a. State the multiple regression equation. ₁ =+ x₁ + x2i (Round to two decimal places as needed.)

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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.)
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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