28. What is the correct interpretation of the R-squared in Mo48% of the variation in household savings can be explained by household income, the age of thousehold head, and the level of education of the household headb) 8% of the variation in the residuals of the model can be explained try householdthe household head, and the level of education of the household head8% of the variation in household savings cannot be explained by the explanatory variablesmodel 6.e., household income, the age of the household head, and the level of education of thousehold head)d) 8% of the variation in the residuals of the model cannot be explained by the explanatory variables inthe model (.e., household income, the age of the household head, and the level of education of thehousehold head)29. Which of the two models (Model 1 vs Model 2) has a better finModel 2 because the R-squared is largerb)Model 1 because the adjusted R-squared is largerc) Both models have the same fitd) Model 2 because it has more variables to predict the outcomea)30. Use the p-value approach and a significance level of 5% to test the null hypothesis that Model 2 issignificant Ho: B₁ B₂Ba=0. What do you conclude?a) We fail to reject the null hypothesis since the p-value of the test is 2. 80, and conclude that the modelis significant.b)We fail to reject the null hypothesis since the p-value of the test is 0.044, and conclude that themodel is significant.c)We reject the null hypothesis since the p-value of the test is 2. 80, and conclude that the model is notsignificant.d) We reject the null hypothesis since the p-value of the test is 0.044, and conclude that the model issignificant.31. Suppose your data analyst re-estimates Model 2 with a different random sample of 102 individuals andfinds b₁ = 0.249. Are these differences in the value of b, an indication that the sample estimator is biased?a) Yes, if the estimator were unbiased, the value of b, would be the same regardless the sampleb) No, the value of b, is expected to vary across samples due to sampling error. The estimator by isonly expected to be biased if the sample is not representative of the target populationc) Yes, if the sample were truly selected at random, there would not be a sampling error.d) No, the value of b₁ is expected to vary across samples due to sampling error. The estimator by isonly expected to be biased if the sample is smaller than 30 observationsAnswer questions 32-36 based on the following information:Monica Kratz, a market specialist, is analyzing household budget data collected by her firm.Monica's dependent variable is weekly household expenditures on groceries, and her independentvariables are annual household income (in $1,000's) and household size (1 = large, 0 = small).Regression analysis of the data yielded the following table.Coefficients Standard Error Statistic p-value19.6831.965934 0.0781.7359.9406120.00049.1256.416667Interceptincomelarge10.0120.1757.6560.000 Answer questions 21-31 based on the following information:Suppose you have the following data for a sample of 102 households:Savings: annual savings in dollars. Income: annual income in dollarsAnd you estimate the two models:Model 1: Savings, = Bo + B,Income, +Model 2: Savings, Bo+B,Income, + B₂Education, + B3Age, + E₁You get the following Excel output:ANOVAR SquareAdjusted R SquareObservationsRegressionResidualTotalInterceptIncome.ANOVAEducation: years of education of household headAge: age of household head in yearsRegressionResidualTotalInterceptIncomeEducationAgeRegression StatisticsR SquareAdjusted R SquareObservationsRegression Statistics0.0620.053102Coefficients124.8420.1470.080.049102Coefficients-995.1240.108141.923-3.58255Results of Model 1:Standard Error665.3930.058S5MSStandard Error2390.3500.071113.84348.592StotMSF6.49Results of Model 2:Stot-0.4201.5301.250-0.941P-value0.849Significance F0.0124F2.8P-value0.6780.1300.2160.678Significance F0.0442

The two models are given as:Model 1: Model 2: Regression outputs for these two models are provided.

28. What is the correct interpretation of the R-squared in Model 2 4) of the variation in household savings can be explained by household income, the household head, and the level of education of the household head b) 8% of the variation in the residuals of the model can be explained by household the household head, and the level of education of the household head 8% of the variation in household savings cannot be explained by the explanatory variables model 6e, household income, the age of the household head, and the level of education household head) d) 8% of the variation in the residuals of the model cannot be explained by the explanatory variables in the model (e., household income, the age of the household head, and the level of education of the household head) 29. Which of the two models (Model 1 vs Model 2) has a better f a) Model 2 because the R-squared in larger b) c) Both models have the same fit Model 1 because the adjusted R-squared is larger d) Model 2 because it has more variables to predict the outcome 30. Use the p-value approach and a significance level of 5% to test the null hypothesis that Model 2 is significant Ho: B₁ B₂=B₂ 0. What do you conclude? = a) We fail to reject the null hypothesis since the p-value of the test is 2. 80, and conclude that the model is significant. b) We fail to reject the null hypothesis since the p-value of the test is 0.044, and conclude that the model is significant. c) We reject the null hypothesis since the p-value of the test is 2. 80, and conclude that the model is not significant. d) We reject the null hypothesis since the p-value of the test is 0.044, and conclude that the model is significant.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P