Question

In: Statistics and Probability

Compute the mean square error using equation s2 = MSE =

Consider the data.

xi

1 2 3 4 5

yi

4 8 6 12 14

(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.

Do not 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.      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.

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

Solutions

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