Please see attached
MEAT MINICASE
An analyst wanted to study the total consumption of processed meats in the U.S. for a period of 12 years. He was able to obtain data on:
| Total consumption of processed meat | = | TOTCON |
| Consumption expenditure on food Ratio of consumer price indexes of | = | FDEXP |
| processed meat to all meats | = | RELIND |
The data are stored in the file MEAT.MTW, and are tabulated on the following page. TOTCON is in billions of pounds. FDEXP is in billions of constant dollars.
The rationale behind the choice of variables should be apparent. You would expect the consumption of processed meat to be affected by the total expenditure on food. You would also expect that consumption will be affected by the price of processed meat relative to the price of all meats. The variable RELIND (relative index) is a measure of the relative prices of processed meat to all meats.
Before doing any analysis, and to make sure that you have understood the background of the problem,write down the algebraic signs of the regression coefficients that you expect to find when you fit the model
TOTCON = β0 + β1(FDEXP) + β2(RELIND) + ε
to the data. In other words, from what you know about economics, what do you expect the signs of β0, β1 and β2 to be? Plus or minus?
DATA
| ROW | TOTCON | FDEXP | RELIND |
| 1 | 12.572 | 100.074 | 0.959 |
| 2 | 11.497 | 104.470 | 1.015 |
| 3 | 11.541 | 107.580 | 1.062 |
| 4 | 12.813 | 109.608 | 1.000 |
| 5 | 13.359 | 114.213 | 0.979 |
| 6 | 13.256 | 115.926 | 0.979 |
| 7 | 13.741 | 118.831 | 0.986 |
| 8 | 15.261 | 118.916 | 0.900 |
| 9 | 13.616 | 112.079 | 0.941 |
| 10 | 12.219 | 120.293 | 1.004 |
| 11 | 14.324 | 118.912 | 0.981 |
| 12 | 11.902 | 121.151 | 1.079 |
MINITAB REGRESSION RESULTS
- Regression Analysis of TOTCON ON FDEXP
Predictor Coef SE Coef T P
Constant 3.080 4.614 0.67 0.519
FDEXP 0.08756 0.04028 2.17 0.055
Analysis of Variance
Source DF SS MS F P
Regression 1 4.4112 4.4112 4.73 0.055
Residual Error 10 9.3353 0.9335
Total 11 13.7464
- Regression Analysis of TOTCON on RELIND
Predictor Coef SE Coef T P
Constant 31.564 4.258 7.41 0.000
RELIND -18.651 4.295 -4.34 0.001
Analysis of Variance
Source DF SS MS F P
Regression 1 8.9834 8.9834 18.86 0.001
Residual Error 10 4.7631 0.4763
Total 11 13.7464
- Regression Analysis of TOTCON on FDEXP and RELIND
Predictor Coef SE Coef T P
Constant 21.890 3.762 5.82 0.000
FDEXP 0.07214 0.01893 3.81 0.004
RELIND -17.211 2.826 -6.09 0.000
Analysis of Variance
Source DF SS MS F P
Regression 2 11.9239 5.9619 29.44 0.000
Residual Error 9 1.8226 0.2025
Total 11 13.7464
Write down the fitted regression connecting TOTCON and FDEXP. What percentage of variation in total consumption of processed meat can be explained by expenditure on food along? What is the standard error of estimate?
Write down the fitted regression connecting total consumption of processed meat and the relative price index (RELIND) of the processed meat to the price of all meats. What percentage of the variation is explained by the relative index? What is the standard error of estimate?
Write down the fitted regression connecting total consumption, food expenditure and the relative index. What percentage of the variation in total consumption can be explained by these two variables? What is the standard error of estimate?
Of the three fitted models, which would you use for forecasting the total consumption of processed meat? Justify your answer.
