Math Problem Statement
Solution
To determine the equation of the line of regression (Price = ), we need to calculate:
-
The slope ():
-
The y-intercept (): where is the mean of Age, and is the mean of Price.
I’ll compute this step by step using the provided data:
Data Points:
- Age (): 1, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10
- Price (): 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:
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:
- How do we interpret the slope () in this context?
- How accurate is the regression line in predicting prices? (Would you like to calculate ?)
- Can we use this model for predicting prices of cars older than 10 years?
- What does the intercept () represent?
- 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!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Regression
Statistics
Algebra
Formulas
b1 = Σ((x - x̄) * (y - ȳ)) / Σ((x - x̄)^2)
b0 = ȳ - b1 * x̄
Price = b0 + b1 * Age
Theorems
Least Squares Method
Suitable Grade Level
Grades 11-12 or College Level