Consider the data. 2 3 4 8. 11 13 SSE (a) Compute the mean square error using equation s = MSE = (Round your answer to two decimal places.) n- 2 SSE (b) Compute the standard error of the estimate using equation s = MSE = (Round your answer to three decimal places. n - 2 (c) Compute the estimated standard deviation of b, using equation s, = (Round your answer to three decimal places (d) Use the t test to test the following hypotheses (a = 0.05): Hoi B, = 0 H B, 0 %3D 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. O Do not reject H We conclude that the relationship between x and y is significant. O Reject H We conclude that the relationship between x and y is significant. O Do not reject H. We cannot conclude that the relationship between x and y is significant. O Reject H. We cannot conclude that the relationship between x and y is significant.

Note: According to the guidelines, only first three subparts have been solved. Given information: x 1 2 3 4 5 y 2 8 6 11 13a) The required calculations are shown in this table : x 1 2 3 4 5 ∑x=15 y 2 8 6 11 13 ∑y=40 xy 2 16 18 44 65 ∑xy=145 x2 1 4 9 16 25 ∑x2=55 Firstly, calculation of regression line is necessary for MSE: y^=a+bx^ where, y^=dependent variablex^=independent variable a = y intercept. b = slope of the regression line. Now, b=n∑xy-∑x∑yn∑x2-∑x2=5(145)-15405(55)-152=2.5 a=y¯-bx¯=405-2.5155=0.5 Therefore, y^=0.5+2.5 x^ Hence, for the different value of x, y^ 3 5.5 8 10.5 13 ∑y=40 (y-y^)2 1 6.25 4 0.25 0 ∑y-y^2=11.5 Calculation of mean square error is: s2=SSEn-2=∑(y-y^)25-2=11.53=3.83 Therefore, the value of mean square error is 3.83. b) Calculation of standard error: s=SSEn-2=∑(y-y^)25-2=11.53=1.958 Therefore, the value of standard error is 1.958.c) Calculation of estimated standard deviation of b1: Mean of x is computed as: x¯=∑xn=155=3 x 1 2 3 4 5 ∑x=15 (x-x¯)2 4 1 0 1 4 ∑(x-x¯)2=10 sb1=s∑(x-x¯)2=1.95810=0.619 Therefore, the value of estimated standard deviation is 0.619.

Answered: Consider the data. 2 3 4 8. 11 13 SSE (a) Compute the mean square error using equation s = MSE = (Round your answer to two decimal places.) n- 2 SSE (b) Compute…

MATLAB: An Introduction with Applications

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ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

The second slide is the first part of the question and the first slide is the second part of the question.

(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 Fto two decimal places, and your p-value to three decimal places.)
Source
of Variation
Sure
of Squares
Hean
N Freedonn
pvalue
Regression
Error
Total
Find the value of the test statistic. (Round your answer to two decimal places.)
tFind the p-value. (Round your answer to three decimal places.)
p-value
State your conclusion.
O Do not reject H. We conclude that the relationship between x and y is significant.
O Reject H,. We conclude that the relationship between x and y is significant.
O Do not reject H,. We cannot conclude that the relationship between x and y is significant.
O Reject H,. We cannot conclude that the relationship between x and y is significant.

Consider the data.
1.
2.
4
2 8
1
13
SSE
(a) Compute the mean square error using equation s = MSE
(Round your answer to two decimal places.)
2
SSE
(b) Compute the standard error of the estimate using equation s = V MSE =
(Round your answer to three decimal places.)
n- 2
(c) Compute the estimated standard deviation of b, using equation s, = =Z
V>(x, - x)*
(Round your answer to three decimal places.)
(d) Use the t test to test the following hypotheses (a = 0.05):
Hg: B, = 0
H. B, 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.
O Do not reject H. We conclude that the relationship between x and y is significant.
O Reject H.. We conclude that the relationship between x and y is significant.
O Do not reject H,. We cannot concl ude that the relationship between xand y is significant.
O Reject H,. We cannot conclude that the relationship betweenx and y is significant.

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