Question

1. Estimate the demand for soft drinks using the data provided below. 2. Interpret the coefficients and calculate the price elasticity of soft drink demand at the mean. 3. Omit price from the regression equation. Describe the signs of the estimated coefficients and the statistical significance of the coefficients. 4. Now omit both price and temperature from the regression equation. Should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Why or why not? Justify your answer.

Sate	Cans/Capita/year	6-Pack Price	Income/Capita	Mean Temp
Alabama	200	2.19	11.7	66
Arizona	150	1.99	15.3	62
Arkansas	237	1.93	9.9	63
California	135	2.59	22.5	56
Colorado	121	2.29	17.1	52
Connecticut	118	2.49	24.3	50
Delaware	217	1.99	25.2	52
Florida	242	2.29	16.2	72
Georgia	295	1.89	12.6	64
Idaho	85	2.39	14.4	46
Illinois	114	2.35	21.6	52
Indiana	184	2.19	18	52
Iowa	104	2.21	14.4	50
Kansas	143	2.17	15.3	56
Kentucky	230	2.05	11.7	56
Louisiana	269	1.97	13.5	69
Maine	111	2.19	14.4	41
Maryland	217	2.11	18.9	54
Massachusetts	114	2.29	19.8	47
Michigan	108	2.25	18.9	47
Minnesota	108	2.31	16.2	41
Mississippi	248	1.98	9	65
Missouri	203	1.94	17.1	57
Montana	77	2.31	17.1	44
Nebraska	97	2.28	14.4	49
Nevada	166	2.19	21.6	48
New Hampshire	177	2.27	16.2	35
New Jersey	143	2.31	21.6	54
New Mexico	157	2.17	13.5	56
New York	111	2.43	22.5	48
North Carolina	330	1.89	11.7	59
North Dakota	63	2.33	12.6	39
Ohio	165	2.21	19.8	51
Oklahoma	184	2.19	14.4	82
Oregon	68	2.25	17.1	51
Pennsylvania	121	2.31	18	50
Rhonde Island	138	2.23	18	50
South Carolina	237	1.93	10.8	65
South Dakota	95	2.34	11.7	45
Tennessee	236	2.19	11.7	60
Texas	222	2.08	15.3	69
Utah	100	2.37	14.4	50
Vermont	64	2.36	14.4	44
Virginia	270	2.04	14.4	58
Washington	77	2.19	18	49
West Virginia	144	2.11	13.5	55
Wisconsin	97	2.38	17.1	46
Wyoming	102	2.31	17.1	46

Answer 1

1).

So, consider the given problem here the given regression model is given by.

=> Q = b0 + b1*P + b2*M + b3*T, where “Q=demand for cans”, “P=Price of cans”, “M=income” and “T=mean temperature”. So, the following table shows the regression result on the basis of the given data.

So, here the estimated equation is given by.

=> Q = 514.27 + (-242.97)*P + 1.36*M + 2.93*T.

2).

So, here the coefficient of “P” is “(-242.97)”, => as “P” increases by “$1”, => the demand will decreases by “242.97 = 243 units”. Now, the coefficient of “M” is “1.36”, => if “M” increases by “$1”, => the demand will increases by “1.36 units” and the coefficient of “mean temperature” is “2.93”, => if “T” increases by “1unit”, => the demand will increases by “2.93 units, =>3 units”.

Now, “dQ/dP = (-242.97)”, => the elasticity is given by, => e = (dQ/dP)*(P/Q) = (-242.97)*(P/Q), be the elasticity of demand.

3).

Now, let’s assume the “P” is omitted, => the new model is given by.

=> Q = b0 + b2*M + b3*T.

Now, if we regress the new model then the estimated model is given by.

=> Q = (-56.61) + (-2.28)*M + 4.7*T. So, here the intercept term is negative economically which don’t make sense, as we know that demand can’t be negative. Now, the coefficient of “M” is “(-2.28)” which is negative, => as “M” increases by “$1”, => “Q” decreases by “2.28 units”. Now the “’p” value of “M” is “0.2638”, => the variable is insignificant either at “5% level of significance” or “1% level of significance”.

Now, the coefficient of “T” is “4.7” which is positive, => as “T” increases by “1 unit”, => “Q” also increases by “4.7 units”. Now the “’p” value of “T” is “0.000001 < 1%”, => the variable is significant either at “1% level of significance”.

4).

Now, omit both “P” and “T”,= > the new model is given by “Q = b0 + b1*M”. Consider the following table.

So, here the estimated regression equation is given by, => Q = 254.56 + (-5.97)*M”. So, here also the sig of “M” is negative which is “(-5.97)”, => as “M” increases by “$1” the demand decrease by “5.97 = 6 units”. Now, the “p-value” of “M” is “0.02016 < 5%”, => the “M” is significant at the “5%” level of significance”. Now, even if “M” is significant here the estimated values are unbiased because we have omitted “P” and “T” these are the most important variables here, => if we omit these variables, => the problem of omitted variable will be created, => the estimated value of “M’ is biased. So, the marketing plan should not design their plan in that way.