3. Computing heteroskedasticity-robust LM testsSuppose you are estimating the following multiple regression model using 3,800 observations:y = Bo+B₁21+ B₂x2 + B3x3 + B4T4+ B5x5 + uAfter estimating the model with OLS, you propose the following hypothesis: Ho: 25= 0,24= 0,23 = 0. You would like to test this hypothesis withan LM test; however, you are unsure whether the model suffers from heteroskedasticity.Outline the steps needed to obtain a heteroskedasticity-robust LM statistic to test these restrictions.1.2. Regress #3 on3. Regress #4 on4. Regress #5 onto obtain the residuals T₁.to obtain the residuals T2.to obtain the residuals 73.5. Regress on T1, 72, and T30 with no intercept to obtain SSR₁. Then calculaten - SSR₁.Suppose, after following steps 1-5, you obtain a value for SSR₁ of 3,794. You would like to test the exclusion restrictions at the 99% level.The resulting heteroskedasticity-robust LM statistic iscritical value in this case is 11.34.)Fand you wouldthe null hypothesis. (Hint: The chi-squared Outline the steps needed to obtain a heteroskedasticity-robust LM statistic to test these restrictions.1.2. F3. F4. F5. FRegress y on #₁, x2, 3, 4, and as to obtain the residuals ūRegress y on ₁ and ₂ to obtain the residuals ūRegress y on #3, 4 and 5 to obtain the residuals ūSR₁. Then calculate n - SSR₁.

Given the multiple regression model asGiven the hypothesis for an LM test is

Answered: 3. Computing heteroskedasticity-robust…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Solve the second question in regression analysis
ANSWER THE FOLLOWING QUESTION.
Bxi + €i, where €; are independently and Consider a simple linear regression model Y; = identically distributed with mean 0 and variance o?, and i = 1,..., n. Note: this model does not have a intercept term. Derive the Best Linear Unbiased Estimator (BLUE) for B. Denote this by BBLUE. Make sure to state why this is the BLUE.
In the multiple regression model with a quarterback's salary the response variable Y and the X variables pass completion percentage (PCT), number of touchdowns (TD), and age; the test of joint significance rejected HO: beta1 = beta2 = beta3 = 0. What does that mean? O Most of these X variables are significant in explaining salary. O At least one of these X variables is significant in explaining salary. O Each of these X variables is significant in explaining salary. O The model with all three X variables is significantly better than using sample mean salary alone to estimate expected salary
With multiple regression, the null hypothesis for the entire model now uses the p test. True False
Espan Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x). LinReg y=a+bx a = 2.39562641 do b=0.37929688 2=0.4130321711 r=0.64267579 Part: 0 /3 Part 1 of 3 Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers). Regression line equation: y = Part 2 of 3 What is the correlation between the interest rate and the yield of the stock? The correlation coefficient is Part: 2 /3 Part 3 of 3 Predict the price when the prime interest rate is 6%. Round the answer to at least four decimal places. When the prime interest rate is 6%, the price is predicted to be
5
The data from exercise 3 follow. xi 2 6 9 13 20 yi 7 18 9 26 23 The estimated regression equation is = 7.6 + .9x. What is the value of the standard error of the estimate (to 4 decimals)? What is the value of the t test statistic (to 2 decimals)? What is the p-value? Use Table 1 of Appendix B.Selectless than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3 What is your conclusion ( = .05)?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4 Use the F test to test for a significant relationship. Use = .05.Compute the value of the F test statistic (to 2 decimals). What is the p-value?Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6 What is your conclusion?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…
A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…

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