Answer to Question #269850 in Statistics and Probability for Matilda

Question

a study was conducted to determine if a linear relationship exist between math 31(y) grades and math 1(x). the grades of 6 randomly selected students from the college of business administration were obtained and the data are shown below.

Math 31 grade (y)

1.5

3.0

1.75

2.0

2.5

1.25

Math 1 grade (x)

2.0

2.50

2.25

1.75

2.0

1.75

a) Plot the scatter diagram for the given data.

b) Estimate the simple regression equation.

c) Estimate math 31 grade when the math 1 is 2.25.

Answer 1

a) Scatter diagram

b) Simple regression equation

$y=bX+a$

Where;

a = intercept

b = slope coefficient

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

$a=\frac{[(12)(25.4)-(12.3)(25.1)]}{[6(25.4)-(12.3)^2]}=-0.9878$

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

$b=\frac{[(6)(25.1)-(12.3)(12)]}{[6(25.4)-(12.3)^2]}=1.4634$

Regression equation is:

$y=1.4634X-0.9878$

c) Prediction of math 31 grade

If the math 1 grade is 2.25 then math 31 grade will be:

$y=1.4634*2.25-0.9878$

$y=2.30$