Question

For these data, what is the unbiased estimate of the error 
variance?  (Give a number.)

x    y
77.5 45
80 73
78 43
78.5 61
77.5 52
83 56
83.5 70
81.5 70
75.5 53
69.5 51
70 39
73.5 55
77.5 55
79 57
80 68
79 73
76 57
76 51
75.5 55
79.5 56
78.5 72
82 73
71.5 69
70 38
68 50
66.5 37
69 43
70.5 42
63 25
64 31
64.5 31
65 32
66.5 35
67 32
66.5 34
67.5 35
75 41
75.5 51
71.5 34
63 19 
60 19
64 30
62.5 23 
63.5 35
73.5 29
68 55
77.5 56

Answer 1

Sol:

MSE from regression output is unbiased estimate of the error variance

In excel install analysis toolpak and then go to

Data>Data analysis>Regression you get

Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.842883
R Square	0.710452
Adjusted R Square	0.704018
Standard Error	8.399174
Observations	47
ANOVA
	df	SS	MS	F	Significance F
Regression	1	7789.339	7789.339	110.4148	1.08E-13
Residual	45	3174.576	70.54613
Total	46	10963.91
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-98.2417	13.88044	-7.07771	7.82E-09	-126.198	-70.2851
x	2.005686	0.190875	10.50785	1.08E-13	1.621244	2.390129

regression equation is

y=-98.2417+2.005686*x

MSE=70.54613

unbiased estimate of the error 
variance=70.54613