Question

In: Statistics and Probability

To test whether extracurricular activity is a good predictor of college success, a college administrator records...

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

Extracurricular
Activity
College
Freshman GPA
Yes 3.57
Yes 3.34
Yes 3.90
Yes 3.67
No 3.00
No 3.88
No 3.45
No 2.80
No 3.90
No 2.82

A) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)

_____

Solutions

Expert Solution

Answer:

Given that,

To test whether the extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

Extracurricular Activity College Freshman GPA
Yes 3.57
Yes 3.34
Yes 3.90
Yes 3.67
No 3.00
No 3.88
No 3.45
No 2.80
No 3.90
No 2.82

(A).

Code the dichotomous variable and then compute a point-biserial correlation coefficient:

First converting Yes to 1 and No to 0 we get,

x y
1 3.57 0.6 0.137 0.36 0.0188 0.0822
1 3.34 0.6 -0.093 0.36 0.0087 -0.0558
1 3.90 0.6 0.467 0.36 0.2181 0.2802
1 3.67 0.6 0.237 0.36 0.0562 0.1422
0 3.00 -0.4 -0.433 0.16 0.1875 0.1732
0 3.88 -0.4 0.477 0.16 0.1998 -0.1908
0 3.45 -0.4 0.017 0.16 0.0003 -0.0068
0 2.80 -0.4 -0.633 0.16 0.4007 0.2532
0 3.90 -0.4 0.467 0.16 0.2181 -0.1868
0 2.82 -0.4 -0.613 0.16 0.3758 0.2452
Total 4 34.33 2.4 1.684 0.736
Mean 0.4 3.433 SS_{x} SS_{y} SS_{xy}

The correlation coefficient (r)

=0.736/ 2.0104

=0.366096299

r= 0.366 (Approximately)

** Please do the comment for any doubt or clarification.


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