# Chicken Consumption in the United States

Topics: Regression analysis, Errors and residuals in statistics, Linear regression Pages: 20 (3618 words) Published: June 24, 2008
The Department of Agriculture is currently looking at the nation’s consumption of chicken. Data have been gathered dating back to 1970, in hopes of finding variables that are closely correlated with chicken consumption so that the consumption can be predicted. In the spreadsheet you will find 36 observations…one for each year since 1970. The variables are:

Year = Year
Y = per capita consumption of chicken (lbs.)
X1 = Real disposable income per capita (\$)
X2 = Real retail price of chicken per lb (cents)
X3 = Real retail price of pork per lb. (cents)
X4 = Real retail price of beef per lb. (cents)
X5 = Composite real price of chicken substitutes per lb., which is a weighted average of the real retail prices per lb of pork and beef, the weights being the relative consumption of beef and pork in total beef and pork consumption.

I.Create a model using the 5-step methodology I used in class. Examine and discuss the coefficients you obtained in your model, and the overall significance of your model. Begin with a summary of your findings and then step through your process. Cut and paste your results from Minitab in your report

Dependent variable:
Y = per capita consumption of chicken (lbs.)

Independent variables:
X1 = Real disposable income per capita (\$)
X2 = Real retail price of chicken per lb (cents)
X3 = Real retail price of pork per lb. (cents)
X4 = Real retail price of beef per lb. (cents)
X5 = Composite real price of chicken substitutes per lb.

Step 1)
Check for the overall utility of the model

The regression analysis output is given below.

Regression Analysis: lbs. per Cap versus Real Disposa, Real Retail, ...

The regression equation is
lbs. per Capita Consumed = 39.5 + 0.00204 Real Disposable Income per Capi - 0.129 Real Retail Price of Chicken + 0.446 Real Retail Price of Pork + 0.564 Real Retail Price of Beef - 1.01 Comp real price of Chicken Subs

Predictor Coef SE Coef T P VIF Constant 39.463 1.987 19.86 0.000 Real Disposable Income per Capi 0.0020441 0.0001520 13.44 0.000 30.4 Real Retail Price of Chicken -0.12907 0.06014 -2.15 0.040 29.0 Real Retail Price of Pork 0.4456 0.1675 2.66 0.012 1920.4 Real Retail Price of Beef 0.5635 0.2022 2.79 0.009 5006.3 Comp real price of Chicken Subs -1.0093 0.3584 -2.82 0.009 11822.0

S = 1.33823 R-Sq = 99.3% R-Sq(adj) = 99.2%

Analysis of Variance

Source DF SS MS F P
Regression 5 7791.5 1558.3 870.14 0.000
Residual Error 30 53.7 1.8
Total 35 7845.2

Source DF Seq SS
Real Disposable Income per Capi 1 7738.7
Real Retail Price of Chicken 1 34.5
Real Retail Price of Pork 1 3.3
Real Retail Price of Beef 1 0.9
Comp real price of Chicken Subs 1 14.2

Unusual Observations

Real
Disposable lbs. per
Income per Capita
Obs Capi Consumed Fit SE Fit Residual St Resid 10 7967 47.700 44.400 0.438 3.300 2.61R 30 23968 76.400 74.971 1.005 1.429 1.62 X

R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence.

Summary of findings:

i. Regression equation
The regression equation is
lbs. per Capita Consumed = 39.5 + 0.00204 Real Disposable Income per Capi - 0.129 Real Retail Price of Chicken + 0.446 Real Retail Price of Pork + 0.564 Real Retail Price of Beef - 1.01 Comp real price of Chicken Subs

Multiple regression equation is given as below:
Per capita...