The table below presents financial metrics, including Return on Average Assets (ROAA), Efficiency Ratio, and Total Risk-Based Capital for various entities. These metrics are critical for assessing the financial health and performance of institutions. The ROAA (%) indicates how efficient a company is at using its assets to generate earnings. A higher ROAA suggests better performance. The Efficiency Ratio (%) reflects how well a company manages its expenses; lower values are preferred as they indicate better efficiency. Total Risk-Based Capital (%) evaluates the capital adequacy, ensuring the financial stability of the institution.| 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 | **Understanding Bank Profitability in Relation to ROAA**Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The main question for bank analysts is what factors affect the return on average assets (ROAA), an important measure of how profitable a company is in relation to its total assets. Here, data was collected from a sample of 20 community banks leading to the development of a specific regression model:\[\hat{Y} = -4.511 + 0.037X_{1i} + 0.217X_{2i}\]Where:- $ Y $ = ROAA (%)- $ X_1 $ = Efficiency ratio (%)- $ X_2 $ = Total risk-based capital (%)**Instructions:**Complete the following steps to analyze the data:**b. Plot the Residuals versus $ X_{1i} $. Choose the correct graph below:**You are provided with four graphs labeled A, B, C, and D. Each graph plots the residuals against $ X_1 $ (Efficiency ratio), ranging from 25 to 100 on the $ X $-axis, while the $ Y $-axis represents the residuals ranging from -3 to 3. Select the graph that correctly displays the data distribution.**c. Plot the Residuals versus $ X_{2i} $. Choose the correct graph below:**Select the graph that accurately represents residuals plotted against $ X_2 $ (Total risk-based capital). Similar to the previous graphs, choose the one that reflects the correct pattern of data.

Given regression equation is, Y X1 X2 Residual=Y−Yˆ Yˆi=−4.511+0.037X1i+0.217X2i…

Answered: Profitability remains a challenge for…

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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A 1 ROAA (%) Efficiency Ratio (%) 2 1.04 39.93 3 57.75 4 81.4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0.68 7.27 1.08 0.72 0.92 0.79 1.04 1.76 1.07 1.37 0.93 0.66 1.72 1.5 0.59 2.12 1.11 1.45 1.06 B A 53.49 71.08 65.41 68.07 68.14 68.1 64.82 48.58 63.1 59.16 49.93 54.7 81.6 75.21 69.82 49.47 57.09 с Total Risk-Based Capital (%) 17.04 13.88 27.77 18.31 14.66 14.04 13.38 16.8 16.69 13.86 12 18.65 19.76 17.69 26.6 15.08 14.55 17.5 16.03 14.62 D E F G H |
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Y	X1	X2		$R e s i d u a l = Y - \hat{Y}$
			$Y ˆ i = - 4.511 + 0.037 X 1 i + 0.217 X 2 i = - 4.511 + (0.037 * 39.93) + (0.217 * 17.04) = 0.66409$	1.04-0.66409=0.37591
0.68	57.75	13.88	0.63771	0.04229
7.27	81.4	27.77	4.52689	2.74311
1.08	53.49	18.31	1.4414	-0.3614
0.72	71.08	14.66	1.30018	-0.58018
0.92	65.41	14.04	0.95585	-0.03585
0.79	68.07	13.38	0.91105	-0.12105
1.04	68.14	16.8	1.65578	-0.61578
1.76	68.1	16.69	1.63043	0.12957
1.07	64.82	13.86	0.89496	0.17504
1.37	48.58	12	-0.10954	1.47954
0.93	63.1	18.65	1.87075	-0.94075
0.66	59.16	19.76	1.96584	-1.30584
1.72	49.93	17.69	1.17514	0.54486
1.5	54.7	26.6	3.2851	-1.7851
0.59	81.6	15.08	1.78056	-1.19056
2.12	75.21	14.55	1.42912	0.69088
1.11	69.82	17.5	1.86984	-0.75984
1.45	49.47	16.03	0.7979	0.6521
1.06	57.09	14.62	0.77387	0.28613