## Statistical Calculations and Hypothesis Testing### Consider the following data:\[\begin{array}{|c|c|c|c|c|c|}\hlinex_i & 3 & 12 & 6 & 20 & 14 \\\hliney_i & 55 & 40 & 55 & 5 & 15 \\\hline\end{array}\]### (a) Mean Square Error (MSE)Compute the mean square error using the equation:\[ s^2 = \text{MSE} = \frac{\text{SSE}}{n - 2} \]- Result: **72.92**### (b) Standard Error of the EstimateCompute the standard error of the estimate using the equation:\[ s = \sqrt{\text{MSE}} = \sqrt{\frac{\text{SSE}}{n - 2}} \]- Result: **8.539**### (c) Estimated Standard Deviation of \( b_1 \)Compute the estimated standard deviation of \( b_1 \) using the equation:\[ s_{b_1} = \frac{s}{\sqrt{\sum(x_i - \bar{x})^2}} \]- Result: **0.636**### (d) Hypothesis TestingUse the t-test to evaluate the following hypotheses (\(\alpha = 0.05\)):- \( H_0: \beta_1 = 0 \) - \( H_a: \beta_1 \neq 0 \)#### Test Statistic- Value: **-5.106**#### p-value- Result: **0.0145**#### Conclusion- **Reject \( H_0 \). We conclude that the relationship between x and y is significant.** **ANOVA Table for Hypothesis Testing****Objective**: Use the F test to assess the hypotheses at a 0.05 level of significance. This involves an analysis of variance (ANOVA) table.### ANOVA Table| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value ||---------------------|----------------|--------------------|-------------|------|---------|| Regression | 1901.25 | 1 | 1901.25 | 26.07| 0.015 || Error | 218.75 | 3 | 72.92 | | || Total | 2120 | 4 | | | |### Calculations- **Test Statistic**: \( F = 26.07 \)- **p-value**: \( p = 0.015 \)### Conclusion Options1. Do not reject \( H_0 \). We cannot conclude that the relationship between \( x \) and \( y \) is significant.2. Reject \( H_0 \). We cannot conclude that the relationship between \( x \) and \( y \) is significant.3. Do not reject \( H_0 \). We conclude that the relationship between \( x \) and \( y \) is significant.4. **Reject \( H_0 \). We conclude that the relationship between \( x \) and \( y \) is significant.****Selected Conclusion**: Option 4 is chosen, indicating that there is a significant relationship between \( x \) and \( y \) since the p-value (0.015) is less than the significance level (0.05).

Given,31262014554055515There are sub-parts that need to be answered.

Answered: (a) Compute the mean square error using…

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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