Question

In: Statistics and Probability

(a) Compute the mean square error using equation s2 = MSE =

Consider the data.

xi

1 2 3 4 5

yi

4 6 5 12 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.)

test statistic=

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

p-value =

State your conclusion.

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.    

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

Reject H0. We 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.

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.

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

Solutions

Expert Solution

SSE =Syy-(Sxy)2/Sxx= 12.400

a)

s2 =SSE/(n-2)= 4.13

b)

std error σ              = =se =√s2= 2.033

c)

estimated std error of slope =se(β1) =s/√Sxx= 0.643

d)

test stat t = (bo-β1)/se(β1)= = 3.733
p value: = 0.0168

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

Source SS df MS F p value
regression 57.60 1 57.60 13.94 0.034
Residual error 12.40 3 4.13
Total 70.00 4

  value of the test statistic =13.94

p value =0.034

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


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