Question

The Alexander tool company hires a marketing consultant to estimate the demand function for its product. The consultant believes that price and buyers’ income are the main determinants of demand for the product. He has collected the needed data from the company’s retail distributers. The data consists sales quantity, price, and average household income in each state the product is sold. The data is provided in a file under the title “DATA”

Furthermore, the consultant assumes that the underlying demand relation is a linear function of price and income, [Q_D = a - bP + cM ]. You work as an assistant to the consultant and your task is to use your spreadsheet program to obtain least squares estimates of demand for the product and provide a complete analysis of the result. You can do so by completing the following activities.

a. Paste your regression output (computer printout) here.                                (2 pts)

                                                                                                                                                                                                                                                                                                           

b. Write your estimated demand function for the company’s product.                (2 pts)

c. Evaluate the regression results by filling in the blank spaces in each the following statement.                                                              (2 points each)

i. At the 5% level of significance, the parameter a __ (is, not) significant, the

parameter b __ (is, is not) significant, and the parameter c __ (is, is not)

significant.

ii. The p-value for b indicates that the exact level of significance is __ percent.

iii. At the 5% level of significance, the critical value of the F-statistic is ____. The model as a whole ___ (is, is not) significant at the 5% level.

iii. If P equals $2.85, while M equals $30,000, what is the fitted (or predicted) value of Q?

iv. The percentage of the total variation in Q that is NOT explained by the regression is _____.

Quantity	Price	Income
286	28.09	36.08
75	27.68	5.17
351	28.48	43.92
313	30.24	37.28
368	28.4	47.62
316	26.83	37.65
203	28.18	23.22
205	30.91	22.62
321	30.87	41.12
233	31.56	28.3
261	31.51	32.3
148	30.18	17.17
301	31.95	37.68
270	30.31	34.39
267	27.16	31.65
136	30.25	15.71
394	31.03	51.04
259	30.19	31.05
271	30.82	32.53
264	32.69	35.04
344	28.53	43.82
381	29	48.94
399	30.36	51.63
134	29.34	14.3
158	28.05	14.67
299	25.08	35
205	25.15	24.15
347	28.6	44.22
226	32.75	27.24
249	29.01	29.41
231	30.53	28.61
306	28.46	36.06
363	30.64	46.77
292	33.88	37.25
379	29.34	49.01
419	29.76	52.13
305	31.41	33.75
92	29.76	8.7
273	29.7	31.09
193	26.37	22.47
333	32.81	44.68
191	28.22	21
164	29.38	18.98
257	27.25	27.92
311	30.57	36.99
408	30.07	54.36
281	28.3	36.64
310	28.29	38.53
308	33.85	43.3
285	29.69	35.18

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.152660458
R Square	0.023305215
Adjusted R Square	0.002524475
Standard Error	82.70293429
Observations	49
				`
ANOVA
	df	SS	MS	F	Significance F
Regression	1	7670.681483	7670.681483	1.121481	0.295012023
Residual	47	321469.441	6839.77534
Total	48	329140.1224
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	82.53906614	180.6604604	0.456873994	0.649866	-280.9029013	445.9810336	-280.9029013	445.9810336
28.09	6.436390617	6.077799049	1.059000234	0.295012	-5.790563963	18.6633452	-5.790563963	18.6633452

Answer 1

a.

Regression Statistics
Multiple R	0.99
R Square	0.98
Adjusted R Square	0.98
Standard Error	10.63
Observations	50.00
ANOVA
	df	SS	MS	F	Significance F
Regression	2	323988.262	161994.131	1434.863	0.000
Residual	47	5306.238	112.899
Total	49	329294.500
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	111.0588	23.0397	4.8203	0.0000	64.7088	157.4088
Price	-2.4767	0.7931	-3.1228	0.0031	-4.0723	-0.8812
Income	7.0315	0.1328	52.9605	0.0000	6.7644	7.2986

b. Q = 111.05-2.48*P+7.031*M
c.
i. At the 5% level of significance, the parameter Intercept is significant, the parameter price is significant, and the parameter income is significant.
ii. The p-value for b indicates that the exact level of significance is 1 percent as p-value is less than 0.01
iii. At the 5% level of significance, the critical value of the F-statistic is 3.195. The model as a whole is, significant at the 5% level.
From the F-table distribution at (2,47) degrees fo freedom, we get 3.195 at 5 per cent significant. Since the calculated F value is greater than table value, it is significant
iii. If P equals $2.85, while M equals $30,000, what is the fitted (or predicted) value of Q?
=111.05-2.48*P+7.031*M
= 111.05-2.48*2.85+7.031*30
= 314.91
iv. it is 2%
=1-R^2
=1-0.98
=0.02 or 2 percent