Consider the data. xi 1 2 3 4 5 yi 3 8 5 10 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(xi − x)2. (Round your answer to three decimal places.)
Consider the data. xi 1 2 3 4 5 yi 3 8 5 10 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(xi − x)2. (Round your answer to three decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Consider the data.
|
xi
|
1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
|
yi
|
3 | 8 | 5 | 10 | 14 |
(a)
Compute the mean square error using equation
s2 = MSE=
.
(Round your answer to two decimal places.)| SSE |
| n − 2 |
(b)
Compute the standard error of the estimate using equation
s =
=
.
(Round your answer to three decimal places.)| MSE |
|
(c)
Compute the estimated standard deviation of
b1
using equation
sb1 =
.
(Round your answer to three decimal places.)| s | ||
|
(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.
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.
(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 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.
Reject H0. We cannot conclude that the relationship between x and y is significant.
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