An executive manager of consumer product company is interested in modeling the q

Question

An executive manager of consumer product company is interested in modeling the quarterly product sales (y, in thousands of units) as a function of the product price (Price, in collars), a time trend (Time), and seasons of the year. The time trend may be used to capture possible trending effects from some omitted variables (e.g., population growth and changes in other social and demographic variables). The analysis further allows for the abnormal impact of the 9-11 event on sales during Fall 2001. The quarterly data are shown below. The following demand equation is to be fitted to the data: y = beta_0 + beta_1 price + beta_2 Time + beta_2 Terror + beta_4 D_sp + beta_2 D_ + beta_6 D_FA + where Time = {1, 2, 3, ...) is a time index; Terror = 1 if Fall 2001 and 0 otherwise; D_SP = 1 if Spring and 0 otherwise D_sv = Summer and 0 otherwise; D_ = 1 if Fall and 0 otherwise; and epsilon captures the unexplained random error. D_SP, D_SU, and D_FA are often referred to as seasonal dummies, while Terror represents an event dummy. a. Report the regression results (including coefficient estimates, standard errors, and R^2) b. Test for the significance of the price effect and the time trend effect on sales. c. Interpret the estimated values of beta_1 and beta_2 in the context of the problem here. d. Use a 95% confidence interval to estimate the difference in average sales between summer and winter quarters. What does the interval estimate tell us about the difference in sales? e. Test H_0: beta_6 = 0 against H_ a: beta_6 > 0. What does the test result suggest? f. Use a 95% confidence interval to estimate the impact of the 9-11 event on unit sales in Fall 2001. What does the interval estimate tell us about the size of the impact? g. Test for the overall usefulness of the above regression model. h. Based on the estimated model, forecast the level of product demand (in 1,000s of units) over the next four quarters if the company decides to set and maintain the price at $14.00 per unit in 2003.

Explanation / Answer

Data input is

All question answer is coming in this table

If the product price increases by 1 dollars, we predict the product sales will decerase by approximately 8.648 and othervariable is ignoring

If the time increases by 1, we predict the product sales will incerase by approximately 2.0138

Sales Price Time Terror Dsp Dsu DFA 76.32 13.5 1 0 0 0 0 69.08 13.5 2 0 1 0 0 92.46 13 3 0 0 1 0 98.55 13.5 4 0 0 0 1 83.42 14 5 0 0 0 0 80.61 14 6 0 1 0 0 95.71 14 7 0 0 1 0 94.55 14 8 0 0 0 1 76 13.5 9 0 0 0 0 99.87 13.5 10 0 1 0 0 108.74 14 11 0 0 1 0 107.6 14 12 1 0 0 1 105.76 14 13 0 0 0 0 93.46 14.5 14 0 1 0 0 113.75 15 15 0 0 1 0 94.65 15 16 0 0 0 1 100.96 14 17 0 0 0 0 108.37 14 18 0 1 0 0 111.45 14.5 19 0 0 1 0 95.04 14 20 1 0 0 1 116.18 13.5 21 0 0 0 0 112.47 13.5 22 0 1 0 0 145.88 13 23 0 0 1 0 138.98 13 24 0 0 0 1

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