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A soft-drink bottler collected the following monthly data on its sales (measured in thousand units) of 12-ounce cans at different prices.
Month
1
2
3
4
5
6
7
8
9
10
11
12
Price
$0.45
0.50
0.45
0.40
0.35
0.55
Quantity
98
80
95
123
163
168
82
68
96
77
130
125
(a) Using Excel run a linear regression with Quantity the dependent variable and price the independent variable. Provide detailed regression output. Explain if the intercept and the price coefficients are significant. Write the estimated demand equation. Determine by how much the sales volume will increase if price is cut by 10 cents.
(b) Use a log-linear (or log-log) regression to estimate a demand curve of the form Q=APα . Provide detailed regression output. Write the estimated demand equation.
Does this regression fit the data better than the linear regression in (a). Determine the price elasticity of demand.
(Hint: The log-linear (or log-log) regression requires you to run a regression of ln Q on ln p, instead of a regression of Q on P. You need to calculate the natural log (or ln) of Q and the natural log of P and run a regression with these natural log data where lnQ is the dependent variable and lnP is the independent variable.)
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