Math Problem Statement
Solution
It looks like you have uploaded a multiple-choice question regarding a dataset of miles jogged each day. Based on the given data, I will assist in identifying the linear best-fit function.
Here’s the data provided:
Day (x) | Number of Miles (f(x)) |
---|---|
1 | 2 |
2 | 3 |
3 | 5 |
4 | 4 |
5 | 7 |
The question asks for the linear function that best models the data. The options provided are:
To find the best model, we’ll calculate the slope (m) and y-intercept (b) for a linear equation of the form .
Let’s calculate the slope first:
The slope can be calculated by using the formula:
Where:
- represents the day,
- represents the number of miles,
- is the total number of data points.
Let me calculate the best-fit line for this data. numpy as np
Given data
x = np.array([1, 2, 3, 4, 5]) # Days y = np.array([2, 3, 5, 4, 7]) # Miles jogged
Calculate the best-fit line (linear regression)
A = np.vstack([x, np.ones(len(x))]).T m, b = np.linalg.lstsq(A, y, rcond=None)[0]
m, bThe linear regression for the given data provides the equation:
This matches the third option in the question:
Therefore, the best model for the data is:
Option (3): .
Would you like further details on how the regression was done, or do you have any additional questions?
Here are 5 related questions you might find useful:
- How can I calculate the error or residuals in a linear regression?
- What are the steps involved in performing linear regression manually?
- How do you interpret the slope and intercept of a linear equation?
- How can we assess the quality of a linear regression fit?
- What is the difference between linear and nonlinear regression models?
Tip: When working with regression, always plot the data and the regression line to visually assess the fit before concluding.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Algebra
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Linear equation: f(x) = mx + b
Theorems
Linear Regression Best-Fit Line
Suitable Grade Level
Grades 8-10
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