Question

Q (actual):

4

6

7

10

13

Q*:

5

6

6

8

10

From the above table,

What is SSE?

What is TSS?

What is R-squared?

Answer 1

Solution:

Sum of squared errors, SSE is the sum of square of deviations in actual and estimated values. TSS is total sum of squares, which is sum of squares of deviations in actual values and average value.

Average value of Q = sum of all Q values/total number of observations; total number of observations here = 5

Q(bar) = (4 + 6 + 7 + 10 + 13)/5 = 40/5 = 8

Then, consider the following table:

Q (actual)	Q*(estimated)	Q - Q*	(Q - Q*)2	(Q - Q(bar))	(Q - Q(bar))2
4	5	4 - 5 = -1	(-1)2 = 1	4 - 8 = -4	(-4)2 = 16
6	6	6 - 6 = 0	(0)2 = 0	6 - 8 = -2	(-2)2 = 4
7	6	7 - 6 = 1	12 = 1	7 - 8 = -1	(-1)2 = 1
10	8	10 - 8 = 2	22 = 4	10 - 8 = 2	22 = 4
13	10	13 - 10 = 3	32 = 9	13 - 8 = 5	52 = 25

So,

i) SSE = sum of all (Q - Q*)²

SSE = 1 + 0 + 1 + 4 + 9 = 15

ii) TSS = sum of all (Q - Q(bar))²

TSS = 16 + 4 + 1 + 4 + 25 = 50

iii) R-squared tells the goodness of fit of a model, that is how well the model is being explained by regression line (or in a way, how close are the estimated values to actual values)

R-squared = 1 - (SSE/TSS)

R2 = 1 - (15/50)

R2 = 1 - 0.3 = 0.7 (which is moderate level of goodness of fit)