Shown below is a portion of a computer output for regression

Shown below is a portion of a computer output for regression analysis relating y (dependent variable) and x (independent variable).

ANOVA

df

SS

Regression

1

882

Residual

20

4000

Total

21

4882

Coefficients

Standard Error

t Stat

Intercept

5.00

3.56

Variable x

6.30

3.00

a.    What has been the sample size for the above? Complete the above regression table. [5pt.]

b.    Perform a t-test and determine whether or not x and y are related. Use a = 0.05. [5pt.]

c.     Perform an F-test and determine whether or not x and y are related. Use a = 0.05. [5pt.]

d.    Compute the coefficient of determination. [2pt.]

e.     Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific. [3pt.]

	ANOVA
		df	SS
	Regression	1	882
	Residual	20	4000
	Total	21	4882
		Coefficients	Standard Error	t Stat
	Intercept	5.00	3.56
	Variable x	6.30	3.00

Solution

A.

Note that

N = df(tot) + 1 = 22

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B.

As

t = B1/sB1

and

B1 = 6.30
sB1 = 3.00

Then

t = 2.1

As there are 22 data points, the df of this t test is

df = n - 2 = 20

Thus, using technology to get the p value,

p = 0.048617587

As p < 0.05, then there is significant evidence that THEY ARE RELATED.

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c.

As

F = [SS(reg) df(res)] / [SS(res) df(reg)]

Thus,

F = 4.41

Using technology to get the p value, as df1 = 1, df2 = 20,

P = 0.048617587   

As p < 0.05, then there is significant evidence that THEY ARE RELATED.

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D.

As

t = r sqrt[(n - 2)/(1 - r^2)]

and t = 2.1, n = 22, then solving for r^2,

r^2 = 0.09502 [ANSWER]

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E.

It means that 0.09502 of the total variation is explained by the dependence of y to the independent variable, x. This is the interpretation of r^2, by definition.