1. Consider the following linear regression model: (a) Which assumptions are needed to make the B,...
PLEASE ANSWER ALL THE POINTS AND WRITE CLEARLY AND EXPLAIN THANK YOUU!! 1. Consider the following linear regression model: (a) which assumptions are needed to Inake the A i unbiased estimators for the ßi? (b) Explain how one can test the hypothesis that +A-0 by means of a t-test. We were unable to transcribe this image(d) Suppose that r is an irrelevant explanatory variable in the population model and that you estimate the model including both r1 and r2. What...
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant? x2 coefficient? x3 coefficient? x4 coefficient? (c) If x2 = 1, x3 = 8, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how...
Testing the equality of two regression coefficients. Suppose that you are given the following regression model: Yi = β1 + β2X2i + β3X3i + ui and you want to test the hypothesis that β2 = β3. If we assume that the ui are normally distributed, it can be shown that t = βˆ 2 − βˆ 3 var (βˆ 2) + var (βˆ 3) − 2 cov (βˆ 2, βˆ 3) follows the t distribution with n − 3...
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be biased. the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients...
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null hypothesis H0 : β1 = 0 and β2 = 0 at 5% when: a) A F test of H0 : β1 = 0 and β2 = 0 give us a p value of 0.001 b) A t test of H0 : β1 = 0 give us a p value of 0.06 and a t test of H0 : β2 = 0 a p value...
1. Consider the following model where y denotes the tool life and xi, x2, and tz denote the cutting speed, tool type, and type of cutting oil, respectively. There are two different tool types, A and B, and there are two type of cutting oils, low-viscosity oil and medium-viscosity oil. The two categorical predictors are 1 if type A 1 f low-viscosity oil used defined as *20 if type B and c3 0 if medium-viscosity oil used (a) Interpret the...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
1.Which of the following assumptions is required to obtain a first-differenced estimator in a two-period panel data analysis? a. The idiosyncratic error at each time period is uncorrelated with the explanatory variables in both time periods. b. The variance of the error term in the regression model is not constant. c. The explanatory variable does not change over time for any cross-sectional unit. d. The explanatory variable changes by the same amount in each time period. 2.A Chow test _____....
Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 - 8.1X3 + 1.9x4 (a) Which variable is the response variable? O O O O Which variables are the explanatory variables? (Select all that apply.) o X3 O X4 Сх, (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient Xz coefficient x4 coefficient (C) If x2 = 8, X3 = 3, and X4 = 1, what...