The marketing manager at the Dean Dome is interested in estimating the demand fu
ID: 3315961 • Letter: T
Question
The marketing manager at the Dean Dome is interested in estimating the demand function for concert T-shirts. He obtains data regarding the sales (in hundreds) of t-shirts at various prices (in dollars) over the last twelve months and runs a regression with Sales as the dependent variable and Price as the independent variable.
(a) Express sales as a linear function of price and test the significance of your model at = 0.05.
(b) Construct a 99% confidence interval for the change in expected sales, i.e., 1, when the price is increased by $1.
(c) A T-shirt seller claims that a $1 increase in price will only reduce expected sales by 1 unit (i.e. one hundred t-shirts). In order to weigh in on this claim construct a 95% confidence interval for the slope coefficient of Price. Does the confidence interval provide support for the T-shirt seller’s claim?
R R 0.783 0.614 Square Adj.RSqr StErr of Est df F p-value 6.268 0.575 10 15.8890.003 Variable Coeff. Std.Err. t-value p-value Constant 82.083 10.074 8.148 0.000 Price -2.633 0.661 3.986 0.003Explanation / Answer
the regression equation is formed using the coefficients as
Sales = 82.083 -2.633*Price
as the p value of the model is 0.03 , which is less than 0.05 hence we conclude that the model is statistically signficant
b)
we know that CI is given as
coeff +-z*SE
also 99% CI has a z value of 2.58
-2.633 +- 2.58*0.661 , the 99% CI for the change in sales is
-4.33 , -0.927
c)
we know that CI is given as
coeff +-z*SE
also 95% CI has a z value of 1.96
-2.633 +- 1.96*0.661, the CI is
-3.92 , -1.33
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