Consider the data.X;Yi70 40 55 5 10(a) Compute the mean square error using equation s² = MSE =-2862.38 X-2.30212 6 20 14-30.888 X(b) Compute the standard error of the estimate using equation s = ✓MSE1561(c) Compute the estimated standard deviation of b₁ using equationXSSEn - 2(d) Use the t test to test the following hypotheses (α = 0.05):Ho: B₁ = 0Ha: B₁ * 0(Round your answer to two decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value = 1.7374X=SSEn-2'√(x;-x)²Find the value of the test statistic. (Round your answer to three decimal places.)-4X(Round your answer to three decimal places.)(Round your answer to three decimal places.)State your conclusion.● Reject Ho. We conclude that the relationship between x and y is significant.O Reject Ho. We cannot conclude that the relationship between x and y is significant.O Do not reject Ho. We cannot conclude that the relationship between x and y issignificant.O Do not reject Ho. 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 tableformat.Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)Sourceof VariationRegressionErrorTotal189Sumof SquaresXXXDegreesof Freedom1562.5XMeanSquare4912.5051 X1562.5X3350.0051 X 418.7506 X3.7313Find the value of the test statistic. (Round your answer to two decimal places.)3.7313XFFind p-value. (Round your answer to three decimal places.)p-value = 0895XState your conclusion.Reject Ho. We conclude that the relationship between x and y is significant.O Reject Ho. We cannot conclude that the relationship between x and y is significant.XDo not reject Ho. We cannot conclude that the relationship between x and y is significant.O Do not reject Ho. We conclude that the relationship between x and y is significant.p-value.0895X

Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Consider the data. X; Yi 3 12 6 20 14 70 40 -2.302 SSE (a) Compute the mean square error using equation s² = MSE = n-2 -2862.38 X 55 5 10 (b) Compute the standard error of the estimate using equation s = √ MSE = -30.888 X pb1 (c) Compute the estimated standard deviation of b₁ using equation Sp. (Round your answer to two decimal places.) X = SSE n-2 ν Σ(Χ S . (Round your answer to three decimal places.) - x)² (Round your answer to three decimal places.)

Consider the data. X; Yi 3 12 6 20 14 70 40 -2.302 SSE (a) Compute the mean square error using equation s² = MSE = n-2 -2862.38 X 55 5 10 (b) Compute the standard error of the estimate using equation s = √ MSE = -30.888 X pb1 (c) Compute the estimated standard deviation of b₁ using equation Sp. (Round your answer to two decimal places.) X = SSE n-2 ν Σ(Χ S . (Round your answer to three decimal places.) - 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

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Question

100%

Consider the data.
X;
Yi
70 40 55 5 10
(a) Compute the mean square error using equation s² = MSE =
-2862.38 X
-2.302
12 6 20 14
-30.888 X
(b) Compute the standard error of the estimate using equation s = ✓MSE
1561
(c) Compute the estimated standard deviation of b₁ using equation
X
SSE
n - 2
(d) Use the t test to test the following hypotheses (α = 0.05):
Ho: B₁ = 0
Ha: B₁ * 0
(Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value = 1.7374
X
=
SSE
n-2'
√(x;
-x)²
Find the value of the test statistic. (Round your answer to three decimal places.)
-4
X
(Round your answer to three decimal places.)
(Round your answer to three decimal places.)
State your conclusion.
● Reject Ho. We conclude that the relationship between x and y is significant.
O Reject Ho. We cannot conclude that the relationship between x and y is significant.
O Do not reject Ho. We cannot conclude that the relationship between x and y is
significant.
O Do not reject Ho. 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
Regression
Error
Total
1
8
9
Sum
of Squares
X
X
X
Degrees
of Freedom
1562.5
X
Mean
Square
4912.5051 X
1562.5
X
3350.0051 X 418.7506 X
3.7313
Find the value of the test statistic. (Round your answer to two decimal places.)
3.7313
X
F
Find p-value. (Round your answer to three decimal places.)
p-value = 0895
X
State your conclusion.
Reject Ho. We conclude that the relationship between x and y is significant.
O Reject Ho. We cannot conclude that the relationship between x and y is significant.
X
Do not reject Ho. We cannot conclude that the relationship between x and y is significant.
O Do not reject Ho. We conclude that the relationship between x and y is significant.
p-value
.0895
X

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Follow-up Questions

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Follow-up Question

parts d and e

Consider the data.
96.67
X;
Yi
(a) Compute the mean square error using equation s² = MSE =
9.832
3 12 6 20 14
.733
70 40 55 5 10
(b) Compute the standard error of the estimate using equation s = √MSE =
SSE
n - 2
1501
(c) Compute the estimated standard deviation of b, using equation
1
(d) Use the t test to test the following hypotheses (α = 0.05):
Ho: B₁ = 0
Ha: B₁ # 0
(Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value = 1.7374
X
Σ(Χ
SSE
n - 2
S
- x)²
Find the value of the test statistic. (Round your answer to three decimal places.)
-4
X
(Round your answer to three decimal places.)
(Round your answer to three decimal places.)
State your conclusion.
● Reject Ho. We conclude that the relationship between x and y is significant.
O Reject Ho. We cannot conclude that the relationship between x and y is significant.
O Do not reject Ho. We cannot conclude that the relationship between x and y is
significant.
O Do not reject Ho. We conclude that the relationship between x and y is significant.

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