Suppose you are a manager for a carnival game at the local fair. You want to estimate how many prizes you will need to have in stock to give out, based on the number of tickets purchased before the fair begins. You examine the past 24 fair openings to make your regression model, and find the following information. Σ(x − x)² = 791.5 Σ e = 223.1 and ŷ = 294. 21 +0. 186x, where is the number of tickets purchased before the fair begins, and ŷ is the predicted demand for prizes during the first day of the fair. What is the standard error of the slope of the regression line? 3.184 0.024 8.1 1.654 0.054
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- Suppose that you had data on the amount of pollution in London every year. Write down the regression equation that you would need to estimate to measure the effect of ULEZ on pollution. Describe carefully what the dependent variable, the independent variable, the unit of observation (time or location), and the main coefficient of interest are. What control variables do you think should be included in this regression?(Econmetrics) Q.1 How can you test for general misspecification of model if it would have only (any of) two independent variables?You are interested in how the number of hours a high school student has to work in an outside job has on their GPA. In your regression you want to control for high school standing and so you run the following regression: GPA = 3.4 0.03 * HrsWrk - 0.7 * Frosh - 0.3 * Soph +0.1 * Junior (1.1) (0.013) (0.23) (0.14) (0.08) where HrsWrk is the number of hours the student works per week, and Frosh, Soph, and Junior are dummy variables for the student's class standing. a) If you include a dummy variable for seniors, that would cause a Hint: type one word in each blank. For the rest of questions, type a number in one decimal place. b) The expected GPA of a Sophomore who works 10 hours per week is c) The expected GPA of a Senior who works 10 hours per week is d) If Dom and Sarah work the same number of hours per week, but Dom is a Junior and Sarah is a Freshman. Dom is expected to have a higher GPA than Sarah. e) Suppose you rewrite the regression as: problem. GPA = ₁HrsWrk + ß2Frosh + B2Soph +…
- (2)What would the consequence be for a regression model if theerrors were not homoscedastic?What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) + 0. Letting a, = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value. 3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu- dents. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 3.6 29 6 3.0 25 7 2.7 25 3.7 30 (i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPA = B, + B¡ACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? (ii) Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum…
- If we run a regression where y (bankruptcy) = f (factors potentially predicting bankruptcy), what is the dependent variable?3. To explain what determine the price of air conditioners, B.T. Ratchford, obtained the following regression results based on a sample of 19 air conditioners: R²=0.84 y=-68.236 +0.023x, +19.729x3, +7.653x (0.005) (8.992) (3.082) se= Where y the price, in dollars x2= the BTU rating of air conditioner x3 the energy efficiency ratio x, the number of settings se standard errors a) Interpret the regression results. b) Do the results make economic sense? c) At 5% significance level, test the hypothesis that the BTU rating has no effect on the price of an air conditioner vs. that it has a positive effect. d) Would you accept the null hypothesis that the three explanatory variables explain a substantial variation in the prices of air conditioners? Show clearly all your calculations.The table to the right contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions (A) - (D). (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. X 270 360 520 780 The fixed costs are $. (Round to the nearest dollar as needed.) ITTI y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector. The variable costs are $ per projector. (Round to the nearest dollar as needed.) (C) Find the break even points. The break even points are (Type ordered pairs. Use a comma to separate answers as needed. Round to the nearest integer as…
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