Question

QUESTION 8 Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc + B2price + B3educ + B4female + u, E(ulinc, price, educ, female) = 0 and Var(ulinc, price, educ, female) = o inc. Which of the following transformed equation has a homoscedastic error term? a. beer = Bo + B1inc + B2price + B3educ + B4female + u b.beer/inc= Bo(1/inc) + B1(1/inc) + B2(price/inc-) + B3(educ/inc?) + B4(female/inc?) + (u/inc) OC beer/inc = Bo(1/inc) + B1 + B2 (price/inc) + B3(educ/inc) + B4(female/inc) + (u/inc) a beer/inc1/2 = Bo(1/ inc1/2) + B1(inc1/2) + B2(price/ inc1/2) +B3(educ/ inc1/2) + Ba(female/ inc1/2) + (u/inc1/2) QUESTIONS Refer to your text MEAPOO 01 data set (posted under the "Additional Resources" section of our course) and use Excel's regression data analysis tool or Stata to compute the answers to the questions asked. Consider the following regression model: math4 = Bo + Bilunch + Bzlog(enroll) + Bzlog(exppp) + u, where math4 is the percentage of 4th graders with satisfactory math grades, lunch is the percentage of students eligible for free or reduced price lunch, enroll is school enrollment and exppp is expenditures per pupil. Estimate the equation using the feasible GLS procedure based on equation (8.34) in your text. Based on this estimated equation, you predict that, if expenditures per pupil increase by 10%, the percentage of 4th graders with satisfactory math grades increase by percentage points. Let a = 5%. Based on this estimated equation, you conclude whether expenditures per pupil is statistically significant: . (NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. For your second answer, write either YES or NO. HINT: See Example 8.7.)

Answer 1

8) Considering a linear model to explain monthly beer consumption:

beer = β0 + β1inc + β2price + β3educ + β4female + u,

E(u|inc, price, educ, female) = 0,

With Var(u|inc,price,educ,female) = σ²inc² , h(x) = inc² , where h(x) is the heteroskedasticity function i.e, h(x) is a function of the explanatory variables that determines the heteroskedasticity (defined as Var(u|x) = σ²h(x)).

Hence, √h(x) = inc and

The transformed equation can be obtained by dividing the original equation by inc.

beer / inc = β0 (1 / inc) + β1 (inc / inc) + β2 (price / inc) + β3 (educ / inc) + β4 (female / inc) + u / inc

= β0 (1 / inc) + β1 + β2 (price / inc) + β3 (educ / inc) + β4 (female / inc) + u / inc

So you can see that β1 ( the slope on inc in the original model) is now a constant in the transformed equation. This is a consequence of the form of the heteroskedasticity and in the original equation, the functional forms of the explanatory variables.

So, the correct option is option c

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