Question

You are given the following data set: {(0,0), (0.5,0.6), (1,0.9), (1.1, 1), (1.5, 1.7)}, where the first coordinate is the independent (explanatory) variable, and the second coordinate is the dependent variable.

(a) Find a best fit model if the model is restricted to just be a constant (i.e. the best fit line has slope 0). (b) What is the mean squared error of (a)?

(c) What is the mean squared error of the model that has y-intercept 0 and slope 1? How much of the variation of the data can be explained by the independent variable (i.e. what is the R2) using the model from part (c)?

Answer 1

Solution:

X	Y
0	0
0.5	0.6
1	0.9
1.1	1
1.5	1.7

Go tot data analysis>Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.978388
R Square	0.957243
Adjusted R Square	0.94299
Standard Error	0.147766
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.466496	1.466496	67.16317	0.003802
Residual	3	0.065504	0.021835
Total	4	1.532
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.01528	0.123525	-0.12371	0.909364	-0.40839	0.37783
X	1.043027	0.127271	8.195314	0.003802	0.637993	1.44806

Solutionc:

MSE=0.021835

model is

y=-0.01528+1.043027X

R sq=0.9572=0.9572*100=95.72% varaition in dependent varaible is expalined by independent variable good model.