Question 1163538
```python?code_reference&code_event_index=2
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression

# Data
taxes = np.array([21902, 17316, 18208, 15632, 43990, 33662, 15172, 16742, 18286, 16073, 15200, 36052, 31023, 42089, 14413, 38913, 25354, 22985, 16195, 29289])
size = np.array([2370, 2352, 1930, 1137, 5626, 2575, 2222, 1923, 2041, 1267, 1398, 3085, 2869, 3343, 1632, 3902, 3940, 2550, 3563, 2898])

# Reshape for regression
X = size.reshape(-1, 1)
y = taxes

# Fit model
model = LinearRegression()
model.fit(X, y)

# Get parameters
intercept = model.intercept_
slope = model.coef_[0]

print(f"Intercept: {intercept}")
print(f"Slope: {slope}")

# Prediction for 1600 sq ft
prediction = intercept + slope * 1600
print(f"Prediction for 1600 sq ft: {prediction}")


```
```text?code_stdout&code_event_index=2
Intercept: 5929.920950651071
Slope: 7.029199798319719
Prediction for 1600 sq ft: 17176.64062796262

```
To find the relationship between property taxes and home size, we perform a simple linear regression analysis using the provided data.

### 1. Sample Regression Equation
Using the data provided, the calculated coefficients for the regression line ($\text{Taxes} = \beta_0 + \beta_1 \cdot \text{Size}$) are:
* **Intercept ($\beta_0$):** $5929.92$
* **Slope ($\beta_1$):** $7.03$

The estimated regression equation is:
$$\text{Taxes} = 5929.92 + 7.03 \cdot \text{Size}$$

---

### 2. Interpretation of the Slope Coefficient
The slope coefficient ($7.03$) represents the average change in the dependent variable (Taxes) for every one-unit increase in the independent variable (Size).

* **Correct Interpretation:** **a. As Size increases by 1 square foot, the property taxes are predicted to increase by $7.03.**

---

### 3. Prediction for a 1,600-Square-Foot Home
To predict the taxes for a house with a size of $1,600$ square feet, we use the regression equation with higher precision coefficients as requested:
* Intercept $\approx 5929.9210$
* Slope $\approx 7.0292$

$$\text{Taxes} = 5929.9210 + 7.0292 \times (1600)$$
$$\text{Taxes} = 5929.9210 + 11246.72$$
$$\text{Taxes} = 17176.641$$

Rounding to two decimal places, the predicted property taxes are:
**Taxes = $17,176.64**