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.
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- 8. Which of the following best describes the linear probability model? The model is the application of the linear multiple regression model to a binary dependent variable The model is an example of probit estimation The model is another form of logit estimation The model is the application of the multiple regression model with a binary variable as at least one of the regressors OOd. If the director used these 4 weeks of data to create a linear regression, what does that linear regression formula suggest for this week's forecast of employee appointments? What does the regression analysis suggest in general about employee appointments for Director Very Busy?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?
- As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?
- Describe the important characteristics of the variance of a conditional distribution of an error term in a linear regression. What are the implicationsfor OLS estimation?The Results below show the output of the following model: ?=?0+?1?1+?2?2+? Coefficient St. Error t-ratio Intercept 10.492 0.6655 15.77 ?1 0.0154 0.1889 0.08 ?2 0.1353 0.1889 0.72 Observations 100 ?2 0.985 Correlation matrix: X1 X2 X1 1 X2 0.950 1 Instructions: a. The above results show that the model has the problem of multicollinearity, what are the indicators of multicollinearity that can be identified from these results? b. What are the solutions to rectify multicollinearity?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…
- Only typed answer and please don't use chatgpt otherwise I downvote the answer Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average B) result in a test score of 698.9 C) reduce test scores by 2.56 on average D) reduce test scores by 4.56 for every school district PLEASE EXPLAIN WHY C IS CORRECT.1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity1.1 Which of the following is NOT a good reason for including a disturbance term in a regression equation?/ A. To allow for random influences on the dependent variable/ B. To allow for errors in the measurement of the dependent variable/ C. It captures omitted determinants of the dependent variable D. To allow for the non-zero mean of the dependent variable/ 1.2 Consider the equation Y = B1 + B2X2 + u. A null hypothesis of H0: B2 = 0 means that/ A. X2 has no effect on the expected value of Y / B. B2 has no effect on the expected value of Y/ C. X2 has no effect on the expected value of B2 / D. Y has no effect on the expected value of X2/ 1.3 The OLS residuals in the multiple regression model/ A. can be calculated by subtracting the fitted values from the actual values / B. are zero because the predicted values are another name for forecasted values / C. are typically the same as the population regression function errors / D. cannot be calculated because there…