Suppose You Are Interested in Estimating How the Test Scores

Essay

Suppose you are interested in estimating how the test scores of elementary schools are related to average class size,parents education level (in years),and percent of English learners at the school.To do so,you collect a sample of 200 California public schools and specify the following model: $$\text { Score } = \beta _ { 0 } + \beta _ { 1 } \text { Class Size } + \beta _ { 2 } \text { Education Level } + \beta _ { 3 } \text { Percent English Learners } + \varepsilon$$
Suppose you are concerned that the proposed model needs higher order polynomials.
a)Initially you believe that class size is the only variable that should be entered as a higher order polynomial.Propose a new model and explain how you would test for this possibility.
b)After thinking about it,you believe that all of the independent variables may need to be entered in as a higher order polynomial.What type of test would you perform? Describe the steps you would take to implement this test.
c)Now instead you believe that the model estimated above is not appropriate and a better model would be $$\ln ( \text { Score } ) = \beta _ { 0 } + \beta _ { 1 } \text { Class Size } + \beta _ { 2 } \text { Education Level } + \beta _ { 3 } \text { Percent English Learners } + \varepsilon$$
How would you test between the initial model and this model? Be as specific as possible.