Doug wanted to use simple linear regression to study the relation between the time to complete a marathon (in hours) (Y) and the fluid intake (in ml) during the race (X). Based on the same data set, he estimated two models. Model 1: X₁ = total amount of fluid intake; Y = .00028X₁ + 3.97. R₁² = .014. Model 2: X₂ = amount of fluid intake per hour; Y = -.0052X₂ + 7.84. R₂² = .65. Suppose for both models, all assumptions for linear regression are satisfied. Compare the two models. A) Doug should use model 1, because the correlation between X₁ and Y is stronger than that between X₂ and Y (b_YX₁ b_YX₂). B) Doug should use model 2, because it gives more accurate prediction of Y (the finishing time) than model 1 (R₁²

Question

Doug wanted to use simple linear regression to study the relation between the time to complete a marathon (in hours) (Y) and the fluid intake (in ml) during the race (X). Based on the same data set, he estimated two models. Model 1: X₁ = total amount of fluid intake; Y = .00028X₁ + 3.97. R₁² = .014. Model 2: X₂ = amount of fluid intake per hour; Y = -.0052X₂ + 7.84. R₂² = .65. Suppose for both models, all assumptions for linear regression are satisfied. Compare the two models. A) Doug should use model 1, because the correlation between X₁ and Y is stronger than that between X₂ and Y (b_YX₁ > b_YX₂). B) Doug should use model 2, because it gives more accurate prediction of Y (the finishing time) than model 1 (R₁² < R₂²). C) Doug should use model 1, because model 2 will give unreasonable (negative) predicted values of Y when X is large. D) Both models are problematic, because the units of X are different from the unit of Y.

Quizplus · Accepted Answer

Model 2 is preferred because it has a higher R-squared value (0.65) compared to model 1 (0.014), indicating a stronger relationship between the variables and thus a better fit for predicting Y.

Doug Wanted to Use Simple Linear Regression to Study the Relation