Question: The problem facing a manager is to assess the impact of factors on full-time (FT) job growth. Specifically, the manager is interested in the impact of total worldwide revenues and full-time voluntary turnover on the number of full-time jobs added in a year. Data were collected from a sample of 20 "best companies to work for." The data includes the total number of full-time jobs added in the past year, total worldwide revenue (in $millions), and the full-time voluntary turnover (%). Use the accompanying data to complete parts (a) through (d) below.
Click the icon to view the data table.
a. State the multiple regression equation.
Let $X_1$ represent the Total Worldwide Revenues ($millions$) and let $X_2$ represent the FT Voluntary Turnover (%).
$$\hat{Y}_i = \square + ( \square ) X_{1i} + ( \square ) X_{2i}$$
(Round the constant and $X_{1i}$-coefficient to the nearest integer as needed. Round the $X_{2i}$-coefficient to four decimal places as needed.)
1. **State the problem:** We need to write the multiple regression equation that predicts the number of full-time jobs added ($\hat{Y}_i$) based on total worldwide revenues ($X_1$) and full-time voluntary turnover ($X_2$).
2. **General form of multiple regression equation:**
$$\hat{Y}_i = b_0 + b_1 X_{1i} + b_2 X_{2i}$$
where:
- $b_0$ is the intercept (constant term),
- $b_1$ is the coefficient for total worldwide revenues,
- $b_2$ is the coefficient for full-time voluntary turnover.
3. **Important rounding rules:**
- Round $b_0$ and $b_1$ to the nearest integer.
- Round $b_2$ to four decimal places.
4. **Using the data (assumed from the problem context):**
- Suppose the intercept $b_0$ is approximately 50.3, rounded to 50.
- Suppose the coefficient $b_1$ for $X_1$ is approximately 2.7, rounded to 3.
- Suppose the coefficient $b_2$ for $X_2$ is approximately -0.123456, rounded to -0.1235.
5. **Write the final regression equation:**
$$\hat{Y}_i = 50 + 3 X_{1i} - 0.1235 X_{2i}$$
This equation means:
- For each additional million in worldwide revenue, the number of full-time jobs added increases by about 3.
- For each 1% increase in voluntary turnover, the number of full-time jobs added decreases by about 0.1235.
**Note:** The exact coefficients depend on the data provided, so replace these example values with the actual computed values from the data.