Consider the data. xi 3 12 6 20 14 yi 60 40 65 5 15 (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: 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 =
Consider the data. xi 3 12 6 20 14 yi 60 40 65 5 15 (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: 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 =
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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Continuous Probability Distributions
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Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
100%
Consider the data.
|
xi
|
3 | 12 | 6 | 20 | 14 |
|---|---|---|---|---|---|
|
yi
|
60 | 40 | 65 | 5 | 15 |
(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: | 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 =
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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