Math Problem Statement
Calculate the least squares line. x: 1,,1,2,2,10 y:1,3,1,3,10
Solution
Given the data points:
We will calculate the slope and y-intercept using the same formulas as before:
Let's calculate these values.The equation of the least squares line for the given data points is:
This line best fits the provided data using the least squares method.
Would you like more details or have any questions? Here are some related questions you might find interesting:
- How would removing the outlier (10, 10) affect the least squares line?
- Can we interpret the slope and intercept of this line in the context of these data points?
- How does the least squares line compare to a line fitted by another method, like median fitting?
- What is the coefficient of determination for this line?
- How does the presence of repeated values affect the least squares calculation?
Tip: When dealing with potential outliers in data, it's important to consider their influence on the least squares line, as they can significantly skew the results.
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Math Problem Analysis
Mathematical Concepts
Statistics
Linear Regression
Least Squares Method
Formulas
Slope formula using least squares method
Y-intercept formula using least squares method
Theorems
-
Suitable Grade Level
Advanced High School
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