From the data below; 2 Х1 3 4 5 4 уг 8 6 12 15 a) Compute the mean square error b) Compute the standard error of the estimate c) Compute the estimated standard deviation of bl d) Use the t-test to test the following hypothesis (a .05) Ho B1 0 Ha: Bl 0 e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in the analysis of variance format

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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From the data below;
2
Х1
3
4
5
4
уг
8
6
12
15
a) Compute the mean square error
b) Compute the standard error of the estimate
c) Compute the estimated standard deviation of bl
d) Use the t-test to test the following hypothesis (a .05)
Ho B1 0
Ha: Bl 0
e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in
the analysis of variance format
Transcribed Image Text:From the data below; 2 Х1 3 4 5 4 уг 8 6 12 15 a) Compute the mean square error b) Compute the standard error of the estimate c) Compute the estimated standard deviation of bl d) Use the t-test to test the following hypothesis (a .05) Ho B1 0 Ha: Bl 0 e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in the analysis of variance format
Expert Solution
Step 1

Hey, since there are multiple subpart questions posted, we will answer first three subparts. If you want any specific subpart to be answered, then please submit that subpart only or specify the subpart number in your message.

Step 2

a) Computation of mean square error:

Step-by-step procedure to obtain the mean square error using EXCEL software:

  • Create the variable time in first column and 2 indicator variables in second and third columns.
  • Select Data > Data Analysis > Regression.
  • Click OK.
  • Under Input Y Range enter $B$1:$B$6.
  • Under Input X Range enter $A$1:$A$6.
  • Check Labels.
  • Click OK.

Output using EXCEL software is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
0.919238816
0.845
Adjusted R Square
0.793333333
Standard Error
2.033060091
5
Observations
ANOVA
df
Significance F
SS
MS
F
Regression
Residual
1
67.6
67.6 16.35483871
0.027214829
12.4 4.133333333
Total
80
4
Upper 95.0 %
Coefficients Standard Error
Lower 95%
Upper 95%
Lower 95.0 %
t Stat
P-value
-1.4
2.727636339 -0.513264903 0.643173407 -10.08055619
7.28055619 -10.08055619
7.28055619
Intercept
2.6
0.642910051 4.044111609 0.027214829
0.553973284 4.646026716 0.553973284 4.646026716
Step 3

Mean square error:

From the ANOVA table in the output, the mean square error of the regression is found to be 67.6.

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