Suppose You Are Interested in Estimating How the Test Scores

question 5

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.

Apply knowledge of molecular structure to predict molecular shapes and angles.

Analyze molecular formulas to deduce structural features.

Understand the concept of hypothesis testing, including null and alternative hypotheses.

Interpret p-values and use them to make decisions about hypotheses.

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Definitions:

Critical Thinking

Diligently appraising and studying a situation to formulate an assessment.

Succesful Studying

The process of learning effectively, often involving techniques and strategies to understand and retain information efficiently.

Passionately Engaged

Describes being deeply involved or committed to an activity, cause, or subject with intense emotion or enthusiasm.

Shortcomings

The flaws or weaknesses in someone or something that prevent them from being perfect or completely effective.