Consider a model to measure students\' performance (score) based on a number of
ID: 3201996 • Letter: C
Question
Consider a model to measure students' performance (score) based on a number of variables, These include school factors (average class size, per-student expenditure, total school enrolment) and student factors (family Income, mother's education and number of siblings). The model is: Score = beta_0 + beta_1Class_size + beta_2expenditure + beat_3 enrolment + beta_4fam_income + beta_5 mothers_educ + beta_6 siblings + epsilon State a null hypothesis to test if school specific factors have no effect on test scores, Using words, explain how you would test the hypothesis in part (a)?Explanation / Answer
Testing the Significance of a Model
An important application of the F-test is for what is called “testing the overall significance of a model.” Consider again the general multiple regression model with (K 1) explanatory variables and K unknown coefficients yt = 1 + 2xt2 + 3xt3 +…+ K xtK + et
• To examine whether we have a viable explanatory model, we set up the following null and alternative hypotheses H0: 2 = 0, 3 = 0,…, K = 0 H1: at least one of the K is nonzero
The null hypothesis has K 1 parts, and it is called a joint hypothesis. It states as a conjecture that each and every one of the parameters K, other than the intercept parameter 1, is zero. • If this null hypothesis is true, none of the explanatory variables influence y, and thus our model is of little or no value. If the alternative hypothesis H1 is true, then at least one of the parameters is not zero. The alternative hypothesis does not indicate, however, which variables those might be. • Since we are testing whether or not we have a viable explanatory model, the test for Equation (8.2.2) is sometimes referred to as a test of the overall significance of the regression model. • The unrestricted model is that given in Equation.
To test the joint null hypothesis H0: 2 = 3 =…= K = 0, which actually is K 1 hypotheses, we will use a test based on the F-distribution.
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