Question

The following data set shows the entrance exam score​ (Verbal GMAT) for each of eight MBA students along with his or her grade point average​ (GPA) upon graduation. Calculate the slope and​ y-intercept for the linear regression equation for these data.

Calculate the slope and​ y-intercept for the linear regression equation for these data

GMAT   GPA
310   3.6
300   2.9
260   3.1
290   3.1
340   3.9
270   3.1
290   3.7
310   3.1

Answer 1

Solution:

Here, we have to find the values for y-intercept and slope of the regression line. The formulas for y-intercept and slope of regression line are given as below:

Slope = b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

y-intercept = a = Ybar – b*Xbar

The calculation table is given as below:

No.	x	y	xy	x^2	y^2
1	310	3.6	1116	96100	12.96
2	300	2.9	870	90000	8.41
3	260	3.1	806	67600	9.61
4	290	3.1	899	84100	9.61
5	340	3.9	1326	115600	15.21
6	270	3.1	837	72900	9.61
7	290	3.7	1073	84100	13.69
8	310	3.1	961	96100	9.61
Total	2370	26.5	7888	706500	88.71

From above table, we have

∑x = 2370

∑y = 26.5

∑xy = 7888

∑x^2 = 706500

∑y^2 = 88.71

n = 8

Xbar = ∑x/n = 2370/8 = 296.25

Ybar = ∑y/n = 26.5/8 = 3.3125

b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

b = (7888 - 8*296.25*3.3125)/( 706500 - 8*296.25^2)

b = 0.008519

Slope = b = 0.008519

a = Ybar – b*Xbar

a = 3.3125 - 0.008519*296.25

a = 0.788746

y-intercept = a = 0.788746