Question

In: Statistics and Probability

Compute the mean square error using equation s2 = MSE =

Consider the data.

x_i	1	2	3	4	5
y_i	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 s_b₁ =

s

Σ(x_i − x)²

. (Round your answer to three decimal places.)

(d)

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

H₀:	β₁	=	0
H_a:	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.

Expert Solution

orchestra answered 2 years ago

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