John Smith did not report how much he smokes. We know only his values of the exp

Question

John Smith did not report how much he smokes. We know only his values of the explanatory variables in Model 1: price =100, income = 30, dadeduc = 12, momeduc = 12. We regressed the dependent variable smoke to transformed explanatory variables: dprice = price - 100, dincome = income - 30, ddadeduc = dadeduc -12, and dmomeduc = momeduc - 12. The results are: i. Give the point predictor of smoke for John Smith. ii. Give the 95% confidence interval predictor of E(smoke) for John Smith. iii. Give the 95% confidence interval predictor of smoke for John Smith.

Explanation / Answer

Part-i

Point prediction for John Smith

yhat=2.312461+0.0140*(100-100)-0.0203*(30-30)-0.1014*(12-12-0.3443*(12-12)

yhat=2.312461

Part-ii

For 95% confidence interval ,degree of freedom error=1195-4-1=1190 and critical t=1.96

95% confidence interval =yhat± t(0.05,1190)*se*sqrt(1/n+(x0-xbar)2/(n-1)sx2)

=2.312461±1.96*5.20652*sqrt(1/1195+0),as all predictors measured at mean

=(2.017258752            2.607663248)

For 95% prediction interval ,degree of freedom error=1195-4-1=1190 and critical t=1.96

95% prediction interval =yhat± t(0.05,1190)*se*sqrt(1+1/n+(x0-xbar)2/(n-1)sx2)

=2.312461±1.96*5.20652*sqrt(1+1/1195+0),as all predictors measured at mean

=( -7.896587089         12.52150909)

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.