Math Problem Statement
Enter your answer in the form y
m x + b , with m and b both rounded to two decimal places. x y 0 3.16 1 4.72 2 4.5 3 6.6 4 7.72 5 7.39 6 11.11 7 10.57 8 11.06
Solution
To find the equation of the line that best fits the given data, we can perform a linear regression analysis. Here’s how it’s done:
- We calculate the slope and intercept using the least-squares method.
- The slope and intercept are rounded to two decimal places as per the instructions.
Let's calculate these values.The equation of the line that best fits the given data is:
Here, and , both rounded to two decimal places.
Would you like more details on the calculation or have any questions?
Here are some related questions for further exploration:
- How is the least-squares method used in linear regression?
- What is the significance of the slope and intercept in a linear model?
- How can we measure the goodness of fit for a regression line?
- What are some applications of linear regression in real-world data analysis?
- How would this regression change if there were more outliers in the data?
Tip: Linear regression can also be extended to multiple variables (multivariable linear regression) when there is more than one predictor.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Least Squares Method
Slope and Intercept of a Line
Formulas
y = mx + b
Theorems
Least Squares Regression Theorem
Suitable Grade Level
Grades 9-12
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