Individual Assignment – Regression Case
The risk manager for Big Mac is undertaking a comprehensive analysis of the workers’ compensation injury claims for the firm’s U.S. operations. She has collected monthly data over the last three years with regard to workers’ compensation claims and several other items that she feels may be helpful in predicting future claims.
You are a consultant with a risk management consulting firm specializing in detailed quantitative analysis of problems facing corporate risk managers. Your firm has been retained by Big Mac to perform a comprehensive regression analysis of its workers’ compensation claims.
The data provided to you by Big Mac consists of the following information stored in the file data.XLS.
Variable Name Description of Variable
CLAIMS The number of workers’ compensation injury claims.
MALE The proportion of the work force that is male.
SAFETY The dollar amount of expenditures on safety programs in thousands.
SALES The dollar amount of gross sales in millions.
PARTTM The proportion of the work force that is part-time.
EMPLOYS The number of employees in thousands.
Before you start, please make sure you understand the underlying analytical techniques that you are using (regression analysis). In your written report, please address all of the following points and/or recommendations to the risk manager at Big Mac:
1. Before looking at the data, please use intuition to describe each variable’s probable predictive power and direction of relationship with CLAIMS.
2. Calculate and analyze the correlation matrix. Explain some of the more significant correlations between the independent variables and CLAIMS, as well as between the independent variables themselves. Please make sure to include in your report the correlation
table you obtain from Excel.
3. Perform a comprehensive regression analysis for CLAIMS. This includes calculation and analysis of coefficients, p-values (or t-values), coefficients of determination (R2), etc. Please make sure to include in your report the regression output from Excel including the following: Regression Statistics including R Square, Adjusted R Square, Standard Errors; as well as coefficient, standard error, p-value and t stat for all explanatory/independent variables.
4. Identify and describe the model (i.e., which independent variables should be included – a hint here, not all variables are necessarily needed, pending on statistical significance) that you feel best predicts CLAIMS. Justify the selection of this model from both conceptual and statistical viewpoints. This includes a statement of the identified model that a “non-statistician” could understand.
5. Is there an alternative model that is almost as good as your first choice as identified in your answer to number 4? If so, describe it.
6. State several managerial recommendations that you would make based on the model identified in number 4.
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