Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which result in the following function: Ý= 33 + 8X1 – 6X2 + 16X3 + 18X4 For this model, there were 35 observations; SSR= 1,432 and SSE= 600. Assume a 0.01 significance level. Based on the given information, which of the following conclusions is correct about the statistical significance of the overall model?
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- Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function:Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4For this model, there were 35 observations; SSR = 1,544 and SSE = 600. Assume a 0.01 significance level.Based on the given information, which of the following conclusions is correct about the statistical significance of the overall model? Multiple Choice Reject the null hypothesis that β3 = 0. Do not reject the null hypothesis that β1 = β2 = β3 = β4 = 0. Reject the null hypothesis that β1 = 0. Reject the null hypothesis that β1 = β2 = β3 = β4 = 0.A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for 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=0.05α=0.05. X1X1 X2X2 YY 65.4 65.8 57.3 72.8 70.8 55.1 63.3 59.9 66.9 59.1 60.4 60.4 65.4 66.9 56.2 58.3 61.9 50.4 57.1 57.1 54.2 78.2 62.5 67.5 54.2 55.9 57.1 56.5 55.5 57.8 57.9 56.2 60.8 54.3 54.8 61.8 68.2 70.5 71.8 60 64.1 58.8 66.6 60.5 54.6 66.7 68.5 51.7 45.1 48.6 57.1 58.4 59.9 55.9 58.6 66.3 52.5 56 60.5 67.1 SSreg=SSres=R2=F=P-value =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 researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=10N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.01α=0.01. X1X1 X2X2 YY 58.8 29.9 63.1 64.1 57.3 40.1 51.4 35.3 46.2 77.1 88.5 30 60.6 67.5 16.2 68.3 63.4 62 44.8 6.6 77.6 49 29.3 65.5 55.5 25.8 62.5 57.5 30.2 62 R2=R2= F=F= P-value for overall model = t1=t1= for b1b1, P-value = t2=t2= for b2b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.01α=0.01. The overall regression model is not statistically significant at α=0.01α=0.01. Which of the regression coefficients are statistically different from zero? neither regression coefficient is…Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data, SST = 15,189.8 and SSR = 14,056.9. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Does the estimated regression equation explain a large amount of the variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to one decimal place.) , after adjusting for the number of independent variables in the model, we see that % of the variability in y has been accounted for.
- The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variableThe regression equation isSALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA Predictor Coef SE Coef T P Constant 1470 5746 0.26 0.801 LANDVAL 0.8145 0.5122 1.59 0.131 IMPROVAL 0.8204 0.2112 3.88 0.0001 AREA 13.529 6.586 2.05 0.057 S = 79190.48 R-Sq = 89.7% R-Sq(adj) = 87.8% Analysis of Variance Source DF SS MS Regression 3 8779676741 2926558914 Residual Error 16 1003491259 62718204 Total 19 9783168000 For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant? 46.66, significant 2.05, significant 1.59, not significant 0.26, not significantIf the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methods
- Which regressors are meaningful at the 5% significance level according to the Minitab output given below for regression analysis? (n=12) A)Only x3 B)Only x1 C)x2 and x3 D)x1 and x2Calculate the R2of the following multivariate sample regression functions and interpret theanswers.3.1 Investment-hat = β1-hat + β2-hat*Interest rate + β3-hat*Exchange rateESS = 900RSS = 1003.2 Investment-hat = β1 + β2-hat*Interest rate + β3-hat*number of 311 studentsESS = 400RSS = 6003.3 Salary-hat = β1 + β2-hat*Frequency of blinking eyes + β3-hat*Colour of hairRSS = 950TSS = 1000Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.