Question

III.    Texas Southern University ‘s housing department has collected the following information for the

          Past 8 semesters.

             

         

	University	Number of
Semester	Enrollment	Units leased
	(1000)'s
1	7.2	291
2	6.3	228
3	6.7	252
4	7	265
5	6.9	270
6	6.4	240
7	7.1	258
8	6.7	246

a)Compute the regression equation.

b)Interpret a and b in the context of this problem.

Answer 1

a. Here the equation will be in the form: y = a+bx , where y = no. of units leased and x = university enrolments

We will first compute "b" and then "a"

b = n*(sum of x*y) - (sum of x*sum of y)/n*(sum of x^2) - (sum of x)^2

a = sum of y - (b*sum of x)/n

n = 8

	x	y	x*y	x^2
	7.20	291.00	2,095.20	51.84
	6.30	228.00	1,436.40	39.69
	6.70	252.00	1,688.40	44.89
	7.00	265.00	1,855.00	49.00
	6.90	270.00	1,863.00	47.61
	6.40	240.00	1,536.00	40.96
	7.10	258.00	1,831.80	50.41
	6.70	246.00	1,648.20	44.89
Total	54.30	2,050.00	13,954.00	369.29

Thus b = (8*13954 - 54.3*2050)/(8*369.29 - 54.30^2)

= 317/5.83

= 54.37

a = (2050-54.37*54.30)/8

= -902.5/8

= -112.81

Thus the regression equation is: y = -112.81+54.37x

b. In this context "a" is the intercept point of the regression line which is in the y axis. So when x is 0 y will be -112.81

"b" is the slope of the regression line and is also known as regression coefficient. Here b is 54.37 and this means that as the value of x variable inceases by 1 the value of y variable will increase by 54.37.