MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Statements and Logic
Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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Kindly do not reject helping me with the questions. I am really having trouble understanding and I actually tried to solve by myself and I want to tally my answer. a) I fot F= 32 and p value as 0.000478. However, I am not sure how to calculate c). And I would appreciate if you solve BEING AN EXPERT and do not reject the questions. 

### Simple Linear Regression Analysis: Significance Testing #### Problem 2 The coefficient of determination (\(R^2\)) of a simple linear regression model based on 10 sample points is 0.80. **a)** Would this regression model be deemed significant (using an F-test) at the significance level of \( \alpha = 0.01 \)? **b)** Find the P-value for the significance of the regression test in (a). **c)** What is the minimum value of \(R^2\) for this model that would lead to significant regression at \( \alpha = 0.01 \)? --- In addressing these points, the following steps and explanations are crucial: 1. **Coefficient of Determination (\(R^2\))**: This value explains the proportion of the variance in the dependent variable that is predictable from the independent variable. Here, \(R^2 = 0.80\) means 80% of the variance in the dependent variable is predictable from the independent variable. 2. **Significance Testing Using F-test**: The F-test helps in determining if the regression model is statistically significant. - **Null Hypothesis (H0)**: The model is not significant, i.e., all the regression coefficients are zero. - **Alternative Hypothesis (H1)**: The model is significant, i.e., at least one of the coefficients is not zero. - Using the F-distribution, the critical value for the F-test at \( \alpha = 0.01 \) and with degrees of freedom \( df_1 = 1 \) (numerator) and \( df_2 = 8 \) (denominator, calculated as sample size minus 2) can be used to compare against the computed F-statistic from the regression model. 3. **P-Value Calculation**: The exact P-value can determine how extreme the results are assuming the null hypothesis is true. This involves computing the F-statistic and then using statistical tables or software to find the corresponding P-value. 4. **Minimum \(R^2\) Value for Significance**: To determine the minimum \(R^2\) leading to significant regression at \( \alpha = 0.01 \), we need to use the F-distribution tables to find the critical F-value and then solve for \(R^2\). These steps provide a comprehensive review and analysis for significance testing of a simple
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Transcribed Image Text:### Simple Linear Regression Analysis: Significance Testing #### Problem 2 The coefficient of determination (\(R^2\)) of a simple linear regression model based on 10 sample points is 0.80. **a)** Would this regression model be deemed significant (using an F-test) at the significance level of \( \alpha = 0.01 \)? **b)** Find the P-value for the significance of the regression test in (a). **c)** What is the minimum value of \(R^2\) for this model that would lead to significant regression at \( \alpha = 0.01 \)? --- In addressing these points, the following steps and explanations are crucial: 1. **Coefficient of Determination (\(R^2\))**: This value explains the proportion of the variance in the dependent variable that is predictable from the independent variable. Here, \(R^2 = 0.80\) means 80% of the variance in the dependent variable is predictable from the independent variable. 2. **Significance Testing Using F-test**: The F-test helps in determining if the regression model is statistically significant. - **Null Hypothesis (H0)**: The model is not significant, i.e., all the regression coefficients are zero. - **Alternative Hypothesis (H1)**: The model is significant, i.e., at least one of the coefficients is not zero. - Using the F-distribution, the critical value for the F-test at \( \alpha = 0.01 \) and with degrees of freedom \( df_1 = 1 \) (numerator) and \( df_2 = 8 \) (denominator, calculated as sample size minus 2) can be used to compare against the computed F-statistic from the regression model. 3. **P-Value Calculation**: The exact P-value can determine how extreme the results are assuming the null hypothesis is true. This involves computing the F-statistic and then using statistical tables or software to find the corresponding P-value. 4. **Minimum \(R^2\) Value for Significance**: To determine the minimum \(R^2\) leading to significant regression at \( \alpha = 0.01 \), we need to use the F-distribution tables to find the critical F-value and then solve for \(R^2\). These steps provide a comprehensive review and analysis for significance testing of a simple
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