Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The business problem facing a bank analyst relates to the factors that af return on average assets (ROAA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 20 community banks resulted in the regression model Y₁ = -4.511 +0.037X₁ +0.217X2, where Y is the ROAA (%), X₁ is the efficiency ratio (%), and X₂ is the total risk-based capit (%). Complete parts (a) through (d) below. c. Plot the residuals versus X2₁. Choose the correct graph below.
Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The business problem facing a bank analyst relates to the factors that af return on average assets (ROAA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 20 community banks resulted in the regression model Y₁ = -4.511 +0.037X₁ +0.217X2, where Y is the ROAA (%), X₁ is the efficiency ratio (%), and X₂ is the total risk-based capit (%). Complete parts (a) through (d) below. c. Plot the residuals versus X2₁. Choose the correct graph below.
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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Problem 1P
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Transcribed Image Text:### Financial Performance Metrics
#### Table of Metrics
The table below displays key financial metrics used to analyze the performance of financial institutions.
- **ROAA (%):** Return on Average Assets, indicating the efficiency of assets in generating profits.
- **Efficiency Ratio (%):** A measure of a bank's overhead as a percentage of its revenue.
- **Total Risk-Based Capital (%):** Indicates a bank's capital level in relation to its risk-weighted assets.
| ROAA (%) | Efficiency Ratio (%) | Total Risk-Based Capital (%) |
|----------|----------------------|------------------------------|
| 1.04 | 39.93 | 17.04 |
| 0.68 | 57.75 | 13.88 |
| 7.27 | 81.4 | 27.77 |
| 1.08 | 53.49 | 18.31 |
| 0.72 | 71.08 | 14.66 |
| 0.92 | 65.41 | 14.04 |
| 0.79 | 68.07 | 13.38 |
| 1.04 | 68.14 | 16.8 |
| 1.76 | 68.1 | 16.69 |
| 1.07 | 64.82 | 13.86 |
| 1.37 | 48.58 | 12 |
| 0.93 | 63.1 | 18.65 |
| 0.66 | 59.16 | 19.76 |
| 1.72 | 49.93 | 17.69 |
| 1.5 | 54.7 | 26.6 |
| 0.59 | 81.6 | 15.08 |
| 2.12 | 75.21 | 14.55 |
| 1.11 | 69.82 | 17.5 |
| 1.45 | 49.47 | 16.03 |
| 1.06 | 57.09 | 14.62 |
This data can be utilized
![**Educational Website Text Transcription and Analysis**
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**Text Transcription:**
Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The business problem facing a bank analyst relates to the factors that affect return on average assets (ROAA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 20 community banks resulted in the regression model:
\[
\hat{Y}_i = -4.511 + 0.037X_{1i} + 0.217X_{2i}
\]
where \(Y\) is the ROAA (%), \(X_1\) is the efficiency ratio (%), and \(X_2\) is the total risk-based capital (%). Complete parts (a) through (d) below.
---
**Graphs: Explanation and Analysis:**
The task in part (c) is to plot the residuals versus \(X_{2i}\). Four graphs labeled A, B, C, and D are presented for selection, each plotting residuals on the vertical axis against \(X_2\) on the horizontal axis.
- **Graph A:** Displays a scatter plot where residuals range from -3 to 3, with points seemingly randomly distributed around the zero line across the \(X_2\) scale from 10 to 30.
- **Graph B:** Also plots residuals from -3 to 3, but the distribution of points suggests a pattern, which might indicate a potential problem with the regression model (e.g., non-linearity).
- **Graph C:** Shows a scatter plot where points cluster in a specific pattern, potentially implying a different kind of model misfit, such as curvature or a trend over the \(X_2\) range.
- **Graph D:** Similar to Graph A in the residual range (-3 to 3) and spans the same range for \(X_2\) (10 to 30), with more uniformly random distributed points regarding residuals.
Each graph has been visualized with precision, aiding in the choice of the graph, which best represents the residuals without systemic pattern or dependence on \(X_2\).
#### Choice
The primary objective of part (c) is to identify the graph where residual errors are randomly distributed, which indicates the absence of a systematic relationship between residuals and \(X_2\). In practice, a good fit should show](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc91d435c-8a20-4fa9-b80f-5aaeb9e13244%2Fcbe39e28-5aeb-44b0-86e7-0228c1981747%2Fwezgip_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Text Transcription and Analysis**
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**Text Transcription:**
Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The business problem facing a bank analyst relates to the factors that affect return on average assets (ROAA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 20 community banks resulted in the regression model:
\[
\hat{Y}_i = -4.511 + 0.037X_{1i} + 0.217X_{2i}
\]
where \(Y\) is the ROAA (%), \(X_1\) is the efficiency ratio (%), and \(X_2\) is the total risk-based capital (%). Complete parts (a) through (d) below.
---
**Graphs: Explanation and Analysis:**
The task in part (c) is to plot the residuals versus \(X_{2i}\). Four graphs labeled A, B, C, and D are presented for selection, each plotting residuals on the vertical axis against \(X_2\) on the horizontal axis.
- **Graph A:** Displays a scatter plot where residuals range from -3 to 3, with points seemingly randomly distributed around the zero line across the \(X_2\) scale from 10 to 30.
- **Graph B:** Also plots residuals from -3 to 3, but the distribution of points suggests a pattern, which might indicate a potential problem with the regression model (e.g., non-linearity).
- **Graph C:** Shows a scatter plot where points cluster in a specific pattern, potentially implying a different kind of model misfit, such as curvature or a trend over the \(X_2\) range.
- **Graph D:** Similar to Graph A in the residual range (-3 to 3) and spans the same range for \(X_2\) (10 to 30), with more uniformly random distributed points regarding residuals.
Each graph has been visualized with precision, aiding in the choice of the graph, which best represents the residuals without systemic pattern or dependence on \(X_2\).
#### Choice
The primary objective of part (c) is to identify the graph where residual errors are randomly distributed, which indicates the absence of a systematic relationship between residuals and \(X_2\). In practice, a good fit should show
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