Let be the residual for observation i for an estimated regression model. If 1.2 and ez = -0.33 R2 is definitely less than 1 O R2 is definitely greater than 1 O R2 is definitely greater than 0 O RSS is definitely positive O Both (a) and (d) are correct answers.
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- 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.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 squaresThe OLS estimators of the coefficients in multiple regression will have omitted variable bias: a. i only if an omitted determinant of b. if an omitted variable is correlated with at least one of the regressors, even though it is not a determinant of the dependent variable. C. only if the omitted variable is not normally distributed. d. if an omitted determinant of is a continuous variable. Y; i is correlated with at least one of the regressors. e. if the degree of freedom is less than 50.
- 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…QUESTION 2 Consider the following bivariate linear regression model y = a+3x+u. Suppose that E[u]x] #0 and that z is a valid instrument for r. Knowing that Cov(y, z) = 0.5 and Cov(z, x) = 0.5, the IV estimate of 3 is 1. %3D O True O FalseYou are given the following data: The regression equation is: A. -0.66 B. -1.20 (X'X)*¹ C. 1.12 O D. 2.06 = 1.3 2.1 0.8 -1.4 1.9 2.1 -1.4 s² = 0.86. T = 103 The correlation between ₁ and 3 (i.e., corr(Â₁, Â3)) is: -1.6] 1.9 (X'y) = 2.9 3.4 0.8 Yt = B₁ + B₂X2+ + B3X3t + Ut.
- 5 We are given a sample of n observations which satisfies the following regression model: yi = β0 + β1xi1 + β2xi2 + ui , for all i = 1, . . . , n. This model fulfills the Least-Squares assumptions plus homoskedasticity. (a) Explain how you would obtain the OLS estimator of the coefficients {β0, β1, β2} in this model. (You do not need to show a full proof. Writing down the relevant conditions and explain)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) ¹3True 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.
- 5. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Yt = 2.20+ 0.104Xt₁ - 3.48 Xt₂ + 0.34Xt3 (3.4) (0.005) (2.2) (0.15) Standard errors are in parentheses, the explained sum of squares was 109.6, and the residual sum of squares 18.48. a. Test at the 5% level for the statistical significance of the parameter estimates. b. Calculate the coefficient of determination.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 researcher estimates a regression using two different software packages.The first uses the homoskedasticity-only formula for standard errors. Thesecond uses the heteroskedasticity-robust formula. The standard errors arevery different. Which should the researcher use? Why?