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- 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…2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.1. For a regression model y = XB + u where u is N(0, o?1), y is nx1 matrix, X is nxp matrix, B is px1 matrix and u is nx1 matrix, a. derive the estimators B using the method of least squares
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.4. From the regression output, report the coefficients, standard errors, t-statistics, probability and R-squared (report the results in a table). 5. Re-write the specified model in (a) with values from the regression results and interpret the coefficients.The best way to interpret polynomial regressions is to: A. look at the t-statistics for the relevant coefficients. B. analyze the standard error of estimated effect. C. plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X. D. take a derivative of Y with respect to the relevant X.
- 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) ¹3(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 a multiple regression of y on x1, x2, and x3, including additional variables on the right-hand side of the model always increases R2. (True/False).Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm³, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. Regression Analysis: cuberoot (Volume) versus Time Predictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Time 0.640 0.000018 35512.6 0.000 s=0.030 R-Sq=1.000 R-sq (adj)=1.000 What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Volume = 0.640 - 0.006(Time) Volume = -0.006 + 0.640(Time) Volume = - 0.006 + 0.640(Time?)A scatter plot shows data for the cost of a vintage car from a dealership (y in dollars) in the year a years since 1990. The least squares regression line is given by y-25,000 + 500z. Interpret the y intercept of the least squares regression line. Select the correct answer below O The predicted cost of a vintage car from a dealership in the year is 820.000 O The predicted cost of a vintage car from a dealershpin the year 1090 is 85,000. O The predicted cost of a vintage car from a dealershp in the year 1990 is sse. The yintercept should not be interpreted.