State the multiple regression equation. ]+ OX + (O×2 Round to two decimal places as needed.)
State the multiple regression equation. ]+ OX + (O×2 Round to two decimal places as needed.)
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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Transcribed Image Text:### Table: Regression Analysis Results
This table presents the results of a regression analysis, showcasing the relationships between different variables. The table includes columns for the variable, coefficients, standard error, T statistic, and p-value.
- **Variable**
- **Intercept**
- Coefficient: 11.144293
- Standard Error: 7.196818
- T Statistic: 1.55
- p-Value: 0.1248
- **Revenue**
- Coefficient: 0.6787574
- Standard Error: 0.321135
- T Statistic: 2.11
- p-Value: 0.0372
- **Efficiency**
- Coefficient: 0.8446421
- Standard Error: 0.077995
- T Statistic: 10.83
- p-Value: <0.0001
### Explanation
- **Coefficients**: Indicate the change in the dependent variable for a one-unit change in the independent variable, holding other variables constant.
- **Standard Error**: Measures the accuracy of the coefficients' estimates.
- **T Statistic**: Used to determine if a coefficient is significantly different from zero.
- **p-Value**: Assesses the significance of the results. A lower p-value (< 0.05) suggests strong evidence against the null hypothesis, indicating that the variable is a significant predictor.
In this analysis:
- The Revenue variable's coefficient is 0.6787574 with a p-value of 0.0372, suggesting a statistically significant positive effect.
- The Efficiency variable's coefficient is 0.8446421 with a highly significant p-value of <0.0001.
This table helps in understanding the impact each independent variable has on the outcome of the model.
![A nonprofit analyst seeks to determine which variables should be used to predict nonprofit charitable commitment, a nonprofit organization's commitment to its charitable purpose. Two independent variables under consideration are Revenue, a measurement of total revenue, in billions of dollars, as a measure of nonprofit size \(X_1\), and Efficiency, a measurement of the percent of private donations remaining after fundraising expenses as a measure of nonprofit fundraising efficiency \(X_2\). The dependent variable \(Y\) is Commitment, a measurement of the percent of total expenses that are allocated directly to charitable services. Both variables \(X_2\) and \(Y\) are encoded as percents. Data are collected from a random sample of 98 nonprofit organizations, with the results provided in the accompanying table. Complete parts (a) through (c) below.
a. State the multiple regression equation.
\[
\hat{Y}_i = \boxed{} + \left( \boxed{} \right) X_{1i} + \left( \boxed{} \right) X_{2i}
\]
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6116b766-b867-459f-b6a8-afb2e2c6f764%2Fd3848afb-6542-4e62-bcc8-26a781596023%2Flmej5ur_processed.png&w=3840&q=75)
Transcribed Image Text:A nonprofit analyst seeks to determine which variables should be used to predict nonprofit charitable commitment, a nonprofit organization's commitment to its charitable purpose. Two independent variables under consideration are Revenue, a measurement of total revenue, in billions of dollars, as a measure of nonprofit size \(X_1\), and Efficiency, a measurement of the percent of private donations remaining after fundraising expenses as a measure of nonprofit fundraising efficiency \(X_2\). The dependent variable \(Y\) is Commitment, a measurement of the percent of total expenses that are allocated directly to charitable services. Both variables \(X_2\) and \(Y\) are encoded as percents. Data are collected from a random sample of 98 nonprofit organizations, with the results provided in the accompanying table. Complete parts (a) through (c) below.
a. State the multiple regression equation.
\[
\hat{Y}_i = \boxed{} + \left( \boxed{} \right) X_{1i} + \left( \boxed{} \right) X_{2i}
\]
(Round to two decimal places as needed.)
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