You may need to use the appropriate technology to answer this question. Consider the data. xi 3 12 6 20 14 yi 70 40 55 5 10 (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(xi − x)2. (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (? = 0.05): H0: ?1 = 0 Ha: ?1 ≠ 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 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. 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. (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 =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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

Consider the data.

x_i	3	12	6	20	14
y_i	70	40	55	5	10

(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 =

Σ(x_i − x)²

(Round your answer to three decimal places.)

(d)

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

H₀:	?₁	=	0
H_a:	?₁	≠	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 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. 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.

(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 =

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