Math Problem Statement
Solution
To solve for the regression line based on the given data, I will calculate the equation of the line , where is the slope and is the y-intercept.
Let me calculate these values step by step:
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Compute the slope using the formula:
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Compute the y-intercept using:
Where is the number of data points. Let me calculate this. pandas as pd
Data from the image
data = { 'x': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 'y': [26.52, 27.3, 23.28, 23.66, 21.24, 18.42, 18.5, 16.98, 14.46, 14.64, 12.72, 9.5] }
Convert data to a DataFrame
df = pd.DataFrame(data)
Calculate sums needed for the regression line calculation
n = len(df) sum_x = df['x'].sum() sum_y = df['y'].sum() sum_xy = (df['x'] * df['y']).sum() sum_x2 = (df['x']**2).sum()
Calculate slope (m) and intercept (b)
m = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x**2) b = (sum_y - m * sum_x) / n
m, bThe regression line for the given data is:
Would you like to see the detailed steps for calculating this, or have additional questions? Here are 5 related questions you might explore:
- How is the slope calculated step by step for regression?
- How can we interpret the slope and intercept in this context?
- How would the regression line change if more data points were added?
- Can you provide a plot of the data and the regression line?
- How can we use this regression line to predict values for new ?
Tip: Always check the scatterplot of the data to visually verify the fit of your regression line!
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Statistics
Algebra
Formulas
Slope formula: m = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)
Intercept formula: b = (Σy - mΣx) / n
Theorems
Least Squares Method
Suitable Grade Level
Grades 11-12, College
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