Math Problem Statement
Use your regression equation to predict the cost of a house that is 4000 square feet.
Is your answer from the previous question reasonable?
Use your regression equation to predict the cost of a house that is 4000 square feet. Is your answer from the previous question reasonable?
Solution
Let's perform linear regression using the given data to predict the cost of a 4000 square foot house.
Data:
- Size (sq. ft.) = [1200, 1339, 1382, 2351, 2369, 3600]
- Price (in $1000) = [320, 430, 389, 635, 689, 750]
Step 1: Calculate the slope (m) and intercept (b) for the regression line equation .
- Calculate the mean of the size and price:
- Mean size =
- Mean price = ( \frac{320 + 430 + 389 + 635
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Algebra
Statistics
Formulas
y = mx + b
Mean Calculation
Slope Formula: m = Σ((x - x̄)(y - ȳ)) / Σ((x - x̄)²)
Intercept Formula: b = ȳ - m * x̄
Theorems
Least Squares Regression Theorem
Suitable Grade Level
Grades 10-12