Calculate the test statistic. (Round your answer to two decimal places.) F= Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= What can you conclude? and 14 are all not 0. and 14 • Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁, ₂ O Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that A₁, A₂ O Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of P₁, P₂, or P14 is not 0. O Reject Ho. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of P₁, P₂r. ) Calculate SSResid. (Round your answer to four decimal places.) SSResid= Interpret SSResid. O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. Calculate R². (Round your answer to three decimal places.) R²=[ Interpret R². O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. or $₁4 is not 0. O This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P₂, and ₁4 are all 0. This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation. are all not 0. O This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁ P2 and ₁4 are all 0. O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation. Calculate - (Round your answer to four decimal places.) Interpret s O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁ P₂ and ₁4 are all 0. O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation. X X

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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Question
Calculate the test statistic. (Round your answer to two decimal places.)
F=
Use technology to calculate the P-value. (Round your answer to four decimal places.)
P-value=
What can you conclude?
ⒸReject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁, Par and 14 are all not
O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that P₁, P₂ and 14 are all not 0.
O Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of P₁, P₂r.. or P14 is
not 0.
O Reject Ho. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of P₁, P₂,
(c) Calculate SSResid. (Round your answer to four decimal places.)
SSResid=
or P₁4 is not 0.
Interpret SSResid.
O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model.
O This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation.
O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model.
O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P₂, and ₁4 are all 0.
**
O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation.
Calculate R². (Round your answer to three decimal places.)
R²
Interpret R².
O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model.
This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation.
O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model.
O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P2, and ₁4 are all 0.
O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation.
Calculate s. (Round your answer to four decimal places.)
Interpret s
O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model.
This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression
equation.
O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model.
O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P2, and ₁4 are all 0.
14
O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation.
Transcribed Image Text:Calculate the test statistic. (Round your answer to two decimal places.) F= Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= What can you conclude? ⒸReject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁, Par and 14 are all not O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that P₁, P₂ and 14 are all not 0. O Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of P₁, P₂r.. or P14 is not 0. O Reject Ho. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of P₁, P₂, (c) Calculate SSResid. (Round your answer to four decimal places.) SSResid= or P₁4 is not 0. Interpret SSResid. O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. O This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P₂, and ₁4 are all 0. ** O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation. Calculate R². (Round your answer to three decimal places.) R² Interpret R². O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P2, and ₁4 are all 0. O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation. Calculate s. (Round your answer to four decimal places.) Interpret s O This tells us the proportion of the observed variation in brightness that can be explained by the fitted model. This is the interquartile range of the deviations of the brightness values in the sample from the values predicted by the estimated regression equation. O This is the sum of the squares of the deviations of the actual values from the values predicted by the fitted model. O This is the probability of observing a value of the F-statistic at least as extreme as the observed F-statistic when P₁, P2, and ₁4 are all 0. 14 O This is a typical deviation of a brightness value in the sample from the value predicted by the estimated regression equation.
A statistical program is recommended.
The accompanying data resulted from a study of the relationship between y = brightness of finished paper and the independent variables x₁ = hydrogen peroxide (% by weight), x₂ = sodium hydroxide (% by weight), x3 =silicate (% by weight), and x = process temperature.+
4
X₂
X3 X4
y
0.2 0.2 1.5 145 83.9
84.9
0.4 0.2 1.5 145
0.2 0.4 1.5 145 83.4
0.4 0.4 1.5 145 84.2
0.2 0.2 3.5 145 83.8
0.4 0.2 3.5 145 84.7
0.2 0.4 3.5 145 84.0
0.4 0.4 3.5 145 84.8
0.2 0.2 1.5 175 84.5
0.4 0.2 1.5 175 86.0
82.6
0.4 0.4 1.5 175 85.1
0.2 0.4 1.5 175
0.2 0.2 3.5 175 84.5
0.4 0.2 3.5 175 86.0
0.2 0.4 3.5 175 84.0
0.4 0.4 3.5 175 85.4
Hg: P₁ P₂P₁40
=
OH: at least one of P₁ P₂ or ₁4 is not 0.
1'
14
(a) Find the estimated regression equation for the model that includes all independent variables, all quadratic terms, and all interaction terms. (Round your numerical values to five decimal places.)
ŷ =
Hg: P₁ P₂P₁40
= =
x1
X₁ X₂
0.1 0.3 2.5 160 82.9
(b) Using a 0.05 significance level, perform the model utility test.
State the null and alternative hypotheses.
о
Ho: P₁ P₂ and ₁4 are all not 0
14
○ Ho² B₁₂ = P₂ = = P₁4 = 0
0.5 0.3 2.5 160 85.5
0.3 0.1 2.5 160 85.2
0.3 0.5 2.5 160 84.5
Ha: P₁ P₂ and ₁4 are all not 0.
14
| ⒸH₁² B₁ = B₂ = - = ₁4 = 0
0.3 0.3 0.5 160 84.7
0.3 0.3 4.5 160 85.0
0.3 0.3 2.5 130 84.9
0.3 0.3 2.5 190 84.0
0.3 0.3 2.5 160 84.5
0.3 0.3 2.5 160 84.7
0.3 0.3 2.5 160 84.6
0.3 0.3 2.5 160 84.9
0.3 0.3 2.5 160 84.9
0.3 0.3 2.5 160 84.5
0.3 0.3 2.5 160 84.6
Transcribed Image Text:A statistical program is recommended. The accompanying data resulted from a study of the relationship between y = brightness of finished paper and the independent variables x₁ = hydrogen peroxide (% by weight), x₂ = sodium hydroxide (% by weight), x3 =silicate (% by weight), and x = process temperature.+ 4 X₂ X3 X4 y 0.2 0.2 1.5 145 83.9 84.9 0.4 0.2 1.5 145 0.2 0.4 1.5 145 83.4 0.4 0.4 1.5 145 84.2 0.2 0.2 3.5 145 83.8 0.4 0.2 3.5 145 84.7 0.2 0.4 3.5 145 84.0 0.4 0.4 3.5 145 84.8 0.2 0.2 1.5 175 84.5 0.4 0.2 1.5 175 86.0 82.6 0.4 0.4 1.5 175 85.1 0.2 0.4 1.5 175 0.2 0.2 3.5 175 84.5 0.4 0.2 3.5 175 86.0 0.2 0.4 3.5 175 84.0 0.4 0.4 3.5 175 85.4 Hg: P₁ P₂P₁40 = OH: at least one of P₁ P₂ or ₁4 is not 0. 1' 14 (a) Find the estimated regression equation for the model that includes all independent variables, all quadratic terms, and all interaction terms. (Round your numerical values to five decimal places.) ŷ = Hg: P₁ P₂P₁40 = = x1 X₁ X₂ 0.1 0.3 2.5 160 82.9 (b) Using a 0.05 significance level, perform the model utility test. State the null and alternative hypotheses. о Ho: P₁ P₂ and ₁4 are all not 0 14 ○ Ho² B₁₂ = P₂ = = P₁4 = 0 0.5 0.3 2.5 160 85.5 0.3 0.1 2.5 160 85.2 0.3 0.5 2.5 160 84.5 Ha: P₁ P₂ and ₁4 are all not 0. 14 | ⒸH₁² B₁ = B₂ = - = ₁4 = 0 0.3 0.3 0.5 160 84.7 0.3 0.3 4.5 160 85.0 0.3 0.3 2.5 130 84.9 0.3 0.3 2.5 190 84.0 0.3 0.3 2.5 160 84.5 0.3 0.3 2.5 160 84.7 0.3 0.3 2.5 160 84.6 0.3 0.3 2.5 160 84.9 0.3 0.3 2.5 160 84.9 0.3 0.3 2.5 160 84.5 0.3 0.3 2.5 160 84.6
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