190) 1. Prove that the slope of the sample regression function (B2) is the BLUE if the assumptions of Gauss Marko theorem are satisfied. Make sure to show all the steps and the underlying assumptions (30 points)
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- 1. R-squaredSuppose regression of y on an intercept and x with 50 observations yields total sum of squares 100 andexplained sum of squares 36.(a) What is ?^2?(b) What is the correlation coefficient between y and x?(c) What is the standard error of the residual?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…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 OO
- 1. You are running a probability regression. If your data contains many outliers, you’d be better off using (A) A linear probability model. (B) Probit. (C) Logit. (D) Either probit or logit would work fine. (E) Any of the above regression models would work fine.2. Which of the following types of regressions will always have a binary outcome variable? (A) Probit (B) Difference-in-differences (C) Regression discontinuity (D) (A) and (B) will both have binary outcome variables1. 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 multicollinearity
- 11. Which of the following statements is not true about multicollinearity? (a) Perfect multicollinearity will prevent you from being able to estimate a linear regression model. (b) Imperfect mulitcollinearity affects the individual t-statistics of the regressors. (c) Multicollinearity is defined as a linear relationship between different independent variables. (d) Imperfect multicollinearity affects model validity of the model. (e) The least squares estimators are unbiased in the presence of imperfect multicollinearity.5. In classical linear regression model, Var (u) = o² refers to the assumption of Zero mean value of disturbance term a. b. Homoscedasticity c. No autocorrelation5. Among important factors that affecting the price of land lot are size, number of mature trees and distance to the lake. Using data for 60 recently sold land lots are shown below: B 1 SUMMARY OUTPUT 2 3. Regression Statistics 4 Multiple R 5 R Square 6 Adjusted R Square 7 Standard Error 0.4924 0.2425 0.2019 40.24 8 Observations 60 9. 10 ANOVA Significance F 5.97 11 df S MS 9676.6 0.0013 12 Regression 13 Residual 3 29,030 90,694 56 1619.5 14 Total 59 119,724 15 16 Coefficients Standard Error t Stat P-value 0.0331 0.2156 17 Intercept 51.39 23.52 2.19 18 Lot size 0.700 0.559 1.25 19 Trees 0.679 0.229 2.96 0.0045 20 Distance -0.378 0.195 -1.94 0.0577 a) Write the regression equation b) What is the standard error of estimate? Interpret its value. c) What is the coefficient of determination? Interpret its value. d) What is the adjusted coefficient of determination? Interpret its value. e) Test the validity of the model. f) Interpret each of the coefficients. g) Test at 5% level of…
- 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?1. A Travel-Cost Method Now it is time for your first consulting job as an environmental economist. The Forest Service would like to know whether they should preserve some national forest land, previously slated to be logged, for hiking. You are helping do a travel-cost analysis to estimate the annual benefits of hiking in this area. Survey data has been gathered from 500 hikers who visited the forest last year. This forest did not charge an entrance fee. Using a statistical technique called regression analysis, you have controlled for differences in income, employment status, age, and other important factors that might affect the number of hiking trips taken. Taking these factors into account, you have developed the following relationship: Zone 1 2 3 Population in zone 1,000 3.000 2,000 Cost Per Hiking Trip Per Person 20 40 80 Hiking Trips Taken Per Zonal Person Per Year 8 6 2 where cost includes gas, tolls, fares, hotels, entry fees, and the value of time spent traveling. a. Graph a…1. A Travel-Cost Method Now it is time for your first consulting job as an environmental economist. The Forest Service would like to know whether they should preserve some national forest land, previously slated to be logged, for hiking. You are helping do a travel-cost analysis to estimate the annual benefits of hiking in this area. Survey data has been gathered from 500 hikers who visited the forest last year. This forest did not charge an entrance fee. Using a statistical technique called regression analysis, you have controlled for differences in income, employment status, age, and other important factors that might affect the number of hiking trips taken. Taking these factors into account, you have developed the following relationship: Zone Population in Cost Per Hiking Hiking Trips zone Trip Per Person Taken Per Zonal Person Per Year 1 1,000 2 3,000 3 2,000 20 8 40 6 80 2 where cost includes gas, tolls, fares, hotels, and the value of time spent traveling. a. Graph a linear…