To determine the equation of the line of regression (Price = $b_0 + b_1 \cdot \text{Age}$), we need to calculate:

1. The slope ($b_1$): $b_1 = \frac{\text{Covariance of Age and Price}}{\text{Variance of Age}}$

2. The y-intercept ($b_0$): $b_0 = \bar{y} - b_1 \cdot \bar{x}$ where $\bar{x}$ is the mean of Age, and $\bar{y}$ is the mean of Price.

I’ll compute this step by step using the provided data:

Data Points:

• Age ($x$): 1, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10
• Price ($y$): 17619, 14959, 15998, 14008, 14988, 14628, 14018, 12019, 10028, 11528, 10828, 9899

Let me calculate this. numpy as np import pandas as pd

Data

age = np.array([1, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10]) price = np.array([17619, 14959, 15998, 14008, 14988, 14628, 14018, 12019, 10028, 11528, 10828, 9899])

Mean of Age and Price

mean_age = np.mean(age) mean_price = np.mean(price)

Slope (b1)

numerator = np.sum((age - mean_age) * (price - mean_price)) denominator = np.sum((age - mean_age) ** 2) slope = numerator / denominator

Intercept (b0)

intercept = mean_price - slope * mean_age

Linear equation components rounded to nearest integer

slope_rounded = round(slope) intercept_rounded = round(intercept)

slope_rounded, intercept_roundedThe equation of the regression line is:

$\text{Price} = 17946 - 818 \cdot \text{Age}$

Would you like a detailed explanation of how this was calculated or assistance with additional parts of the problem?

Here are 5 related questions to consider:

1. How do we interpret the slope ($-818$) in this context?
2. How accurate is the regression line in predicting prices? (Would you like to calculate $R^2$?)
3. Can we use this model for predicting prices of cars older than 10 years?
4. What does the intercept ($17946$) represent?
5. How can we visualize this linear regression on a graph?

Tip: Always check the scatterplot of your data to ensure the linear regression is a good fit!