Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α = .05. The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though β ̂_2 > β ̂_3.
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε to n = 30 data points and obtain SSE = 282 and R^2 = 0.8266 a.) Find an estimate of s^2 for the multiple regression model (a) s^2 ≈ 30.9856 (b) s^2 ≈ 28.6021 (c) s^2 ≈ 1.3111 (d) s^2 ≈ 29.7938 (d) b.) Based on the data information given in a.), you use F-test to test H0...
When estimating y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to test H0: β1 = β2 = 0 versus HA: At least one βi ≠ 0. The value of the test statistic is F(2,20) = 2.50 and its associated p-value is 0.1073. At the 5% significance level, the conclusion is to ________. Multiple Choice a. reject the null hypothesis; we can conclude that x1 and x2 are jointly significant b. not reject the null hypothesis;...
2) Suppose the original regression is given by y = β0 + β1x1 + β2x2 + β3x3 + u. You want to test for heteroscedasticity using F test. What auxiliary regression should you run? What is the null hypothesis you need to test?
12.3 Suppose you fit the multiple regression model y = Bo + B1x1 + Bzxz + Bzxz + e to n = 30 data points and obtain the following result: ŷ = 3.4 - 4.6x + 2.7x2 + .93xz The estimated standard errors of B, and Bs are 1.86 and .29, respectively. a. Test the null hypothesis Ho: B2 = 0 against the alternative hypothesis He: B2 + 0. Use a = .05. b. Test the null hypothesis Ho: Bz...
1.The following tables give the results for the full model, as well as a reduced model, containing only experience Test Ho: ß,-Bs-0 vs HA: β2 and/or β3 # 0 Complete Model: Y-βο + β1X1 + β2X2 + β3Xs + ε ANOVA MS P-value df 76.9 Regression Residual Total 2470.4 823.5 224.7 2695.1 .0000 10.7 21 24 Reduced Model: Y = β0 + β X + ε MS df 1 23 24 value 2394.9 2394.9 183.5 0.0000 300.2 13.1 2695.1 Regression...
Use the Excel output in the below table to do (1) through (6) for each ofβ0, β1, β2, and β3. y = β0 + β1x1 + β2x2 + β3x3 + ε df = n – (k + 1) = 16 – (3 + 1) = 12 Excel output for the hospital labor needs case (sample size: n = 16) Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 1946.8020 504.1819 3.8613 0.0023 848.2840 3045.3201 XRay (x1) 0.0386...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming a conditional variance function Varux=σ2h(x). Which of the following statements is correct? A) The function h(x) does not need to be estimated as part of the procedure B) If the assumption about the conditional variance of the error term is incorrect, then FWLS is still consistent. C) FWLS is the best linear unbiased estimator when there is heteroscedasticity. D) None of the above answers...
Suppose you fit the first rder mu ple egression model y = po + β1x1 + a. Test Ho βι-o against h, β1 , 0 Use α-D 05 b. Find a 99% confidence interval for P2 interpret the interval 2x2 + ε to n= 25 data points and obtain the prediction equation y = 37.1 + 1.19x1 + 1 3 2 Th° estimated standard deviations ofthe sampling distributions of βι and P2 are 0.23 and 0.18, espec ve y ....
You may need to use the appropriate technology to answer this question. In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,550 and SSE = 550. (a) At α = 0.05, test whether x1 is significant. State the null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 ≠ 0 Ha: β1...