a. State the multiple regression equation. ₁ =+ x₁ + x2i (Round to two decimal places as needed.)
a. State the multiple regression equation. ₁ =+ x₁ + x2i (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
Related questions
Question
![A nonprofit analyst seeks to determine which variables should be used to predict nonprofit charitable commitment, defined as a nonprofit's dedication to its charitable purpose. Two independent variables under consideration are:
- **Revenue (\(X_1\))**: Total revenue, in billions of dollars, representing the measure of nonprofit size.
- **Efficiency (\(X_2\))**: The percentage of private donations remaining after fundraising expenses, representing the measure of nonprofit fundraising efficiency.
The dependent variable \(Y\) is **Commitment**, which is a measure of the percentage of total expenses allocated directly to charitable services. Both variables \(X_2\) and \(Y\) are expressed as percentages. Data were collected from a random sample of 99 nonprofit organizations.
The analysis includes a table of results which presents the following data for the regression analysis:
### Table of Results
| Variable | Coefficients | Standard Error | T Statistic | p-Value |
|--------------|--------------|----------------|-------------|---------|
| Intercept | 10.884592 | 7.120425 | 1.53 | 0.1296 |
| Revenue | 0.6979138 | 0.321499 | 2.17 | 0.0324 |
| Efficiency | 0.8470845 | 0.077161 | 10.98 | <0.0001 |
#### Task:
a. State the multiple regression equation.
The regression equation can be expressed as:
\[
\hat{Y_i} = 10.88 + 0.70X_{1i} + 0.85X_{2i}
\]
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd53ca50-2c2e-4126-b6b0-02eef52f78ac%2F5fc84004-841b-491a-9607-049ac18548f3%2Fvx2sggb_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, defined as a nonprofit's dedication to its charitable purpose. Two independent variables under consideration are:
- **Revenue (\(X_1\))**: Total revenue, in billions of dollars, representing the measure of nonprofit size.
- **Efficiency (\(X_2\))**: The percentage of private donations remaining after fundraising expenses, representing the measure of nonprofit fundraising efficiency.
The dependent variable \(Y\) is **Commitment**, which is a measure of the percentage of total expenses allocated directly to charitable services. Both variables \(X_2\) and \(Y\) are expressed as percentages. Data were collected from a random sample of 99 nonprofit organizations.
The analysis includes a table of results which presents the following data for the regression analysis:
### Table of Results
| Variable | Coefficients | Standard Error | T Statistic | p-Value |
|--------------|--------------|----------------|-------------|---------|
| Intercept | 10.884592 | 7.120425 | 1.53 | 0.1296 |
| Revenue | 0.6979138 | 0.321499 | 2.17 | 0.0324 |
| Efficiency | 0.8470845 | 0.077161 | 10.98 | <0.0001 |
#### Task:
a. State the multiple regression equation.
The regression equation can be expressed as:
\[
\hat{Y_i} = 10.88 + 0.70X_{1i} + 0.85X_{2i}
\]
(Round to two decimal places as needed.)
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