For my regression I observed food consumption rates in dollars, plotted against income level as the explanatory variable. I used a measurement of income before taxes separated into 9 different brackets: <$15,000, <$30,000, <$40,000, <$50,000, <$70,000, <$100,000, <$150,000, <$200,000, and <$250,000. I ran a cross sectional regression to observe changes in food consumption due to increases in annual income. For a second regression, I included alcohol consumption in dollars to observe its effect on food consumption under the same income brackets.

 

In my first test, I found that each additional dollar of income will lead to a $0.04 dollar increase in food consumption. For my second model, I found that each additional dollar spent on alcohol consumption causes a $1.95 decrease in spending on food, holding the other variable (income) constant. My R squared statistics of .993 and .995 (respectively) suggests this regression, and its independent variables, hold a high strength of explanation for the dependent variable (food consumption). These findings align with our common assumptions about food, that it is a highly normal good.

 

Output information is presented below.

 

The SAS System

 

The REG Procedure
Model: MODEL1
Dependent Variable: Food
Number of Observations Read 9
Number of Observations Used 9

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 1 133051467 133051467 1059.56 <.0001
Error 7 879010 125573
Corrected Total 8 133930477

Root MSE 354.36261 R-Square 0.9934
Dependent Mean 8111.88889 Adj R-Sq 0.9925
Coeff Var 4.36844

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1 3126.16650 193.42381 16.16 <.0001
Inc 1 0.04958 0.00152 32.55 <.0001
The SAS System
The REG Procedure
Model: model1
Dependent Variable: Food
Number of Observations Read 9
Number of Observations Used 9

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 2 133279356 66639678 614.08 <.0001
Error 6 651121 108520
Corrected Total 8 133930477

Root MSE 329.42404 R-Square 0.9951
Dependent Mean 8111.88889 Adj R-Sq 0.9935
Coeff Var 4.06100

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1 3154.80047 180.89387 17.44 <.0001
Inc 1 0.06212 0.00877 7.08 0.0004
Alc 1 -1.95538 1.34935 -1.45 0.1975
SAS Assignment observing food consumption patterns in an Engel Curve