For the regression model Y = B1 + B₂X2 + B3X3 + e, the following estimation results are obtained: Regression Results coefficient B₁ B₂ B3 estimate O a. 0.3462 O b. 2.7000 O c. 0.8800 O d. 5.1000 0.7 5.1 2.7 If X₂ increases by 1 unit, how much units of Y is expected to increase ordecrease (X3 being fixed)? stanadard error 0.5 0.7 0.8
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- You estimated a regression with the following output. Source | SS df MS Number of obs = 268 -------------+---------------------------------- F(1, 266) = 23.48 Model | 668419.175 1 668419.175 Prob > F = 0.0000 Residual | 7572666.51 266 28468.6711 R-squared = 0.0811 -------------+---------------------------------- Adj R-squared = 0.0777 Total | 8241085.68 267 30865.4895 Root MSE = 168.73 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 1.014128 .2092916 4.85 0.000 .6020489 1.426207 _cons | 9.173163 21.13463 0.43 0.665 -32.43929 50.78561…In an OLS regression, which value represents the "best" R2 in terms of explained variance in the dependent variable? A. 2.53 B. 16.22 C. .001 D. 0.53Still referring to the question above, what is the t-statistic of the slope coefficient when testing Ho : B1 = 0 against Ho : B1 # 0? О -6.2. O 6.2. О 22.333. О -22.333.
- 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.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?You 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.
- 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 Total Residual 46 210,173,612.6150 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 9200.6014 6.9529 0.000000011 2.1126 0.040093183 Lower 95 % Upper 95% 19,380.1442 1670.2789 3031.4553 39.129 1619.5044 Step 2 of 2: How much would you expect your salary to increase if you had one more year of education?2 of 3 2. (a) Consider the generalized linear regression model Yt = a + Bxt + Et. 4 Assume Est = 0 and that we have no serial correlation among the disturbances but More var(t) = σ²x², where we assume that xt 0 for all t. Derive the feasible GLS estimator of a and B. Now consider the following regression, setting == / 7 It 1 Xt and estimate a and B again. How would the estimates differ from GLS. Explain. Yt =a Consider the ARMA(1.1) process : +B+ εi,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?)
- 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 FalseAs 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…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?