There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedastic-ity. One possibility not covered in the text is to run the regressionaf on x1, X2, ..., xg. V7, i = 1, ... , n,where the û; are the OLS residuals and the ŷ; are the OLS fitted values. Then, we would test jointsignificance of x1, x2. ..., Xg and y. (Of course, we always include an intercept in this regression.)(i) What are the df associated with the proposed F test for heteroskedasticity?(ii) Explain why the R-squared from the regression above will always be at least as large as theR-squareds for the BP regression and the special case of the White test.(iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP orspecial case of the White statistic? Explain.(iv) Suppose someone suggests also adding ŷ; to the newly proposed test. What do you think of this idea?

(i) The proposed test is a hybrid of Breusch-Pagan and White test. There is k+1 regressors, each…

Answered: There are different ways to combine…

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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If the coefficient B₁ has a nonzero value, then it is helpful in predicting the value of the response variable. If B₁ = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that B₁ = 0 use the test statistic t = (b₁-0) /sp. Critical values or P-values can be found using the t distribution with n - (k+1) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error sp, is often provided by software. For example, see the accompanying technology display, which shows that sp=0.076885101 (found in the column with the heading of "Std. Err." and the row corresponding to the first predictor variable of height). Use the technology display to test the claim that B₁ = 0. Also test the claim that B₂ = 0. What do the results imply about the regression equation? Click the icon to view the technology output. Test the claim that B₁ = 0. For…
17. Additional information was obtained from EXCEL. Conduct a test of hypothesis to determine if any of the regression coefficients do not equal 0 Use the 005 significance level. The regression equation is: Salary = 19.2 + 3.10 Years + 0.269 Perform - 0.704 Absent Intercept Years Perform Absent Coefficients Standard Error 19.186 3.096 0.269 -0.704 12.146 0.706 0.120 0.586 -1.202 t Stat 1.580 4.385 P-value 0.143 0.001 0.046 0.255 2.252 а. Но: H: Họ: H1: Họ: H1: b. The decision rules are to reject Ho if What is your decision? Interpret. c. 305 Multiple Regression and Correlation Analysis Chapter 14
3) For a sample of 306 students in a basic business communications course, the sample regression line y = 58.813 + 0.2875x was obtained. Here y = final student score at the end of the course x = score on a diagnostic writing skills test given at the beginning of the course The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566. a) Define and interpret the estimates of the regression equation. b) Interpret the coefficient of determination. c) What will happen to the final student score if his diagnostic writing test score increases by 2? d) How can you inmprove this model?
Give the confidence interval for the regression coefficient Baby considering the following. 40 observations in the sample 90% confidence level • • 4 predictor variables Use the same information in Question 3 to state the hypothesis test, test statistic and decision rule. Write the following regression function in the appropriate matrices if the sample size is 3. Y₁ = Bo + B₁X₁₁ + B₂X₁2 + Ei. Why would we want to obtain a correlation matrix? Explain what 734 means. How would interpret a value of 0.75 for 134? The following data set is obtained. Sixty beetles were researched and the following variables were observed and measured. X₁ = legsize in milimeter X₂=bodylength in grams X3 = weight X₁ = age in months Study the correlation matrix and then formulate a question that can be answered by a regression model. That is, identify a response (dependent variable). X1 X2 X3 X4 X1 1 X2 0.2 1 X3 0.9 0.85 1 X4 0.1 0.13 0.89 1
The statsmodels ols() method is used on an exam scores dataset to fit a multiple regression model using Exam4 as the response variable. Exam1, Exam2, and Exam3 are used as predictor variables. The general form of this model is: If the level of significance, alpha, is 0.10, based on the output shown, is Exam1 statistically significant in the multiple regression model shown above? Select one. A text version of this output is available. OLS Regressin Results Dep. Variable: Model: Method: R-squar ed: Adj. R-squared: F-statistic: Prob (F-statistic): Log-Likelihood: AIC: 0.178 0.125 3.329 0.0276 -169.85 347.7 355.4 Exam4 OLS Date: Time: No. Observations: Least Squares Sun, 18 Aug 2019 10:59:12 Df Residuals: of Nodel: Covarianco Тура: 50 46 3 nonr obust BIC: Coef std err P>|t| [0.025 0.975) t Intercept Examl Exam2 Exam3 46.2612 0.1742 0.1462 0.0575 10.969 0.120 0.078 0.053 4.217 1.453 1.873 1.085 0.000 0.153 0.067 0.284 24.181 -0.067 -0.011 -0.049 68.341 0.416 0.303 0.164 Onnibus: 0.886 0.642…
Suppose that you have estimated coefficients for the regression model Y = B₁ + B₁X₁ + ß2X2 + ß3X3. Test the hypothesis that all three of the predictor variables are equal to 0, given the analysis of variance shown on the right. Use α = 0.05. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternartive hypotheses below. A. Ho: B₁ B₂ =B3 = 0 H₁: at least one ß; #0 C. Ho: B₁ B₂ = 3 = 0 H₁: B₁0, B₂0, B3 > 0 Find the critical value. The critical value is (Round to two decimal places as needed.) Source Regression Residual Error DF SS 3 9,654 23 2,400 B. Hō: at least one ß; ‡0 H₁: B₁ =B₂ =B3 = 0 D. H₁: B₁ = P₂ = ³3 = 0 H₁: B₁ B₂ B3 0 MS
The attached results are for a multiple regression study of smartphone addiction (SSA-SV) proneness in relation to 1) Gender 2)Age 3) Anxiety (GAD-7). I just want to clarify that age is statistically significant with p = 0.006; is this correct? What's throwing me off is the notation "< .001" on the top line under the p category. I was under the impression that the p-value would need to be less than 0.001.
Consider a randomized block design involving three treatments and two blocks. Define all variables. X1 X2 Treatment 1 2. 1 3 Let x, = 0 if ---Select-- v is in effect and 1 if --Select--- v is in effect. Write a multiple regression equation that can be used to analyze the data. E(y) =
Select all statements that are true of the least-squares regression line. ) It assumes a linear relationship between the explanatory and the response variable. R-squared is the portion of sample variance in the explanatory variable that can be explained by variation in the response variable. ) It can be used to predict the mean response of the explanatory variable. | R-squared is the portion of sample variance in the y variable that can be explained by variation in the x variable.
5.
Compute the value of the test statistic and Conclusion
A random sample of 8 applicants for a certain foreign job is selected. The number of years that these applicants have studied French in high school or university, X, and the mark which they obtained in a proficiency test in French, Y, are recorded. The following information is given: EX =32, Y =528, EXY=2136, X² =130 and y² =34872 Fitting a regression line, which of the following statements is incorrect? Select one: a. b₁ = 12 O b. Ŷ = 12+18X; O c. The predicted mark obtained if an applicant studied French for two years is 42. d. bo 18 e. Mean of X values = 4 Mean of Y values = 66

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