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STA 137

Winter Quarter, 2019

Monday, January 7 Times series examples (Handout 1).

Wednesday, January 9 Review of regression (Handout 2).

Friday, January 11 Review of regression (Handouts 2 and 3).

Homework 1: Due on Friday, January 18

You may form a group of 3 students registered in this course and submit

one completed homework for the group. The front page should display only

the names of the students in the group. The actual work should start from the

second page

You will and a data set (JobProaciency) on the job prociency of 25 applicants

for entry level clerical positions in a government agency. The scores

on four tests (X1; X2; X3; X4) and the job proaciency scores (Y ) for the 25 applicants

are given in the data set. A multiple regression is to be ?tted to this

data

Yi = 0 + 1Xi1 + 2Xi2 + 3Xi3 + i4Xi4 + "i

; i = 1; : : : ; n = 25;

where f"ig are independent N(0; 2

) variables.

1. (a) Obtain a histogram for each of the variables. Are there noteworthy

features in the plots? Comment.

(b) Obtain a matrix plot of the data (ie, plot all the variables against each other

(R command: pairs)). Also obtain the correlation matrix. What do the plots

suggest about the nature of relationship between Y and each of the predictor

variables? Discuss. Does it seem that there is a problem of multicollinearity?

Explain.

(c) Fit a multiple regression model to the data. Obtain the parameter estimates,

their standard errors, analysis of variance table, R2 and R2

adj .

(d) Does it seem that all the independent variables need to be retained in the

regression model? If you consider deleting only one independent variable, which

is the best candidate for deletion? Explain your answers.

2. The questions here are on the atted model in (1c).

(a) Obtain a plot of the observed against the atted Y values. Also plot the

residuals against the atted values. Does it seem that the ?tted model is reasonable?

Do you suspect any nonlinearity? Is the assumption of equal variance of

the errors (ie, "iís) reasonable here? Explain your answers.

1(c) Obtain a histogram of the residuals. Also obtain a normal probability plot of

the residuals, and the correlation between the residuals and the normal scores.

Is the assumption of normality of the errors reasonable? Explain.

3. (a) This question is on model selection by backward elimination. Starting

with the full model, delete one variable at a time. At each step, drop the

variable that is the best candidate for deletion. In this way, you will have 5

models: the largest one with all 4 independent variables, and the smallest one

has none. For each model, and the AIC and BIC values. Find the best model(s)

selected by the AIC and BIC criteria. Fit these anal selected model(s), obtain

the parameter estimates, their standard errors, R2 and R2

adj .

(b) Use the AIC and the BIC criteria to select the best among all possible regression

models. Fit these anal selected model(s), obtain the parameter estimates,

their standard errors, R2 and R2

adj .