Hypothesis Testing for Multiple Regression
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University XYZ offers four different general programs of study, Science, Art, Business, and Social Sciences. They want to build a model to predict how well admissions candidates would perform if they were to be admitted to the university. In building the model, they collect the following information for 9 randomly sampled current students based on their original application to the university: high school GPA, SAT scores, program of study the candidate is applying to, and gender.
a) For the indicator variable "Application Program of Study" how many coefficients will you need in your regression equation?
b) The university decides to initially omit gender from the regression model. What is the regression equation?
c) Interpret the intercept.
d) Interpret the "Application Program of Study" coefficients.
e) Provide a 95% CI for the SAT score slope coefficient.
f) Predict the university GPA for current applicant to the Science program with a 3.4 High School GPA and 1520 SAT Score.
g) What percentage of the variation in university GPA is explained by the model?
h) At the 5% level of significance, is there evidence that the model helps explain university GPA.
i) Determine which of regression coefficients is significantly different from 0.