## Module 15: Practice problems for Interactions, dummy variables, F...

 Author Message NEAS Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K Module 15: Advanced interactions(The attached PDF file has better formatting.) Practice problems for Interactions, dummy variables, F tests(This posting covers Modules 14 and 15.)*Question 15.1: Hypothesis testing We use regression analysis to compare personal auto claim frequency in urban, suburban, and rural areas.Claim frequency = á + â1 D1 + â2 D2 + å, where D1 = 1 for urban and 0 otherwiseD2 = 1 for sub-urban and 0 otherwise　How do we show that territory (urban vs sub-urban vs rural) is significant?The t-values for both â1 and â2 are greater than their critical values.The t-value for either â1 or â2 is greater than its critical value.The t-values for both â1 and â2 are less than their critical values.The F-value for â1 plus â2 is greater than its critical value.The F-value for â1 plus â2 is less than its critical value.Answer 15.1: DBy "â1 plus â2" we mean the F test examining the combination of these two coefficients. Fox uses qualitative explanatory variables in many examples, just as actuaries use age, sex, and other attributes of the insured.*Question 15.2: ParametersWe regress personal auto claim frequency on (i) annual driving and (ii) urban, suburban, and rural areas.Claim frequency = á + â1 D1 + â2 D2 + â3 DD + å, where D1 = 1 for urban and 0 otherwiseD2 = 1 for sub-urban and 0 otherwiseDD = annual driving distance in kilometers What is the predicted difference in claim frequency for urban vs sub-urban insureds driving 30,000 kilometers a years?â1 + â2 + â3 × 30,000â1 – â2 + â3 × 30,000â1 + â2â1 – â2â1 D1 + â2 D2Answer 15.2: D*Question 15.3: Principle of marginalityAn actuary regresses personal auto claim frequency on (i) amount of driving, (ii) income of driver, and (iii) territory. Driving and income are quantitative explanatory variables, and territory is a qualitative factor with three levels: urban, sub-urban, and rural.Which of the following correctly reflects the principle of marginality?The income by territory interaction is marginal to the income effect.The amount of driving effect is marginal to the amount of driving by territory interaction.We do not test the income by territory interaction until we test the income effect.If we can rule out a main effect on theoretical grounds, we test the interaction effect.None of A, B, C, or D is true.Answer 15.3: B(P135)Fox emphasizes the principle of marginality. Some other textbooks do not discuss this topic. It is useful for actuarial analyses, which looks at the interactions of policyholder attributes. Attachments Fox Module 15 pps interactions, dummy variables, F tests df.pdf (1.5K views, 43.00 KB) kanaksharma Forum Newbie Group: Awaiting Activation Posts: 3, Visits: 2 Great share thanks for sharing this post with us. Gear Cutting Tools is the process of creating a gear.
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