Question

A multiple linear regression model of healthcare charges (Y) on BMI (a continuous variable), Smoking Status (A categorical variable where 1=Smoker, 0 = Non-smoker), and their interaction is shown below. (The same as Slide 12 from the handout on Regression-Part 3). Use this to estimate the difference in costs due to smoking for a person with a BMI of 25. I.e. if a person has a BMI of 25, how much greater would the estimated costs be if they were a smoker versus a non-smoker? (please round your answer to the nearest whole number) SUMMARY OUTPUT Regression Statistics Multiple R 0.859 R Square 0.737 Adjusted R Square 0.736 Standard Error 6212 Observations 1200 ANOVA df SS MS F Significance F Regression 3 1.29E+11 4.31E+10 1.12E+03 0 Residual 1196 4.62E+10 3.86E+07 Total 1199 1.76E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5591 1063 5.262 0.000 3506 7676 BMI 94 34 2.762 0.006 27 161 Smoker -18450 2248 -8.207 0.000 -22861 -14040 BMI*Smoker 1368 72 19.092 0.000 1228 1509

Answer 1

To estimate the increase in healthcare costs due to smoking for a person with a BMI of 25 using multiple linear regression, the difference is calculated as 5898 (rounded to the nearest whole number).

Step-by-step explanation:

To estimate the difference in healthcare charges due to smoking status for a person with a BMI of 25 using multiple linear regression, you need to use the coefficients given for each term in the model.

The regression equation is of the form Y = Intercept + (BMI coefficient × BMI) + (Smoker coefficient × Smoker) + (BMI*Smoker interaction coefficient × BMI × Smoker).

From the summary output, we have:

• The Intercept is 5591.
• The BMI coefficient is 94.
• The smoker coefficient is -18450.
• The BMI*Smoker interaction coefficient is 1368.

Using the regression equation:

• For a non-smoker with a BMI of 25, Y = 5591 + (94 × 25) = 7941.
• For a smoker with a BMI of 25, Y = 5591 + (94 × 25) + (-18450) + (1368 × 25) = 13839.

The estimated cost difference due to smoking for a person with a BMI of 25 is 13839 - 7941 = 5898 (rounded to the nearest whole number).