III. Texas Southern University ‘s housing department has collected the following
ID: 333063 • Letter: I
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.
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
Explanation / Answer
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
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.
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