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...

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)?

Homework Answers

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.

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