Below you are given a partial computer output based on a sample of 25 observatio

Question

Below you are given a partial computer output based on a sample of 25 observations, relating a predictor (independent) variable, X, and a response (dependent) variable, Y:

Predictor         Coefficient         Std. Error

Constant          1.4912               0.9926

X                      0.6878               0.1968

Analysis of Variance

Source                           df                      Sum Squares

Regression                     1                       12.807

Error                               23                      24.107

a.Write the estimated regression line.

b.At = 0.05, test for the significance of the slope.

c.At = 0.05, perform an F-test.

d.Determine the coefficient of determination.

e.Determine the coefficient of correlation.

Explanation / Answer

Ans:

a)Regression line:

y'=0.6878x+1.4912

b)Test statistic for slope:

t=0.6878/0.1968=3.495

critical t value(2 tailed)=2.069

As,t>2.069,we reject null hypothesis,there is sufficient evidence to conclude that there is significant relationship.

c)

As,p-value<0.05,we reject null hypothesis.

d)R^2=SSR/SST=12.807/36.914=0.3469

e)r=sqrt(0.3469)=0.5890

Source df SS MS F p-value Regression 1 12.807 12.807 12.219 0.002 Error 23 24.107 1.048 Total 24 36.914

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