Answer to Question #286569 in Statistics and Probability for Xek

Question

Survey tests on leadership skills and on self-concept were administered to student-leaders. Both tests use a 10 point Likert Scale with 10 indicating the highest score for each test. Predict the leadership skill of a student leader whose self-concept skill is 1.5. Scores for the student-leaders on the tests follow

Student Code A B C D E F G H I J

Self-concept 9.5 9.2 6.3 4.1 5.4 8.3 7.8 6.8 5.6 7.1

Leadership Skill 9.2 8.8 7.3 3.4 6.0 7.8 8.8 7.0 6.5 8.3

Answer 1

Following is the regression equation to predict the leadership skill:

$Y=a+bX$

Where;

$b=\frac{n\Sigma XY-\Sigma X \Sigma Y}{n\Sigma X^2-(\Sigma X)^2}$

$a=\frac{\Sigma Y-b\Sigma X}{n}$

The table below summarizes the calculation of inputs:

$b=\frac{(10\times537)-(70.1\times73.1)}{(10\times518.29)-(70.1)^2}=0.914$

$a=\frac{73.1-(0.914\times70.1)}{10}=0.905$

Then, regression equation is:

$Y=0.905+0.914X$

If self-concept skill of a student is 1.5. Scores for the student-leaders then his leadership skill is:

$Y=0.905+(0.914\times1.5)=2.28$