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- 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?"In the regression model InY=b0+b1*InX+u, the coefficient b1 is interpreted as" O the intercept O A covariance O A regressor O An elasticityDiscuss the FIVE (5) importance of adding error term in the regression model.
- Explain what is meant by an error term. What assumptions do we makeabout an error term when estimating an ordinary least squares regression?The 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.The following graph of the estimated residuals from a regression against the observation date (i.e. time period) indicates the residuals are: 2.00 1.50 1.00 0.50 00 0.00 -0.50 -1.00 1.50 -2.00 Time Select one: O A. Serially correlated O B. Normally distributed OC. Homoscedastic O D. Serially uncorrelated O E. Heteroscedastic Estimated residuals
- Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1If two regressors are a linear combination of each other, what is the result if we run an OLS regressions with both of those regressors present? The regressors will cause the variance of the estimates to be higher but the estimates will still be unbiased. O a. We cannot run OLS because we have perfect multicollinearity. Ob. It will ensure our residuals are linear and not plagued by nonlinearity. OC. It will increase the power of our estimates since the two regressors are related. Od. None of these. Oe.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 False
- 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.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…Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.7339 R Square 0.5386 Adjusted R Square 0.5185 Standard Error 2137.5200 Observations 49 ANOVA SS df Regression 2 245,370,679.3850 122,685,339.6925 26.8517 MS F Significance F 1.9E-08 Residual 46 210,173,612.6150 Total 48 455,544,292.0000 4,568,991.5786 Coefficients Standard Error Intercept Education (Years) 14290.37278 2350.8671 2,528.5819 338.1140 Experience (Years) 829.3167 392.5627 t Stat P-value 5.6515 0.000000961 6.9529 0.000000011 2.1126 0.040093183 Lower 95 % Upper 95 % 9200.6014 19,380.1442 1670.2789 3031.4553 39.129 1619.5044 Step 1 of 2: What would be your expected salary with no education and no experience?