In a regression problem with 1 output variable and with a total number of 100 possible input variables, what is the number of all possible models with three input variables?
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In a regression problem with 1 output variable and with a total number of 100 possible input variables, what is the number of all possible models with three input variables?
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- If a regression equation contains an irrelevant variable, the parameter estimates will be Select one: a. Consistent and unbiased but inefficient b. Consistent and asymptotically efficient but biased c. Consistent, unbiased and efficient. d. InconsistentConsider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.(2)What would the consequence be for a regression model if theerrors were not homoscedastic?
- The linear regression equation, Y= a + bX, was estimated. The following computer output was obtained: DEPENDENT VARIABLE: Y OBSERVATIONS: 15 VARIABLE INTERCEPT Multiple Choice O X R-SQUARE 0.6010 PARAMETER ESTIMATE 412.18 0.6358 F-RATIO 19.58 STANDARD ERROR 102.54 0.1765 P-VALUE ON F 0.0001 T-RATIO P-VALUE 0.0015 0.0032 In the regression above, the parameter estimate of b (on the variable X) indicates that 4.02 3.60 X increases by 0.1765 units when Yincreases by one unit. X increases by 0.6358 units when Y increases by one unit. Y increases by 0.1765 units when X increases by one unit. Y increases by 0.6358 units when X increases by one unit. Y increases by 3.60 units when X increases by one unit.In multiple regression model: what is it means for a variable to be significant? Explain the meaning of the significant variable.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
- 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…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?7. Suppose we are interested in the relationship of the union status variable Y (= 1; if in union, = 0, if not in union) to the conditioning variables X₁ = gender (1 if female, 0 if male), and X2 = marital status (1 if married, 0 if not). Table below gives the coefficient estimates obtained in (i) Least squares regression of Y on X₁ and X₂, and, (ii) Nonlinear least-squares estimates of the logistic regression model E(YX1, X2) = G(Z), where Z=80+ B₁X1+B₂X2, and G(Z) = e²/(1+e2). In parenthesis are the conventional standard errors of the coefficient estimates. Also tabulated are the means of the conditioning variables (regressors).
- 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) ¹3A linear regression model for the revenue data for a company is R=27.1t+203 where R is total annual revenue and t is time since 1/31/02 in years. 12 months 12 months 12 months Billions of Dollars Revenue Gross Profit 12 months 12 months ending 1/31/02ending 1/31/03ending 1/31/04 ending 1/31/05 ending 1/31/06 500- 201 49 236 54 255 60 500- 277 65 (A) Draw a scatter plot of the data and a graph of the model on the same axes. OA. B. O.C. KICB Q 2 316 72 500- oo D. 500- Q GYou are interested in the effect rainfall has on the number of traffic accidents in your city. You consider 4 possible specifications for a polynomial regression: (1) Accidents = 15.2 +0.23°Rain - 0.11*Rain2 + 0.08 Rain3 -0.0s Rain (7.1) (0.13) (0.05) (0.03) (0.02) (2) Accidents = 13.2 +0.14*Rain -0.09 Rain?+0.07 Rain3 (5.1) (0.05) (0.03) (0.04) (3) Accidents= 75+0.24*Rain - 0.13 Rain2 (3.6) (0.12) (0.07) (4) Accidents = 94 +0.18°Rain (2.3) (0.05) Based on a 5% significance level, which of the 4 specifications is the most appropriate model? O Specification1 O Specification 2 O Specification 3 O Specification 4 O None of them since Rain does not have a statistically significant effect on Accidents