To solve the problem in the image and find the equation of the line of regression for the data provided, we will calculate the slope ($m$) and y-intercept ($b$) of the linear model:

$\text{Price} = m (\text{Age}) + b$

Given data:

Steps:

1. Calculate the mean of Age ($\bar{x}$) and Price ($\bar{y}$).
2. Compute the slope $m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}$.
3. Compute the y-intercept $b = \bar{y} - m\bar{x}$.

Let me calculate these values. numpy as np

Given data

age = np.array([1, 2, 2, 4, 5, 5, 6, 7, 7, 8, 8, 8, 10]) price = np.array([17599, 15028, 15968, 14028, 15008, 14569, 14009, 11989, 9999, 11539, 10829, 10928, 9979])

Step 1: Calculate means

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

Step 2: Calculate the slope (m)

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

Step 3: Calculate the y-intercept (b)

intercept = mean_price - slope * mean_age

mean_age, mean_price, slope, interceptThe calculated values are as follows:

• Mean of Age ($\bar{x}$): $5.62$
• Mean of Price ($\bar{y}$): $13,190.15$
• Slope ($m$): $-825$ (rounded to the nearest integer)
• Y-intercept ($b$): $17,824$ (rounded to the nearest integer)

Equation of the line of regression:

$\text{Price} = 17,824 - 825 \cdot \text{Age}$

Let me know if you need further clarifications or details!

Follow-up Questions:

1. How is the slope interpreted in the context of this problem?
2. How would the equation change if one data point is significantly different from others?
3. Can we use this model for predicting prices of cars older than 10 years?
4. What are the limitations of this linear regression model?
5. How can we check if this model is a good fit for the data?

Tip: Always visualize your data with a scatter plot and regression line to ensure the relationship is linear.