Question 1164822
```python
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

x = np.array([14, 16, 17, 18, 11, 15, 23, 24, 14, 17])
y = np.array([243, 312, 279, 308, 199, 219, 504, 550, 260, 255])

slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)

print(f"{slope=}")
print(f"{intercept=}")
print(f"{r_value=}")

# For plotting
plt.scatter(x, y, color='blue', label='Data Points')
plt.plot(x, slope * x + intercept, color='red', label='Regression Line')
plt.xlabel('Plans Sold (x)')
plt.ylabel('Commission (y)')
plt.title('Least Squares Regression Line')
plt.legend()
plt.grid(True)
plt.savefig('regression_plot.png')



```

```text
slope=27.894409937888202
intercept=-158.51552795031063
r_value=0.9431913989966259


```

To find the least squares regression line and the correlation coefficient for the given data, we perform a linear regression analysis.

### a. Equation of the Least Squares Regression Line

Using the provided data, we calculate the slope () and the -intercept () for the equation .

* **Slope ():** 
* **-intercept ():** 

**The equation of the regression line is:**


---

### b. Correlation Coefficient and Goodness of Fit

The correlation coefficient () measures the strength and direction of the linear relationship between the two variables.

* **Correlation Coefficient ():** 

**Comment on Goodness of Fit:**
A correlation coefficient of **0.9432** indicates a **very strong positive linear relationship** between the number of plans sold and the commission earned. Since  is close to 1, the regression line provides an excellent fit for the data, meaning that as the number of plans sold increases, the commission tends to increase in a highly predictable manner.

Would you like me to use this equation to predict the commission for a specific number of sales, such as 20 plans?