Question

In: Economics

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

Solutions

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



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