1	1
227.1	2900	4	2	8	1	0
173.6	2100	4	2.5	14	1	1
188.3	2300	5	1.5	20	0	0
310.8	2900	8	2	9	1	0
293.7	2400	6	3	11	1	0
179	2400	3	2	8	1	0
188.3	2100	6	2.5	14	1	1
227.1	2900	4	1.5	20	0	0
173.6	2100	4	2	9	1	0
188.3	2300	5	3	11	1	0
155.4	2400	4	2	16	0	1
186.7	2500	5	2.5	21	0	1
179	2400	3	2	10	1	1
188.3	2100	6	2	15	1	1
227.1	2900	4	2	8	1	0
173.6	2100	4	2.5	14	1	1

1. Use the above table to obtain the correlection coefficient between the "Price" and the "Number of bedrooms" variable in Excel. Please provide a picture of the Excel spreadsheet results.

2. Interpret the correlation coeffcient that you obtained in part (1), i.e., explain what the number means.

3. Use the above table. Data set and run one multiple regression with "Price" as dependent variable on the following independent variables:

(a) Size

(b) Number of Bedrooms

(c) Number of Baths

(d) Distance to Town Center

(e) Garage dummy

(f) Pool dummy

4. Interpret the estimated value of the intercept, i.e., explain what the number means in this regression.

5. Interpret the estimated value of the coefficient on the “Size (in square feet)” variable, i.e., explain what the number means in this regression.

6. Interpret the estimated value of the coefficient on the “Number of bedrooms” variable, i.e., explain what the number means in this regression.

7. Interpret the estimated value of the coefficient on the “Pool dummy” variable, i.e., explain what the number means in this regression.

8. Are there any coefficient estimates that are statistically significant? If so, name one and explain how you can tell that it is statistically significant.

9. Are there any coefficient estimates that are not statistically significant? If so, name one and explain how you can tell that it is not statistically significant.

10. What is the predicted price for a house that has 2,000 square feet, four bedrooms and two baths, is 12 miles away from the town center, and has neither a garage nor a pool?

11. Consider a new “No Garage dummy” variable that is “1” when a house does not have a garage and “0” when it does have a garage. Suppose that we then run a new multiple regression that is the same regression as in Part (a), but with the “No Garage dummy” variable instead of the “Garage dummy.” What would the estimated value of the coefficient on the “No Garage dummy” be?

12. What percentage of the variation in the dependent variable can be explained by variation in the independent variables?

13. What percentage of the variation in the dependent variable cannot be explained by variation in the independent variables?

Answer 1

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(2)

Interpretation:

The interpretation of the correlation coefficient is r=0.4529. The weak positive linear relationship between the variables Price (Y) and the Number of bedrooms (X).

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(3)

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(4)

The estimated value of the intercept is , when the independent variables are all equal to zero.

The number that represents the estimated value of the price (Y). The estimated value of the intercept is equal to the predicted value of the dependent variable price (Y).

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(5)

The interpretation of the slope coefficient of the variable size(X₁):

For a 1-unit increase in the independent variable size(X₁) , keeping constant other independent variables, the estimated mean price increases by an amount of 0.0129.

Or

The estimated value of the dependent variable price (Y) is based on the independent variable size (X₁) changes to 0.01295, while keeping constant the other indepedent variables Number of bed rooms(X₂), Number of bathrooms(X₃), distance to town center(X₄), garage dummy(X₅), and Pool dummy(X₆).