With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on...

With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on from the famous "Got Milk" ad slogan in favor of a new one, "Milk Life." The new tagline emphasizes milk's nutritional benefits, including its protein content. MPEP began collecting data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars) for the period following the launch of the new campaign. These data, in forms to estimate both a linear model and log-linear model, are available via the link below. Use these data to perform two regressions: a linear regression and a log-linear regression.

Excel Data File

Which model does a better job fitting the data?

The --------------- model.

Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use the best-fitting regression model to estimate the weekly quantity of milk consumed after this advertising increase.

Instructions: Round your intermediate calculations and enter your response rounded to three decimal places.

million gallons per week

Linear Model		Log-Linear Model
Q	P	A	lnQ	lnP	lnA
4.76	2.46	472.68	1.56	0.90	6.16
0.90	4.28	326.41	-0.10	1.45	5.79
1.74	3.72	357.36	0.55	1.31	5.88
0.96	4.20	475.82	-0.04	1.43	6.17
2.38	4.14	494.25	0.87	1.42	6.20
1.28	4.59	458.62	0.25	1.52	6.13
2.86	3.30	421.67	1.05	1.19	6.04
1.87	4.34	534.85	0.63	1.47	6.28
2.19	3.31	524.75	0.78	1.20	6.26
1.38	3.35	370.35	0.32	1.21	5.91
0.21	4.53	420.16	-1.54	1.51	6.04
3.55	2.63	333.79	1.27	0.97	5.81
2.44	4.40	437.32	0.89	1.48	6.08
1.94	4.36	442.70	0.66	1.47	6.09
2.50	3.24	375.67	0.91	1.18	5.93
2.92	3.45	546.36	1.07	1.24	6.30
4.94	2.97	391.17	1.60	1.09	5.97
2.14	3.22	498.00	0.76	1.17	6.21
3.89	3.34	530.17	1.36	1.20	6.27
6.91	2.24	527.36	1.93	0.81	6.27
3.41	4.04	440.93	1.23	1.40	6.09
1.16	4.10	480.35	0.15	1.41	6.17
1.60	3.99	404.91	0.47	1.38	6.00
4.09	3.22	512.00	1.41	1.17	6.24
2.69	2.98	346.29	0.99	1.09	5.85
2.41	4.30	383.47	0.88	1.46	5.95
2.25	2.84	434.26	0.81	1.04	6.07
2.48	3.96	548.37	0.91	1.38	6.31
3.79	2.49	357.71	1.33	0.91	5.88
3.33	3.29	445.73	1.20	1.19	6.10
2.61	4.02	524.55	0.96	1.39	6.26
2.40	4.05	487.87	0.88	1.40	6.19
3.92	2.46	343.13	1.37	0.90	5.84
3.42	3.45	353.81	1.23	1.24	5.87
0.80	3.40	334.47	-0.23	1.22	5.81
5.79	2.95	330.57	1.76	1.08	5.80
3.58	2.69	363.91	1.28	0.99	5.90
1.58	3.79	383.71	0.46	1.33	5.95
1.14	3.37	430.37	0.13	1.21	6.06
1.04	4.64	501.84	0.04	1.54	6.22
4.88	2.66	447.12	1.59	0.98	6.10
4.31	2.25	404.38	1.46	0.81	6.00
2.23	3.94	449.29	0.80	1.37	6.11
1.38	4.42	327.99	0.32	1.49	5.79
1.62	3.13	332.39	0.49	1.14	5.81
1.38	4.45	450.16	0.33	1.49	6.11
6.20	2.38	467.40	1.82	0.87	6.15
4.17	3.69	528.60	1.43	1.31	6.27
4.08	4.02	533.73	1.41	1.39	6.28
0.08	4.30	355.81	-2.55	1.46	5.87
3.82	2.80	462.42	1.34	1.03	6.14
1.17	4.51	549.78	0.16	1.51	6.31
3.26	2.42	366.63	1.18	0.88	5.90
2.44	4.37	429.74	0.89	1.47	6.06
4.16	2.53	399.57	1.42	0.93	5.99
2.63	3.63	521.95	0.97	1.29	6.26
4.94	2.80	356.59	1.60	1.03	5.88
1.84	4.36	416.24	0.61	1.47	6.03
4.71	3.12	435.99	1.55	1.14	6.08
6.46	2.40	464.62	1.87	0.87	6.14
2.79	3.51	353.37	1.03	1.25	5.87
4.09	3.07	425.12	1.41	1.12	6.05
4.76	2.32	481.72	1.56	0.84	6.18
3.05	3.45	376.30	1.12	1.24	5.93
0.87	4.44	536.86	-0.13	1.49	6.29
3.12	2.50	493.52	1.14	0.92	6.20
1.34	3.11	454.69	0.29	1.13	6.12
1.93	3.24	487.07	0.66	1.17	6.19
1.64	2.87	461.69	0.50	1.05	6.13
4.39	2.97	410.84	1.48	1.09	6.02
5.76	2.33	480.66	1.75	0.84	6.18
4.40	2.82	381.62	1.48	1.04	5.94
6.22	3.14	456.97	1.83	1.14	6.12
1.10	3.89	461.39	0.09	1.36	6.13
4.12	2.67	430.43	1.42	0.98	6.06
5.40	2.73	438.53	1.69	1.01	6.08
2.75	4.52	336.00	1.01	1.51	5.82
5.12	2.28	519.90	1.63	0.83	6.25
3.94	3.25	536.25	1.37	1.18	6.28
5.69	2.18	439.75	1.74	0.78	6.09
0.44	4.27	352.57	-0.82	1.45	5.87
1.89	3.62	397.69	0.64	1.29	5.99
4.02	3.32	345.17	1.39	1.20	5.84
3.70	3.43	507.56	1.31	1.23	6.23
3.26	2.43	330.67	1.18	0.89	5.80
2.98	2.97	433.20	1.09	1.09	6.07
2.09	4.32	462.14	0.74	1.46	6.14
5.68	2.25	515.33	1.74	0.81	6.24
4.33	2.65	508.14	1.47	0.98	6.23
4.97	3.63	510.41	1.60	1.29	6.24
2.89	3.60	343.16	1.06	1.28	5.84
2.25	3.37	365.82	0.81	1.22	5.90
0.17	3.77	425.56	-1.79	1.33	6.05
3.96	2.87	347.36	1.38	1.06	5.85
4.08	2.97	326.06	1.40	1.09	5.79
3.49	3.94	527.12	1.25	1.37	6.27
4.21	4.10	475.28	1.44	1.41	6.16
2.25	4.09	475.69	0.81	1.41	6.16
2.40	3.93	536.42	0.88	1.37	6.28
1.61	4.10	325.89	0.48	1.41	5.79

Expert Solution

SUMMARY OUTPUT for linear model

Regression Statistics
Multiple R	0.740
R Square	0.547
Adjusted R Square	0.538
Standard Error	1.063
Observations	100

ANOVA
	df	SS	MS	F	Significance F
Regression	2	132.51	66.26	58.61	0.00
Residual	97	109.66	1.13
Total	99	242.17

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.520	0.823	7.921	0.000	4.886	8.153	4.886	8.153
P	-1.614	0.151	-10.658	0.000	-1.915	-1.314	-1.915	-1.314
A	0.005	0.002	2.962	0.004	0.002	0.008	0.002	0.008

SUMMARY OUTPUT for log-linear model

Regression Statistics
Multiple R	0.634
R Square	0.401
Adjusted R Square	0.389
Standard Error	0.587
Observations	100

ANOVA
	df	SS	MS	F	Significance F
Regression	2	22.403	11.201	32.522	0.000
Residual	97	33.409	0.344
Total	99	55.812

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1.989	2.243	-0.886	0.378	-6.441	2.464	-6.441	2.464
lnP	-2.170	0.276	-7.858	0.000	-2.717	-1.622	-2.717	-1.622
lnA	0.911	0.370	2.459	0.016	0.176	1.646	0.176	1.646

	linear model	log-linear model
regression equation
	0.547	0.401
	0.538	0.389
F-statistic	58.61	32.522

For the linear regression model, the estimates indicate that R² = .547, or that 54.7 percent of the variability in the quantity demanded is explained by price and advertising. In contrast, the R² for the log-linear model is 0.401, indicating that only 40.1 percent of the variability in the natural log of quantity is explained by variation in the natural log of price and the natural log of advertising. Therefore, the linear regression model appears to do a better job explaining variation in the dependent variable.

This conclusion is further supported by comparing the adjusted R²s and the F-statistics in the two models, which are higher for the linear model compared to log-linear model

If weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150

Rahul Sunny answered 2 years ago

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