In the following regression, X = total assets ($ billions), Y= total revenue ($ billions), and n= 64 large banks. R2 Std. Error n ANOVA table Source Regression Residual Total Regression output variables Intercept X1 ŷ = 0.519 6.977 64 6.5763+ SS 3,260.0981 3,018.3339 6,278.4320 (a) Write the fitted regression equation. coefficients 6.5763 0.0452 0.0452 X df 1 62 63 MS 3,260.0981 48.6828 std. error 1.9254 0.0055 66.97 t Stat 3.416 8.183 p-value 1.90E 11 p-value .0011 1.90E- 11 confidence interval Lower 95% 2.7275 0.0342 Upper 95% 10.4252 0.0563
In the following regression, X = total assets ($ billions), Y= total revenue ($ billions), and n= 64 large banks. R2 Std. Error n ANOVA table Source Regression Residual Total Regression output variables Intercept X1 ŷ = 0.519 6.977 64 6.5763+ SS 3,260.0981 3,018.3339 6,278.4320 (a) Write the fitted regression equation. coefficients 6.5763 0.0452 0.0452 X df 1 62 63 MS 3,260.0981 48.6828 std. error 1.9254 0.0055 66.97 t Stat 3.416 8.183 p-value 1.90E 11 p-value .0011 1.90E- 11 confidence interval Lower 95% 2.7275 0.0342 Upper 95% 10.4252 0.0563
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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Question
![In the following regression, \( X \) represents total assets (in billions of dollars), \( Y \) represents total revenue (in billions of dollars), and \( n = 64 \) large banks.
### Regression Analysis Summary
- **\( R^2 \)**: 0.519
- **Standard Error**: 6.977
- **Sample Size (\( n \))**: 64
### ANOVA Table
| Source | SS | df | MS | F | p-value |
|-------------|----------|----|----------|-------|------------|
| Regression | 3,260.0981 | 1 | 3,260.0981 | 66.97 | 1.90E-11 |
| Residual | 3,018.3339 | 62 | 48.6828 | | |
| Total | 6,278.4320 | 63 | | | |
### Regression Output
| Variables | Coefficients | Std. Error | t Stat | p-value | Confidence Interval (95%) |
|------------|--------------|------------|--------|----------|---------------------------|
| Intercept | 6.5763 | 1.9254 | 3.416 | 0.0011 | 2.7275 - 10.4252 |
| \( X_1 \) | 0.0452 | 0.0055 | 8.183 | 1.90E-11 | 0.0342 - 0.0563 |
### Fitted Regression Equation
(a) The fitted regression equation is:
\[
\hat{y} = 6.5763 + 0.0452X
\]
This analysis demonstrates the relationship between the total assets and total revenue of a sample of 64 large banks, using a linear regression model. The \( R^2 \) value indicates that approximately 51.9% of the variability in revenue can be explained by assets. The p-values suggest strong statistical significance for both the intercept and the slope (\( X_1 \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7b9bc12-9bec-475d-bc99-e13d2a9b76e2%2F800bbe6a-627e-4787-a162-aeb9ecff7814%2F7ytcexr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the following regression, \( X \) represents total assets (in billions of dollars), \( Y \) represents total revenue (in billions of dollars), and \( n = 64 \) large banks.
### Regression Analysis Summary
- **\( R^2 \)**: 0.519
- **Standard Error**: 6.977
- **Sample Size (\( n \))**: 64
### ANOVA Table
| Source | SS | df | MS | F | p-value |
|-------------|----------|----|----------|-------|------------|
| Regression | 3,260.0981 | 1 | 3,260.0981 | 66.97 | 1.90E-11 |
| Residual | 3,018.3339 | 62 | 48.6828 | | |
| Total | 6,278.4320 | 63 | | | |
### Regression Output
| Variables | Coefficients | Std. Error | t Stat | p-value | Confidence Interval (95%) |
|------------|--------------|------------|--------|----------|---------------------------|
| Intercept | 6.5763 | 1.9254 | 3.416 | 0.0011 | 2.7275 - 10.4252 |
| \( X_1 \) | 0.0452 | 0.0055 | 8.183 | 1.90E-11 | 0.0342 - 0.0563 |
### Fitted Regression Equation
(a) The fitted regression equation is:
\[
\hat{y} = 6.5763 + 0.0452X
\]
This analysis demonstrates the relationship between the total assets and total revenue of a sample of 64 large banks, using a linear regression model. The \( R^2 \) value indicates that approximately 51.9% of the variability in revenue can be explained by assets. The p-values suggest strong statistical significance for both the intercept and the slope (\( X_1 \)).
![### Statistical Analysis of Financial Data
#### Confidence Interval Interpretation
(d-2) The confidence interval does not contain zero, which implies:
- ○ There is no relationship between the total assets (billions) and total revenue (billions).
- ○ There is a relationship between the total assets (billions) and total revenue (billions).
#### Calculations
(e-1) **Calculate \( t^2 \) and \( F_{\text{calc}} \).**
(Round your answers to the nearest whole number.)
| | |
|----|-----|
| \( t^2 \) | [Input Box] |
| \( F_{\text{calc}} \) | [Input Box] |
(e-2) **Calculate \( R^2 \).**
| | |
|----|-----|
| \( R^2 \) | [Input Box] |
### Explanation
In this exercise, you will interpret the implications of a confidence interval that does not contain zero in terms of the relationship between financial variables. You will also perform statistical calculations including \( t^2 \), \( F_{\text{calc}} \), and \( R^2 \). These calculations are crucial to understanding the strength and significance of the relationship between the total assets and total revenue of companies.
Please use the input boxes to record your calculated values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7b9bc12-9bec-475d-bc99-e13d2a9b76e2%2F800bbe6a-627e-4787-a162-aeb9ecff7814%2Ffohsms_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Financial Data
#### Confidence Interval Interpretation
(d-2) The confidence interval does not contain zero, which implies:
- ○ There is no relationship between the total assets (billions) and total revenue (billions).
- ○ There is a relationship between the total assets (billions) and total revenue (billions).
#### Calculations
(e-1) **Calculate \( t^2 \) and \( F_{\text{calc}} \).**
(Round your answers to the nearest whole number.)
| | |
|----|-----|
| \( t^2 \) | [Input Box] |
| \( F_{\text{calc}} \) | [Input Box] |
(e-2) **Calculate \( R^2 \).**
| | |
|----|-----|
| \( R^2 \) | [Input Box] |
### Explanation
In this exercise, you will interpret the implications of a confidence interval that does not contain zero in terms of the relationship between financial variables. You will also perform statistical calculations including \( t^2 \), \( F_{\text{calc}} \), and \( R^2 \). These calculations are crucial to understanding the strength and significance of the relationship between the total assets and total revenue of companies.
Please use the input boxes to record your calculated values.
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