I. Baseball has been called the national pastime in the United States. The Natio

Question

I. Baseball has been called the national pastime in the United States. The National League started play in 1876 and the American League started play in 1901. There have been countless minor league teams over the years. Keeping individual stats on each player is a fun thing to do and every team kees several stats on each player. Some of those stats are Batting Average, runs scored, runs batted in, errors made and many many more. In this study we are going to look at two regression models to predict a player’s batting average. The first model will have the following variables for a full season of play in the year 2016.

Y = batting average (BA)

X1 = games played (G)

X2 = number of times at bat (AB)

X3 = total number of hits (H)

X4 = times a player struckout (K)

X5 = an indicator variable for minor league (X5 = 1) vs major league (X5 =0)

Data was selected for the 9 position players of the Fargo-Moorhead Redhawks (a minor league team) and the Minnesota Twins of the American League.  

The regression model is y=0+1X1+2X2+3X3+4X4+5X5+y=0+1X1+2X2+3X3+4X4+5X5+

Now using the SAS output we will test this model as being useful and then add some more variables.

Linear Regression Results: BASEBALL STATS

The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: Y BA

H0=1=2=3=4=5=0Ha:H0=1=2=3=4=5=0Ha: at least one 00

1. In testing if this model is useful what is the value of the test statistic?

18.95
41.54
3.33
1.96

2. What is the correct decision? Reject H0 or do not reject H0.

Reject
Don't reject

3. What is the conclusion?

This model is useful.
This model is not useful.
None of these

Y (BA) X1 (G) X2 (AB) X3 (H) X4 (K) X5 (team) 0.293 97 406 119 75 1 0.269 98 398 107 90 1 0.259 100 390 101 95 1 0.219 53 183 40 37 1 0.270 41 111 30 25 1 0.291 97 364 106 99 1 0.280 97 396 111 111 1 0.316 99 433 137 87 1 0.261 134 494 129 93 0 0.258 103 345 89 48 0 0.268 155 615 165 138 0 0.236 116 437 103 178 0 0.296 91 371 110 58 0 0.269 92 335 90 91 0 0.235 113 396 93 93 0 0.225 92 298 67 118 0

Explanation / Answer

1. From the given ANOVA summary output,

Test statistic = 41.54

Option B is correct.

2. Since p - value is very small, we reject the null hypothesis.

3. This model is useful.

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