The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y = 47.323x + 18,552.22. Complete parts a and b. 415 454 684 485 475 375 56 73 198 Issues, x Proceeds, 18.867 28.926 43.827 30.645 66.371 66.061 20,396 11,981 30.443 27.958 165 (a) Find the coefficient of determination and interpret the result. (Round to three decimal places as needed.)

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**Table and Regression Analysis**

The table displays data on the number of initial public offerings (IPOs) of stock issued over a 10-year period, alongside the total proceeds from these offerings (in millions):

| Issues, x | 415 | 454 | 684 | 485 | 475 | 375 | 56 | 73 | 198 | 165 |
|-----------|-----|-----|-----|-----|-----|-----|----|----|-----|-----|
| Proceeds, y (in millions) | 18,867 | 28,926 | 43,827 | 30,645 | 26,671 | 16,660 | 21,396 | 11,986 | 30,443 | 27,958 |

The regression line is given by the equation: 
\[ \hat{y} = 47.323x + 18,552.22 \]

### (a) Coefficient of Determination

*Task*: Find the coefficient of determination and interpret the result.

- **Options for Interpretation**:
  - The coefficient of determination represents the fraction of the variation in proceeds that is unexplained and due to other factors or sampling error; the remaining fraction is explained by variation in the number of issues.
  - The coefficient of determination represents the fraction of the variation in proceeds explained by variation in the number of issues; the remaining fraction is unexplained due to other factors or sampling error.

### (b) Standard Error of Estimate \( s_e \)

*Task*: Find the standard error of estimate \( s_e \) and interpret the result.

- **Options for Interpretation**:
  - The standard error of estimate for the proceeds for a specific number of issues is about \( s_e \) million dollars.
  - The standard error of estimate of the issues for a specific number of proceeds is about \( s_e \) million dollars. 

**Instructions**: Round to three decimal places as needed.
Transcribed Image Text:**Table and Regression Analysis** The table displays data on the number of initial public offerings (IPOs) of stock issued over a 10-year period, alongside the total proceeds from these offerings (in millions): | Issues, x | 415 | 454 | 684 | 485 | 475 | 375 | 56 | 73 | 198 | 165 | |-----------|-----|-----|-----|-----|-----|-----|----|----|-----|-----| | Proceeds, y (in millions) | 18,867 | 28,926 | 43,827 | 30,645 | 26,671 | 16,660 | 21,396 | 11,986 | 30,443 | 27,958 | The regression line is given by the equation: \[ \hat{y} = 47.323x + 18,552.22 \] ### (a) Coefficient of Determination *Task*: Find the coefficient of determination and interpret the result. - **Options for Interpretation**: - The coefficient of determination represents the fraction of the variation in proceeds that is unexplained and due to other factors or sampling error; the remaining fraction is explained by variation in the number of issues. - The coefficient of determination represents the fraction of the variation in proceeds explained by variation in the number of issues; the remaining fraction is unexplained due to other factors or sampling error. ### (b) Standard Error of Estimate \( s_e \) *Task*: Find the standard error of estimate \( s_e \) and interpret the result. - **Options for Interpretation**: - The standard error of estimate for the proceeds for a specific number of issues is about \( s_e \) million dollars. - The standard error of estimate of the issues for a specific number of proceeds is about \( s_e \) million dollars. **Instructions**: Round to three decimal places as needed.
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