Details of this Paper

Week Three Homework Assignment - Linear Regression...........

Description

solution


Question

Question;Week Three Homework Assignment - Linear RegressionThe personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings, years of service and relevant certifications. The personnel director believes that an employees pay in this particular shop should be positively correlated to their prior performance rating, years of service and relevant certifications. The personnel director has collected the data shown in thefollowing table pertaining to the employees within the shop.EmployeeCurrentAnnualSalary(Thousands)12345678910111213141516171819202122232448.255.353.761.856.452.554.055.745.167.953.246.858.359.157.848.649.263.053.050.955.451.860.250.1AveragePerformanceRating forPast 3 Years(5 point scale)2.183.313.183.622.623.754.253.431.934.52.813.0654.064.122.313.874.372.52.813.683.532.431 of 8YearsofServiceNumber ofRelevantCertifications920183331132530547251123353921740352333273415667786646856875467645485The personnel director is interested in creating a linear regression model that can be usedto estimate the annual salary an employee might expect to receive based upon his or herpast performance, years of service and/or number of relevant certifications. Theregression model will be used as a basis for determining whether or not there is anyvalidity to the employees complaints regarding salary inequities.Perform each of the following seven regression analyses using a 95% confidence level.Annual salary vs. average performance rating for the past 3 yearsAnnual salary vs. years of serviceAnnual salary vs. number of relevant certificationsAnnual salary vs. average performance rating for the past 3 years and years ofserviceAnnual salary vs. average performance rating for the past 3 years and number ofrelevant certificationsAnnual salary vs. years of service and number of relevant certificationsAnnual salary vs. average performance rating for the past 3 years, years of serviceand number of relevant certificationsHint: Refer to the handouts posted on Blackboard pertaining to interpreting regressionstatistics in order to determine if a given regression model is acceptable. This samehandout also provides guidance regarding how to select a preferred regression modelfrom amongst multiple acceptable regression models, including models with differingnumbers of independent variables.Hint: For the purposes of this homework assignment, the minimum difference betweenthe R2 or Adjusted R2 values for two acceptable models with differing numbers ofindependent variables that would favor selecting the model with the larger number ofindependent variables is 0.03. Please ensure that you fully understand the process forselecting a preferred model before attempting to apply this criterion.Hint: Question 19 is intended to have you demonstrate that you understand how todetermine which univariate models are acceptable, and then select a preferred univariatemodel from amongst the acceptable univariate models. Question 20 is intended to haveyou demonstrate that you understand how to determine which bivariate models areacceptable, and then select a preferred bivariate model from amongst the acceptablebivariate models. Question 21 is intended to have you demonstrate that you understandhow to select a preferred model from amongst multiple acceptable models that havediffering numbers of independent variables. Question 22 is intended to have youdemonstrate that you understand how to determine if the trivariate model is acceptable,and then select a preferred model from amongst multiple acceptable models.Hint: For questions 24 and 25, you need to use the regression equation associated withthe preferred model selected for question 22 in order to calculate the predicted salary foreach of the 24 employees. In order to answer questions 24 and 25 you need to keep inmind that the predicted salary value for each employee is only a point estimate (thisconcept was discussed in week one relative to the mean). While a point estimate is aprecise value, it is not necessarily an accurate value since the standard error value tells usthere is some potential degree of error associated with using the preferred regressionmodel to predict salary values. In order to answer questions 24 and 25 you will need tocreate an interval estimate (this concept was also discussed during week one relative tothe mean) for the predicted salary for each of the 24 employees. To calculate the intervalestimate for each employee, simply multiply the standard error value for the preferredregression model by 1.5 and then subtract this value from the predicted point estimatesalary value to define the lower limit of the interval estimate and add this value to thepredicted point estimate salary value to define the upper limit for the interval estimate.Once you have created an interval estimate for each employee, you will then need tocompare each employee's current salary to their corresponding interval estimate in orderto determine if each employee's current salary falls within their predicted intervalestimate.Use the results for the univariate regression analysis for annual salary vs. averageperformance rating for the past 3 years in order to answer questions 1 through 14.1. What is the degree of correlation between the dependent variable and the independentvariable?o 0.8198o 0.6672o 0.7862o 0.65232. Does the regression model confirm a positive correlation between the dependentvariable and the independent variable as hypothesized?o Yeso No3. What is the desired statistical significance for the regression model?o 0.00o 0.01o 0.05o 0.104. Is the statistical significance of the model as a whole less than the desired statisticalsignificance for the regression model?o Yeso No5. What is the actual confidence level for the regression model as a whole?o 99.97%o 95%o 90.5%o 80.2%6. Is the statistical significance of the linear relationship between the dependent andindependent variables less than the desired statistical significance for the regressionmodel?o Yeso No7. Should the coefficient of determination or adjusted coefficient of determination beused to evaluate this regression model?o Coefficient of determinationo Adjusted coefficient of determination8. What percentage of the observed variation between the actual values of the dependentvariable and the mean value of the dependent variable in the sample data set isexplained by the regression model?o 44.51%o 66.72%o 41.99%o 76.24%9. What is the amount by which we will be off on average when predicting values forthe dependent variable using the regression model?o $12,287o $32,966o $4,169o $25,89610. What is the coefficient for the y-intercept for the regression model?o 39.38o 19.94o 12.29o 2.9611. What is the coefficient for the independent variable for the regression model?o 63.08o 4.52o 12.29o 2.9612. What is the point estimate for the predicted salary for an employee with an averageperformance rating of 3.9?o $71,562o $57,006o $41,299o $50,89613. What is the interval estimate for the predicted salary for an employee with an averageperformance rating of 3.9 based upon taking into consideration the standard error?o $61,913 - $71,562o $57,006 - $64,159o $52,837 - $61,175o $54,896 - $60,87314. What is the 95% confidence level interval estimate for the salary for an employeewith an average performance rating of 3.9?o $60,265 85,789o $75,412 - $78,523o $40,636 - $73,376o $65,141 - $72,269Perform a correlation analysis between the dependent variable and each of the threeindependent variables. Use the results of the correlation analysis to answer questions 15and 16.15. Which independent variables evidence a positive correlation with the dependentvariable?o Average performance rating for the past 3 yearso Years of serviceo Number of relevant certificationso All of the aboveo None of the above16. Which independent variable evidences the highest degree of correlation with thedependent variable?o Average performance rating for the past 3 yearso Years of serviceo Number of relevant certificationso All of the aboveo None of the abovePerform a correlation analysis between each of the three pairs of independent variables.Use the results of the correlation analyses to answer question 17.17. Which pair of independent variable evidences a degree of collinearity that should because for concern when performing multivariate linear regression (i.e., evidences adegree of correlation in excess of 0.5)?o Average performance rating for the past 3 years vs. years of serviceo Average performance rating for the past 3 years vs. number of relevantcertificationso Years of service vs. number of relevant certificationso All of the aboveo None of the aboveUse the regression statistics pertaining to all seven regression analyses in order to answerquestions 15 through 23.18. Of the seven regression models, which model both accounts for the lowest percentageof the observed variation between the actual values of the dependent variable and themean value of the dependent variable in the sample data set and evidences the highestdegree of error for predicting values for the dependent variable?o Annual salary vs. average performance rating for the past 3 yearso Annual salary vs. years of serviceo Annual salary vs. number of relevant certificationso Annual salary vs. average performance rating for the past 3 years and years ofserviceo Annual salary vs. average performance rating for the past 3 years and numberof relevant certificationso Annual salary vs. years of service and number of relevant certificationso Annual salary vs. average performance rating for the past 3 years, years ofservice and number of relevant certifications19. If you were to consider only the three regression models that are based upon a singleindependent variable, which of the following models would be your preferred model?o Annual salary vs. average performance rating for the past 3 yearso Annual salary vs. years of serviceo Annual salary vs. number of relevant certifications20. If you were to consider only the three regression models that are based upon twoindependent variables, which of the following models would be your preferredmodel?o Annual salary vs. average performance rating for the past 3 years and years ofserviceo Annual salary vs. average performance rating for the past 3 years and numberof relevant certificationso Annual salary vs. years of service and number of relevant certifications21. If you were to compare the preferred regression model based upon a singleindependent variable with the preferred regression model based upon twoindependent variables, which model would be preferred overall?o Preferred regression model based upon a single independent variableo Preferred regression model based upon two independent variables22. When you consider all seven regression models, which is the overall preferred regression model?o Annual salary vs. average performance rating for the past 3 yearso Annual salary vs. years of serviceo Annual salary vs. number of relevant certificationso Annual salary vs. average performance rating for the past 3 years and years ofserviceo Annual salary vs. average performance rating for the past 3 years and numberof relevant certificationso Annual salary vs. years of service and number of relevant certificationso Annual salary vs. average performance rating for the past 3 years, years ofservice and number of relevant certifications23. Do any of the regression models offer a higher confidence level for the model as awhole, or a lower standard error in comparison to the overall preferred model?o Yeso NoThe personnel is interested in comparing each employees actual salary to their predictedsalary in order to determine if there are any prevailing salary inequities. Suppose thepersonnel director considers an employees current salary to be fair and reasonable if it iswithin plus or minus 1.5 standard errors of the value estimated by the regression modelselected in response to question 22. For each individual employee, calculate his or herestimated salary using the regression model selected in response to question 22, as wellcalculate his or her upper and lower limits for a fair reasonable salary, in order to answerquestions 24 and 25.24. Of the 24 employees, how many employees current salary is below what isconsidered fair and reasonable?o0o1o2o3o4o525. Of the 24 employees, how many employees current salary is above what is considered fair and reasonable?ooooo12345

 

Paper#52255 | Written in 18-Jul-2015

Price : $29
SiteLock