Module: ADVANCED QUANTITATIVE METHODS FOR MANAGERS AND DECISION MAKING3 rd Written Assignment (WA3)Assignment guidelinesThe assignment should be well structured in a managerial style and easy to read. Explain shortly what you do in each subject. Avoid repeating theory, and/or list basic formulas. Define the quantities in your calculation. Interpret results not in “dry statistical language” nut what they mean for the specificproblem (in context) Try to provide answers not just statistical calculations.The assignment is submitted as a business report in a Word document. You should alsosubmit an Excel (or other statistical package) file with your calculations.PART I (Subjects 1 to 3)For this part you will use the same data set (250 observations) as in your first and second writtenassignments. Variables are indicated in italics.Subject 1 (15%)Investigate whether Job-type is a factor that affects Credit card debt. i.Select the appropriate test of hypothesis and state the null and alternative hypothesis(5%)Test the null hypothesis at 95% confidence level and state your conclusions. (10%).ii. Subject 2 (20%)A two-way ANOVA in SPSS (Excel output would include the same information), regarding the effect offactors Age and Marital status on Household Income produced the following results:Descriptive StatisticsDependent Variable: Household income in thousands AgecategoryMaritalstatusMeanStd. DeviationN18-24 UnmarriedMarriedTotal21.866722.142922.00005.488526.573345.9281415142925-34 UnmarriedMarriedTotal37.500033.521735.027012.3833018.4978416.3800114233735-49 UnmarriedMarriedTotal54.187571.416763.308827.9243746.8970839.8089732366850-64 UnmarriedMarriedTotal82.9310110.500096.473757.4350191.8454876.87585292857>65 UnmarriedMarriedTotal57.592633.156344.339059.6710624.6132845.50506273259 Tests of Between-Subjects EffectsDependent Variable: Household income in thousands SourceType III Sum ofSquaresdfMean SquareFSig.Model1003214.089a10100321.40944.3300.000agecatmaritalagecat * marital151441.306616.06623338.37041437860.326616.0665834.59316.7300.2722.5780.0000.6020.038ErrorTota543137.9111546352.0002402502263.075 i.Interpret the result of the analysis of variance and state your conclusions in context(10%)Explain the interaction effect by plotting the relevant data, and comment on thesignificance of the interaction effect, providing an explanation in business terms. (10%).ii. Subject 3 (10%)Consider the six variables income, debtinc, creddebt, othdebt, age, and ed, which are all numericalvariables. i.Compute (using the proper tools) the pairwise correlation coefficients between thosevariables and indicate which ones are significant at 5% level.You are asked to choose a dependent variable and build a regression model selectingexplanatory variables from the list of the variables above. Make sure that theexplanatory variables you finally choose in the regression are significant.Justify the causality between explanatory and explanatory variable and explain how yourii.iii. model quantifies this association.PART BThe data set for subjects 4 and 5 is given in the file “WA#3 CarSales.xlsx”. The file contains dataregarding sales of different car models along with technical characteristics of the specific cars. Thedescription of the variables is given in the sheet Data.Subject 4 (20%)i. Create two Scatter Plot graphs that show how “Resale Value” is associated to “Price”and to “Fuel Efficiency (mpg)” and comment on the shape of the association in each case. ii.Develop a simple linear regression model between Resale Value as the dependentvariable and Price as the explanatory variable. Use the least squares method to estimatethe regression coefficients (Do not use mathematic formulas. Use available tools in Excel,SPPS or another statistical package).State the regression equation, check the significance of the coefficients at the 5% leveland give the interpretation of the regression coefficients b0 and b1 in context.Based on the regression model, what is the expected average Resale value, for a carpriced at 30 thousand and a car priced at 15 thousand?Provide a range for the resale value of the two prices in (iv), with 95% confidence.Interpret the value of the R2 and the value of the Standard Error of the regressionProduce and examine the residual plot and the normal probability plot of residuals andindicate whether assumptions of regression analysis hold true in this case.Add mileage (mpg) as a second explanatory variable in the regression model and run theregression. Compare your results with those of the model derived in (ii). If you shouldiii.iv.v.vi.vii.viii. choose one of the two models for prediction purposes, which one would you choose?Justify your choice both statistically as well as in business terms.Subject 5 (25%)i. Find the correlation between Resale Value and all other numerical variables in the dataset. Comment on the rationality of the correlation coefficients. ii.According to your results, which of the above correlation coefficients are not significantat 5% level of significance?Develop a regression model with Resale Value as dependent variable, using all variablesthat had a significant correlation coefficient in (ii), as explanatory variables.Do you observe any cases of explanatory variables that had a statistically significantcorrelation coefficient with Resale Value in (ii), but their regression coefficient in (ii) isnot significant. How can you explain that?Rerun the regression in (iii) using only the explanatory variables that were statisticallyiii.iv.v. significant. Interpret the values of the regression coefficients, R square, and standarderror of the regression. vi.Give a numerical example on how you can use this model to predict a resale price of acar.Compare the regression model against the one in 4.viii. Which one would you choose forprediction purposes? Justify your choice both statistically as well as in business terms.vii. Subject 6 (10%)A linear regression of variable Y against two explanatory variables X1 and X2 produced thefollowing estimation model:Y = 160.976 – 1.732X1 – 2.526X2 + e(40.298) (0.427) (1.382)The number in parentheses are the standard errors of each coefficienti. Fill in the cells in the following regression output table CoefficientsStandardErrort StatP-valueLower95%Upper95%InterceptX1X2 ii. Which independent variables are statistically significant at 5% and 10% level?

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