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
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Chapter1: Starting With Matlab
Section: Chapter Questions
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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.
Transcribed Image Text: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
Transcribed Image Text:(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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parts d and e

(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 1
Error
Total
8
9
Sum
of Squares
X
X
X
Degrees
of Freedom
1562.5
X
Mean
Square
4912.5051 X
1562.5
X 3.7313
3350.0051 X 418.7506 X
Find the value of the test statistic. (Round your answer to two decimal places.)
3.7313
X
F
X
Find the 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.
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.
p-value
.0895
X
Transcribed Image Text:(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 1 Error Total 8 9 Sum of Squares X X X Degrees of Freedom 1562.5 X Mean Square 4912.5051 X 1562.5 X 3.7313 3350.0051 X 418.7506 X Find the value of the test statistic. (Round your answer to two decimal places.) 3.7313 X F X Find the 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. 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. p-value .0895 X
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.
Transcribed Image Text: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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