June 2008 exam – question 3

Consider the following five data points:

Y	-1	1	1	2.5	3.5
X	-1	0	1	2	3

Use regression analysis to calculate manually the estimated coefficients of equation Y = a + bX. [14 marks]
What is the predicted value of Y for X = 1.0 ? [3 marks]
What is the predicted value of Y for X = 3.5 ? [3 marks]

Comments [Hide]

Comment 4 @ 2008-09-01 10:51

Y= 0.35 + 1.05X
Answer B.
Y= 0.35 + 1.05 (1) = Predicted value =1.4
Answer C
Y = 0.35 + 1.05 (3.5)
Y = 0.35 +3.675= 4.025

Comment 3 @ 2008-09-01 10:44

Fellow students;

A very good source for simple linear regression equation( and many others) is availavle in the AIDB Quants text book called:
ISBN 0 273 643339
Essential Business Statistics Page 95

Comment 2 @ 2008-09-01 10:06

we need to find the value of a by first getting the value of b. On b and c you substitute for x to find y

Comment 1 @ 2008-09-01 10:00

X Y XY X sq
-1 -1 1 1
0 1 0 0
1 1 1 1
2 2.5 5 4
3 3.5 10.5 9
-----------------------------------------------------------
5 7 17.5 15

y=a + bx
Now calculate B.

b= n Sum xy - Sum X Sum y
----------------------------------
n Sum x sq - ( Sum X) squared

then do

A Sum Y - b Sum X
--------- ------------
n n

or a= average of Y - bX av