Suppose you wish to explain variation in body mass index (BMI)by variation in height (in inches)by estimating the model $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$
And you suspect heteroskedasticity of the form $\operatorname { Var } ( \varepsilon ) = \sigma ^ { 2 } \text { Height } _ { i } ^ { 4 }$
)You could perform Weighted Least Squares by estimating the model
A) $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$ .
B) $\text { BMI } _ { i } / \text { Height } _ { i } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } \right) + \beta _ { 1 }$ .
C) $B M I _ { i } / \text { Height } _ { i } ^ { 2 } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } ^ { 2 } \right) + \beta _ { 1 } \left( 1 / \text { Height } _ { i } \right)$ .
D) $1 = \beta _ { 0 } \left( 1 / B M I _ { i } \right) + \beta _ { 1 } \text { Height } _ { i } / B M I _ { i }$ .

Question

Quizplus · Accepted Answer

Weighted Least Squares (WLS) is used when heteroskedasticity is present in the data. It involves weighting the observations so that each observation makes a proportional contribution to the model fit. In this case, the heteroskedasticity is of the form Var(ε)=σ2Heighti4, which suggests that observations with larger values of Heighti have higher variances. To perform WLS, we need to weight the observations by 1/Heighti2, which means dividing both sides of the model equation by Heighti2. This leads to the model BMIi/Heighti2 = β0(1/Heighti2) + β1(1/Heighti), which is equivalent to choice C. Therefore, C is the best choice for performing WLS on this model.

Suppose You Wish to Explain Variation in Body Mass Index BMIi=β0+β1 Height iB M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }BMIi​=β0​+β1​ Height i​

Suppose You Wish to Explain Variation in Body Mass Index $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$