Create a table for all output presented.Use copy-and-paste appropriately to include necessary R output into

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Computer Project 

We consider the 1992 baseball salary data set, , which is available from

This data set (of dimension 337 × 18 ) contains salary information (and performance measures) of 337 Major League Baseball players in 1992. More detailed information can be found at

The data set contains the following variables.

Table 1:  Variable Description for the 1992 Baseball Salary Data

Var	Columns	Description
salary	1 – 4	Salary (in thousands of dollars)
X1	6 – 10	Batting average
X2	12 – 16	On-base percentage (OBP)
X3	18 – 20	Number of runs
X4	22 – 24	Number of hits
X5	26 – 27	Number of doubles
X6	29 – 30	Number of triples
X7	32 – 33	Number of home runs
X8	35 – 37	Number of runs batted in (RBI)
X9	39 – 41	Number of walks
X10	43 – 45	Number of strike-outs
X11	47 – 48	Number of stolen bases
X12	50 – 51	Number of errors
X13	53	Indicator of “free agency eligibility”
X14	55	Indicator of “free agent in 1991/2”
X15	57	Indicator of “arbitration eligibility”
X16	59	Indicator of “arbitration in 1991/2”
ID	61 – 79	Player’s name (in quotation marks)

The data set can be input into R by reading directly from the website, with the following R commands:

baseball <- read.table(file= "", header = F,

col.names=c("salary", "x1", "x2", "x3", "x4", "x5",

"x6", "x7","x8", "x9", "x10", "x11", "x12", "x13", "x14", "x15", "x16", "ID"))

baseball$logsalary <- log(baseball$salary);

baseball <- baseball[, -c(1, 18)] # REMOVE salary AND ID head(baseball)

Complete the project by following the specific instructions given below.

1. Perform EDA on the data (exclude: x13 − x16) and describe any interesting observation.

2. Starting with the whole model that includes all predictors (i.e., X1, X2, . . . , X16), apply one model selection procedure of your choice to select your best model. Provide the fitting results from your ‘best’ model, i.e., the table of Parameter Estimates and the ANOVA table.

3. Suppose that we are interested in the following model:

Model I: log(salary) = β0 + β1x13 + β2x15 + β3x3 + β4x4 + ε. (1)

Fit Model I in (1) and output the two tables: Table of Parameter Estimates and the ANOVA table.

4. Use BIC to compare the best model that you found with Model I in (1). Which one is better according to BIC? (Hint: May use the R function BIC.)

5. Perform a test of H0 : β3 = β4 = 0 in Model I.

6. Given a player who has 80 runs (X3 = 80) and 120 hits (X4 = 120) in total and is eligible for arbitration (X15 = 1), but not free agency yet (X13 = 0), provide a 95% prediction interval for his salary based on Model I.

Some helpful tips for computer projects are listed below:

• Start early and don’t wait till the last day/minute;

Create a table for all output presented.Use copy-and-paste appropriately to include necessary R output into your final report;

• Remember to interpret every result that you present; • Place your R codes in an appendix.

• Submit your report and code in OneNote.

Attachments:

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