The independent variables shown are Sex, Age, Alcohol Use, Tobacco Use, and Exercise. Sheet 2 gives more detail on how these variables were defined. The dependent variable is Annual Health Care Cost. The second sheet gives the result of running Multiple Linear Regression on the data. At the bottom of that sheet, observe the equation that relates health care costs to the other variables. Answer the following questions: 1. When one of the independent variables changes by a single unit, the coefficient of that variable tells us how much the health care cost changes. 1a. For each increase in age by one year, by how many dollars and cents does the Annual Health Care Cost increase? 1b. Aside from sex, which of the variables has the greatest effect on Annual Health Care Cost? 1c. Interpret the change in Cost due to sex. 2. Why might the definitions of Alcohol Use and Tobacco Use need to be defined more carefully? That is, what assumptions do they seem to be making that might not be accurate? 3. Observe that even with all of these variables, R2 is only 0.395. This is a number between 0 and 1. This is the proportion of variance in the dependent variable accounted for by the entire regression model. What does this indicate about other potential (independent) variables? Sex, Age, Drink, Smoke, Ex Results SUMMARY OUTPUT OF MULTIPLE REGRESSION Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0,628821824 0.395416887 0.389592387 1577.103435 5251 ANOVA Significan 1.54147E-54 Regression Residual Total 519 3241 SS MS 844280800.5 16885616067.888553 1290885473 24872552 2135166273 Intercept Sex Age Alcohol Tobacco Exercise Conflict -3263.58558 509.271359 114,6584615 50.38626575 139,4140145 -271.269896 Standard Error Shar we 1059.163119 -3.0N1287 0.0021705 139,5653196 3.6489823 0.0002899 1245215591 9.2079205 8.17116E-1 10.27477864 4.9038785 0.0000013 17.338465 8.0197449 7.0837781 36 30048032 -7.472901335473E-1 Low 95% Up 598 ww 95.0 95.0 -5344359539 - 1182.812 -3344,36 -1182.812 235.0889888 783.45378 235.0899783,45378 90.1956367 139.12129 90.195637 139.12129 30.20099735 70.571534 30.200997 70.571534 105.26266 173.56537 105.26266 173.56537 -342.5838354 -199956-342.5838 -199.956 Equation: Y-3263.59 +509.27X1 + 114.66X2 + 50.39X3 + 139.41X4 - 271.27X5 Y - Annual Health Care Cost X1 Gender (0 Female: 1-Male) X2 - Age (years) X3 - Number of Alcobohc Drinks Per Week X4 - Number of Cigarettes Per Day X5 = Number of Hours of Weekly Exercise Sex Age, DrinkSmoke, Ex Results ON . + . - . . - . . - . *
