STAT802 – Lab exercises.STAT802 – Lab exercises – Model answers – Q1Exercise 1. Consider the data set ‘binary.csv’.The data set has a binary variable called admit, which is equal to 1 if the individual was admittedto graduate school, and 0 otherwise. There are three predictor variables: gre, gpa, and rank. Wewill treat the variables gre and gpa as continuous. The variable rank takes on the values 1 through4. Institutions with a rank of 1 have the highest prestige, while those with a rank of 4 have thelowest. We start out by looking at some descriptive statistics.Objective 1: To determine to extent to which gpa can be used to predict gre scores, consideringwhether the individual was admitted to graduate school. Then, explore the influence of thevariable rank w.r.t gpa only.Objective 2: To propose a modelling framework to investigate the chances to be admitted toschool upon: gre, gpa, and rank. In other words, to use gre, gpa, and rank to predict admit.Question 1- Regarding Objective 1:a) Perform data exploration. Use, e.g., PROC BOXPLOT, PROC FREQ or PROC TABULATE.Write down 5 – 6 sentences summarizing your results (No Executive summary required).b) Propose a proper regression model to address this objective. Justify your answer.c) Write down the theoretical model. Derive the reduced models.d) Estimate the model using SAS. Write down the estimated model.e) Write down an executive summary.ANSWERS:a) The data set contains 400 observations (prospective students) and four variables: admit, gpa,gre, and rank. The variables are read in properly by SAS (according to PROC CONTENTS).Nearly 15% of the observations come from Rank 1 Institutions (highly prestigious), 38% belongto Rank 2, around 30% are from Rank 3 institutions and 17% are ranked 4. Also, according to thedata, nearly 69% of the individuals were admitted to the graduate school.COMPLETE THE ANSWER for a) – Do it yourselfb) Regression models for prediction (predictive regression models), as we want to assess theability of gpa scores, admission to graduate school, and institution’s rank to predict GPA scores–An ordinary regression model with normal errors is proposed initially.A few notes (justifying):1) We have been asked to “explore the influence of the variable rank w.r.t gpa only”. Whilethis may be confusing, it simply refers to look at the way the variables ‘rank’ and ‘gpa’interact in the model. Put another way: Does the GRE difference by rank differ based onGPA level? This means to explore the effect of GPA over GRE across the differentinstitution ranks(variable ‘rank’). For this reason, (solution) the interaction between theinstitution’s rank and GPA will be added to the model.2) We have been asked to “consider whether the individual was admitted to ‘graduateschool’”. This means to check the degree to which the model GRE ~ GPA is altered in thepresence of the variable ‘admit’. Many books refer to this addition to the model asSTAT802 – Week 3 Model Answers – Q1 Due: —STAT802 – Lab exercises – Model answers – Q1“exploring the relationship between GPA and GRE adjusted by the variable ‘admit’ “ andrefer to these additional variables (such as ‘admit’) as ‘covariates’.Solution: The variable ‘admit’ will be added to the linear predictor as COVARIATE.c) Theoretical full modelGRE | x =The post STAT802 – Lab exercises appeared first on My Assignment Online.STAT802 – Lab exercises
