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Demand function - regression

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Q1) The sales manager for Tide Corporation believes that the sales of the company's famous Sunshine laundry detergent (S) are related to the company's advertising expenditure (A), as well as the combined advertising expenditure of its four biggest competitor detergents (C). The sales manager collected 48 weekly observations on S, A, and C to estimate the following regression: S = a + bA + cC; where S, A, and C are measured in thousands of dollars per week. Tide's sales manager is confident using the parameters that are statistically significant at 10 percent or better level.
(a) What sign does the sales manager expect a, b, and c to have?
(b) Write the regression equation using the estimated coefficients, R2, F-stat, and t-statistics for all coefficients. Interpret the meaning of each coefficient from reported in the table?
(c) Does Tide's advertising expenditure have a statistically significant effect on the sales of Sunshine detergent? Explain using appropriate t-statics from the t-table form your textbook at 10 percent level of significance (remember you need to look for appropriate degree of freedom).
(d) Does advertising by its four largest competitors affect sales of Sunshine detergent in a statistically significant way? Explain using appropriate t-statistics from the table.
(e) What fraction of the total variation in sales of Sunshine remains unexplained? What can the sales manager do to increase the explanatory power of the sales equation? What other explanatory variables might be added to the equation?
(f) What is the expected level of sales each week when Tide spends $40,000 per week and the competitors advertising expenditure for the four companies are $100,000 per week. The results of the estimation are:
Q2) The demand for chicken wings is estimated by Slim Chicken in Kansas as: Q = a + b (Price) + c (Income) + e, The Least squares regression reveals that â = 8.27,

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The expert solves three problems on demand function using regression equation and its interpretation.

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Q1) The sales manager for Tide Corporation believes that the sales of the company's famous Sunshine laundry detergent (S) are related to the company's advertising expenditure (A), as well as the combined advertising expenditure of its four biggest competitor detergents (C). The sales manager collected 48 weekly observations on S, A, and C to estimate the following regression: S = a + bA + cC; where S, A, and C are measured in thousands of dollars per week. Tide's sales manager is confident using the parameters that are statistically significant at 10 percent or better level.
(a) What sign does the sales manager expect a, b, and c to have?
'a' Positive: We expect some positive sales even without any advertising due to other factors i.e. word of mouth, pricing, etc.
'b' Positive: Company's advertising expense will create more awareness about the detergent and generate more demand for the Sunshine deterget.
'c' Negative: Advertising by competitors will take away some of the demand for ...

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