Question

You may need to use the appropriate technology to answer this question. Consider the data. xi...

You may need to use the appropriate technology to answer this question.

Consider the data.

xi

1 2 3 4 5

yi

2 8 6 10 13

(a)

Compute the mean square error using equation s2 = MSE =

SSE
n − 2

 . (Round your answer to two decimal places.)

(b)

Compute the standard error of the estimate using equation s =

MSE

=

SSE
n − 2

 . (Round your answer to three decimal places.)

(c)

Compute the estimated standard deviation of

b1

using equation sb1 =

s
Σ(xix)2

. (Round your answer to three decimal places.)

(d)

Use the t test to test the following hypotheses (α = 0.05):

H0: β1 = 0
Ha: β1 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =  

State your conclusion.

Reject H0. We conclude that the relationship between x and y is significant.Do not reject H0. We cannot conclude that the relationship between x and y is significant.     Do not reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant.

(e)

Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.

Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)

Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F p-value
Regression
Error
Total

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =  

State your conclusion.

Do not reject H0. We cannot conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant.     Do not reject H0. We conclude that the relationship between x and y is significant.Reject H0. We conclude that the relationship between x and y is significant.

Homework Answers

Answer #1

SSE =Syy-(Sxy)2/Sxx= 11.200

a)

s2 =SSE/(n-2)= 3.73

b)

std error σ              = =se =√s2= 1.932

c)

estimated std error of slope =se(β1) =s/√Sxx= 0.611

d)

test stat t = (bo-β1)/se(β1)= = 3.928
p value: = 0.0294

Reject H0. We conclude that the relationship between x and y is significant

e)

Source SS df MS F p value
regression 57.60 1 57.60 15.43 0.029
Residual error 11.20 3 3.73
Total 68.80 4

  value of the test statistic =15.43

p value =0.029

Reject H0. We conclude that the relationship between x and y is significant.

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