Like every other business, insurance companies seek to minimize expenses associated with doing business to enhance profitability. To study expenses, we examine a random sample of 350 insurance companies from the National Association of Insurance Commissioners (NAIC) database of over 3,000 companies. The NAIC maintains one of the world's largest insurance regulatory databases; we consider here data that is based on 2005 annual reports for all the property and casualty insurance companies in United States. The annual reports are financial statements that use statutory accounting principles. The table below provides a description of the variables considered in this problem

Variable	Description
EXPENSES	Total expenses incurred in millions of dollars
AGENTWAGE	Annual average wage of the insurance agent in thousands in dollars
LONGLOSS	Losses incurred for long tail lines in millions of dollars
SHORTLOSS	Losses incurred for short tail lines in millions of dollars
GPWPERSONAL	Gross premium written for personal lines in millions of dollars
GPWCOMM	Gross premium written for commercial lines in millions of dollars
LIQUIDRATIO	The ratio of the liquid assets to the current liabilities level

a. Based on the scatterplot charts (in Appendix 1), which variables seem to be potential predictors for expenses? Justify b. To develop regression models and assess their prediction performance, the dataset is divided into training (70%) and validation data (30%). A regression model (Model 1) with all predictors is considered. The estimates are reported in Appendix 2. What predictors are significant? Justify c. Another regression model (Model 2) that excludes insignificant predictors was estimated and its coefficients are reported in Appendix 2. Compare Model 1 and Model 2 (prediction performance of each model is reported in Appendix 3). Which model would you select to implement? Justify d. Interpret the coefficients of the selected model e. Discuss the implication of your findings for practitioners and the broader literature on the topic. Mention any limitations to this analysis

Appendix 1 Simple Scatter of EXPENSES by AGENTWAGE Simple Scatter of EXPENSES by LONGLOSS 12000060 EXPENSES BODICE EXPENSES DOOMED 30203010 121 10020020 -3:00010E-1 2001006-1 4010806-1 B DOODOOE- 100OWED AGENTWAGE LONGLOSS Simple Scatter of EXPENSES by SHORTLOSS Simple Scatter of EXPENSES by GPWPERSONAL 1.200PECD EXPENSES EXPENSES 301006-1 1 0090 SHORTLOSS GPWPERSONALSimple Scatter of EXPENSES by LIQUIDRATIO Simple Scatter of EXPENSES by GPWCOMM EXPENSES EXPENSES 3003DE-4 1240106040 0 2020CO 0.20000-0 GPWCOMM LIQUIDRATIOAppendix 2 Model 1: ANOVA Model Sum of Squares dif Mean Square F Sig. Regression 4.105 684 567.241 DO0 Residual 270 224 .001 Total 4.375 230 Model1: Coefficients Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta Sig. (Constant) -.005 023 202 840 AGENTWAGE -0.280E-5 -.006 -.382 .717 LONGLOSS 628 073 135 8.636 SHORTLOSS 130 058 121 2 254 025 GPWPERSONAL 081 026 088 2.348 020 GPWCOMM .153 013 408 11.308 .0DO LIQUIDRATIO 000 DO0 017 1.032 303 Model 2: Coefficients Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta Sig. (Constant) 001 002 219 827 LONGLOSS 828 072 435 8.701 000 SHORTLOSS 132 058 123 2 288 023 GPWPERSONAL 061 026 089 2.370 019 GPWCOMM .152 013 -406 11.384 0DOAppendix 3 Model 1: Residuals Statistics split = 1 (Selected) split ~= 1 (Unselected) Std Std. Minimum Maximum Mean Deviation N Minimum Maximum Mean Deviation N Predic 1.1430120E 5.082168 1.335806 23 8.200752 3.603823 9.509169 11 ted 1.178080 +000 PE-002 70E-001 9.433021 7E-001 2E-002 18E-002 Value 4E-002 BE-003 Resid 1.80451155 3.427210 23 1.882883 1.203860 2.426716 11 ual 2.045121 E-001 3.801372 77E-002 1 5.217381 72E-001 40E-003 51E-002 10E-001 40E-017 04E-002 Std. -.460 8.182 .000 1.000 23 -.451 5.758 -.111 712 11 9 Predic ted Value Std. -5.880 5.196 087 23 -1.502 5.364 .035 690 11 Resid ual Model 2: Residuals Statistics split = 1 (Selected) split ~= 1 (Unselected) Std. Std. Minimum Maximum Mean Deviation N Minimum Maximum Mean Deviation N Predic 5.580090 1.14249178 5.082168 1.335686 23 8.105067 3.574076 9.508410 11 ted 4E-004 +000 DE-002 48E-001 1 8.054868 18-001 BE-002 23E-002 Value 5E-003 Resid 1.81204200 3.435784 23 1 872814 1.482324 2.426072 11 jen 2.052620 E-001 2.506828 37E-002 1 5.107269 03E-001 47E-003 21E-002 05E-001 48E-017 44E-002 Std. -.378 8.173 000 1.000 23 -.441 5.756 -.113 712 11 Predic ted Value Sid. -5.922 5.228 000 091 23 -1.474 5.403 043 700 11 Resid Jen