Question

The data for the per capita demand for chicken ( pounds per household) in the United States from 1990 to 2013 is given in the table below.

Daily information

QUANITITY DEMANDED (Qd) PRICE OF CHICKEN FAMILY MEAL (Pc) INCOME (I) ADVERTISING EXPIDENTURE (Ad) PRICE OF 10gallon jug of (Pj) 1990 27.8 42.2 Xxxxxxxx 65.8 78.3 1991 29.9 38.1 413.3 66.9 79.2 1992 29.8 40.3 439.2 67.8 79.2 1993 30.8 39.5 459.7 69.6 79.2 1994 31.2 37.3 492.9 68.7 77.4 1995 33.3 38.1 528.6 73.6 80.2 1996 35.6 39.3 560.3 76.3 80.4 1997 36.4 37.8 624.6 77.2 83.9 1998 36.7 38.4 666.4 78.1 85.5 1999 38.4 40.1 717.8 84.7 93.7 2000 40.4 38.6 768.2 93.3 106.1 2001 40.3 39.8 843.3 89.7 104.8 2002 41.8 39.7 911.6 100.7 114 2003 40.4 52.1 931.1 113.5 124.1 2004 40.7 48.9 1021.5 115.3 127.6 2005 40.1 58.3 1165.9 136.7 142.9 2006 42.7 57.9 1349.6 139.2 143.6 2007 44.1 56.5 1449.4 132.0 139.2 2008 46.7 63.7 1575.5 132.1 165.5 2009 50.6 61.6        1759.1 154.4 203.3 2010 50.1 58.9 1994.2 174.9 219.6 2011 51.7 66.4 2258.1 180.8 221.6 2012 52.9 70.4 2478.7 189.4 232.6 2013 52.8             70.3 2478.6 189.3 232.5 AVG

475 = unique initial income number.

AVG = AVERAGE

The data suggests that the per capita demand for chicken (Qd) depends on the following factors:

Pc = Price of chicken ( $ per capita)

I = real disposable income per capita ($)

Ad = Advertising dollars per capita

Pj = price of juice – ( a related product) per capita ($)

Using regression analysis, the attached data and a linear functional form, estimate the demand for CHICKEN.

Include the computation and explanation of the following in your report:

1. Write your regression equation i.e. demand function
2. Enter data provided into excel or statplus as per instructions attached and run your regression / derive your coefficient estimates. Interpret all the coefficients in % ( .i.e if PC = - 0.06768, interpret as: - 6.77%
3. Use the average values for the independent variables and your estimated demand function, compute the demand for CHICKEN in a typical market.
4. Define and interpret the standard error of the estimate AND estimate the range within which actual demand for Chicken is expected to fall with a 95% confidence level.
5. Define the coefficient of determination (R-squared). What percentage of demand variation is explained by this model?
6. Define and explain the usefulness of the F-Statistics
7. Are the coefficient’s statistically significant? i.e. does each of the independent variables have a significant effect on the dependent variable? Explain using t-stats.
8. Calculate and interpret the point price, cross price, point advertising and point income elasticity of demand for CHICKEN.

Answer 1

• SUMMARY OUTPUT
  Regression Statistics
  Multiple R	0.962154
  R Square	0.925741
  Adjusted R Square	0.910107
  Standard Error	2.306493
  Observations	24
  ANOVA
  	df	SS	MS	F	Significance F
  Regression	4	1260.075	315.0188	59.21505	1.83E-10
  Residual	19	101.0783	5.319911
  Total	23	1361.153
  	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
  Intercept(a)	32.31279	4.221272	7.654753	3.21E-07	23.47757	41.14802	23.47757	41.14802
  Pc(b1)	-0.3008	0.13503	-2.22767	0.038185	-0.58343	-0.01818	-0.58343	-0.01818
  Income(b2)	0.008477	0.005011	1.691666	0.107046	-0.00201	0.018966	-0.00201	0.018966
  Ad (b3)	0.12766	0.08163	1.563888	0.134347	-0.04319	0.298514	-0.04319	0.298514
  Pj (b4)	-0.00674	0.064105	-0.10508	0.917417	-0.14091	0.127437	-0.14091	0.127437
  1) Qc = a +b1Pc+ b2Ad+b3I+ b4Pj
  2) Run the regression using Excel: Go to Data tab and select Data Analysis. From there a window pops up use Regression and select Y and X value.
  3) Qc = 32.31 - 0.30Pc +0.0085I +0.128Ad - 0.007Pj
  4) The coeff of Pc = -0.3 can be interpreted as representing the fall in Qc due to one dollar increase in Price of chicken. For one dollar increase in the price of chicken, the quantity demanded fall by 0.3 pounds.
  										The coeff of Income (I) is 0.0085. It represents increase in demand for chicken for one dollar incraese in income. If Income incraeses by one dollar then the demand for chicken increases by 0.0085 pounds.
  																				The coeff of Advertisement (Ad) is 0.128. This means that if Ad increases by one dollar, the demand for chicken Qd incraese bbby 0.128 pounds.
  The coeff of Pj = -0.0067 imply that if price of jug increases by 1 dollar then the quantity demanded of chicken falls by 0.0067 pounds.