Question

The Demand for soft drink (in cans per capita per year) is estimated as Log Q = a + b log P+ c log I + d log T where Q = Soft drink consumption in cans per capita per year P = 6-pack price I = Income Per capita T = Mean temperature across the 48 contiguous states in the United States

Soft Drink Demand Data:

1. Soft Drink Demand Data: cans/capita/yr 6 pack price income/capita    mean temp Q P I T Alabama 200 2.19 13 66 Arizona 150 1.99 17 62 Arkansas 237 1.93 11 63 California 135 2.59 25 56 Colorado 121 2.29 19 52 Connecticut 118 2.49 27 50 Delaware 217 1.99 28 52 Florida 242 2.29 18 72 Georgia 295 1.89 14 64 Idaho 85 2.39 16 46 Illinois 114 2.35 24 52 Indiana 184 2.19 20 52 Iowa 104 2.21 16 50 Kansas 143 2.17 17 56 Kentucky 230 2.05 13 56 Louisiana 269 1.97 15 69 Maine 111 2.19 16 41 Maryland 217 2.11 21 54 Massachusetts 114 2.29 22 47 Michigan 108 2.25 21 47 Minnesota 108 2.31 18 41 Mississippi 248 1.98 10 65 Missouri 203 1.94 19 57 Montana 77 2.31 19 44 Nebraska 97 2.28 16 49 Nevada 166 2.19 24 48 New Hampshire 177 2.27 18 35 New Jersey 143 2.31 24 54 New Mexico 157 2.17 15 56 New York 111 2.43 25 48 North Carolina 330 1.89 13 59 North Dakota 63 2.33 14 39 Ohio 165 2.21 22 51 Oklahoma 184 2.19 16 82 Oregon 68 2.25 19 51 Pennsylvania 121 2.31 20 50 Rhode Island 138 2.23 20 50 South Carolina 237 1.93 12 65 South Dakota 95 2.34 13 45 Tennessee 236 2.19 13 60 Texas 222 2.08 17 69 Utah 100 2.37 16 50 Vermont 64 2.36 16 44 Virginia 270 2.04 16 58 Washington 77 2.19 20 49 West Virginia 144 2.11 15 55 Wisconsin 97 2.38 19 46 Wyoming 102 2.31 19 46

Data in Excel is here: Data- Soft Drink Demand Estimation.xlsx (Provide answers including brief process of calculation and / or reasoning ) Please answer #1 and #2 and #3

1) What is regression equation using multiple linear regression model? How would you interpret the coefficients of each independent variable in the model?

2) What is price elasticity of demand ? How would you interpret it?

3) The approximate percentage increase or decrease in demand if 6-pack price percentage increases by 10%.

Answer 1

Convert all values to log form as shown above and run regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8194
R Square	0.6714
Adjusted R Square	0.6490
Standard Error	0.1113
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1.11400	0.37133	29.96848	0.00000
Residual	44	0.54519	0.01239
Total	47	1.65919
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.0502	0.6129	1.7133	0.0937	-0.1851	2.2855
Log P	-3.1956	0.6491	-4.9229	0.0000	-4.5038	-1.8873
Log I	0.2206	0.1844	1.1963	0.2380	-0.1510	0.5921
Log T	1.1190	0.2641	4.2368	0.0001	0.5867	1.6513

1. The regression equation, log(Q) = a + b log P+ c log I + d log T
Log(Q)= 1.0501-3.1955*logP+0.22*logI+1.1189logT
2. Interpretation of coefficients :
Log Q =-3.1955*Log P
% change in Q = % change in price*-3.1955, for a 1 percent change in price, the Q decreases by 3.2 percent holding others constant
Log Q =0.22*Log I
% change in Q = % change in I*0.22, for a 1 percent change in I, the Q increases by 0.22 percent holding others constant
Log Q =1.1189*Log T
% change in Q = % change in T*1.1189, for a 1 percent change in T, the Q increases by 1.12 percent holding others constant
3. % log Q =-3.1955*10% = -0.32*100 = -32 percent, so for an 10 percent increase in price, the quantity demanded decreases by 32 percent