Question

n the table below, the x_i column shows scores on the aptitude test. Similarly, the y_i column shows statistics grades.

i) what is the nature of association between X and Y

ii) derive a relation between X and Y

iii) what is the predicted Statistics grade when Attitude score is 75

Student x_i y_i

1 95 85

2 85 95

3 80 70

4 70 65

5 60 70

Answer 1

In order to solve this question we use R software.

R codes and output:

> x=c(95,85,80,70,60)
> y=c(85,95,70,65,70)
> cor(x,y)
[1] 0.6930525
> fit=lm(y~x)
> fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
26.7808 0.6438

i.

Correlation coefficient = r = 0.693

Since correlation coefficient is positive and greater than 0.5, there is high degree positive association between X and Y.

ii.

Following regression equation describe relation between X and Y.

Y = 26.7808 + 0.6438 X

iii.

When Attitude score is 75 then Statistics grade is obtained as follows:

Y = 26.7808 + 0.6438 X

Y = 26.7808 + 0.6438 (75)

Y = 75.0658