It has been well documented that wages of employees increase as employees gain experience and become more valuable on the labour market. However, wage increases vary a lot depending on employer's remuneration policies, employee's profession, education, and experience, and many other factors. A labour union analyst wants to examine part of the picture by looking at how length of service (LOS) relates to wages among their members. The Assign4Data.xlsx file gives data on LOS in months and wages in thousands of dollars for 60 union members. Treating this data as random sample data from the labour union membership, answer the following questions. c) Produce a scatter plot of standardized (or studentized) residuals vs predicted values for the regression (include your StatCrunch output). Which two model assumptions can be checked with this kind of plot? Comment on the validity of these 2 model assumptions (StatCrunch). Remove any observation displaying a standardized residual of more than 2 in the initial model in b) above and run a new regression model; from now on, use the results of this new model to answer the remaining questions. d) Write the new observed regression equation that predicts wages from length of service and report as to how well this new model fits the data (plot of residuals). How does this new model compare with the first model (r², s and F-Stat and t-Stat (include your StatCrunch output)? (StatCrunch). e) Test the significance of the regression slope 1 at the 5% level (use the critical value approach) and interpret it's meaning (specify the units of the coefficient). Make sure to provide hypotheses, test statistic, critical value, decision with justification. (StatCrunch) f) Calculate a 95% confidence interval for the regression slope 1 in part e) above and comment on the consistency of the interval with respect to your conclusion in e) above? (Manual Calculation) g) Compute a 95% confidence interval for the mean wage (in thousands of dollars) of union members with 10 years of service. (You can use summary results from the ANOVA table of the regression; provide a StatCrunch output that confirms your results.) (Manual Calculation).

It has been well documented that wages of employees increase as employees gain experience and become more valuable on the labour market. However, wage increases vary a lot depending on employer's remuneration policies, employee's profession, education, and experience, and many other factors. A labour union analyst wants to examine part of the picture by looking at how length of service (LOS) relates to wages among their members. The Assign4Data.xlsx file gives data on LOS in months and wages in thousands of dollars for 60 union members. Treating this data as random sample data from the labour union membership, answer the following questions. c) Produce a scatter plot of standardized (or studentized) residuals vs predicted values for the regression (include your StatCrunch output). Which two model assumptions can be checked with this kind of plot? Comment on the validity of these 2 model assumptions (StatCrunch). Remove any observation displaying a standardized residual of more than 2 in the initial model in b) above and run a new regression model; from now on, use the results of this new model to answer the remaining questions. d) Write the new observed regression equation that predicts wages from length of service and report as to how well this new model fits the data (plot of residuals). How does this new model compare with the first model (r², s and F-Stat and t-Stat (include your StatCrunch output)? (StatCrunch). e) Test the significance of the regression slope 1 at the 5% level (use the critical value approach) and interpret it's meaning (specify the units of the coefficient). Make sure to provide hypotheses, test statistic, critical value, decision with justification. (StatCrunch) f) Calculate a 95% confidence interval for the regression slope 1 in part e) above and comment on the consistency of the interval with respect to your conclusion in e) above? (Manual Calculation) g) Compute a 95% confidence interval for the mean wage (in thousands of dollars) of union members with 10 years of service. (You can use summary results from the ANOVA table of the regression; provide a StatCrunch output that confirms your results.) (Manual Calculation).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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