**Understanding Profitability Factors for Small Banks**Profitability remains a challenge for banks and thrifts with less than $2 billion in assets. A critical issue for bank analysts is identifying factors that influence the return on assets (ROA), a measure of how profitable a company is in relation to its total assets. This study analyzes data from a sample of 73 community banks, focusing on the efficiency ratio (%) and risk-based capital (%) as potential predictors of ROA. The efficiency ratio reflects bank productivity, where a lower ratio is better, while risk-based capital measures capital adequacy.**Multiple Linear Regression Results:**| Variable | Coefficient | Standard Error | t Statistic | p-value ||---------------------|-------------|----------------|-------------|---------|| Intercept | -0.24116 | 0.30408 | -0.79 | 0.4304 || Efficiency Ratio, X₁| 0.01953 | 0.00539 | 3.62 | 0.0005 || Risk-Based Capital, X₂ | 0.04922 | 0.01517 | 3.24 | 0.0018 |### Analysis:- **Intercept**: The intercept coefficient is -0.24116 with a standard error of 0.30408. The t statistic is -0.79 with a p-value of 0.4304, indicating the intercept is not statistically significant.- **Efficiency Ratio (X₁)**: The coefficient is 0.01953 with a standard error of 0.00539. The t statistic is 3.62 with a p-value of 0.0005, indicating a statistically significant relationship with ROA.- **Risk-Based Capital (X₂)**: The coefficient is 0.04922 with a standard error of 0.01517. The t statistic is 3.24 with a p-value of 0.0018, also indicating a statistically significant relationship.**Task:**a. Construct a 95% confidence interval estimate of the population slope between ROA and efficiency ratio. (Round to four decimal places as needed.)

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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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