2.) Suppose you are hired by a restaurant company to consult on a location for a...

 

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2.) Suppose you are hired by a restaurant company to consult on a location for a new restaurant. Specifically, they want you to estimate the sales they will make at a particular location. To do this, you estimate the following equation: Y₁ = Bo + B₁N₁ + B₂P₁ + B3l₁ + B₁T₁ + U₁ Where: Y = Sales: The amount of sales in dollars per year that a restaurant location makes. N = Competition: The number of direct market competitors within a two-mile radius of the restaurant location. P = Population: The number of people living within a three-mile radius of the restaurant location. 1 = Income: T = Traffic: The average household income of the local population measured in variable P. A variable that is defined as 1 if more than 15,000 cars pass per day pass the restaurant, and 0 otherwise. You run the OLS regression and get the following results: 102,192-9075N + 0.3547P + 1.2881, + 10,9947, (2053) (0.187) 1.90 (0.543) (5577) 2.37 1.97 R² = 0.579 t = 4.42 N = 300 Use the t-table at the end of the exam to obtain critical 1-values, te, if applicable. If you use a formula to calculate an answer, write down the formula and show your work. (a) Write out the null and alternative hypothesis to test if ß₂ = 0. (4pts) (b) What is the critical value used to test if B₂ = 0 if the significance level is 10%? (4pts) (c) Compare t₂ to t, and write your conclusion to the test if ß₂ = 0: do you reject or fail to reject the null hypothesis? (4pts) (d) Explain in your own words what the coefficient on N, means and if it has the sign that you would expect and why. (4pts) (e) Suppose you wanted to minimize the probability of a Type I error. Instead of a significance level of 10%, should you choose significance level of 20%, or 5%? (4pts) (f) Using your chosen significance level in part (e), test the hypothesis that B₂ = 0. First state your null and alternative hypotheses, and then give your conclusion of the test. (4pts) 2.) Suppose you are hired by a restaurant company to consult on a location for a new restaurant. Specifically, they want you to estimate the sales they will make at a particular location. To do this, you estimate the following equation: Y₁ = Bo + B₁N₁ + B₂P₁ + B3l₁ + B₁T₁ + U₁ Where: Y = Sales: The amount of sales in dollars per year that a restaurant location makes. N = Competition: The number of direct market competitors within a two-mile radius of the restaurant location. P = Population: The number of people living within a three-mile radius of the restaurant location. 1 = Income: T = Traffic: The average household income of the local population measured in variable P. A variable that is defined as 1 if more than 15,000 cars pass per day pass the restaurant, and 0 otherwise. You run the OLS regression and get the following results: 102,192-9075N + 0.3547P + 1.2881, + 10,9947, (2053) (0.187) 1.90 (0.543) (5577) 2.37 1.97 R² = 0.579 t = 4.42 N = 300 Use the t-table at the end of the exam to obtain critical 1-values, te, if applicable. If you use a formula to calculate an answer, write down the formula and show your work. (a) Write out the null and alternative hypothesis to test if ß₂ = 0. (4pts) (b) What is the critical value used to test if B₂ = 0 if the significance level is 10%? (4pts) (c) Compare t₂ to t, and write your conclusion to the test if ß₂ = 0: do you reject or fail to reject the null hypothesis? (4pts) (d) Explain in your own words what the coefficient on N, means and if it has the sign that you would expect and why. (4pts) (e) Suppose you wanted to minimize the probability of a Type I error. Instead of a significance level of 10%, should you choose significance level of 20%, or 5%? (4pts) (f) Using your chosen significance level in part (e), test the hypothesis that B₂ = 0. First state your null and alternative hypotheses, and then give your conclusion of the test. (4pts)

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a beta2 0 Null hypothesis Coefficient for Pi equals zero Alternative hy... View the full answer