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 y=mx+by = mx + b that best fits the given data, we can perform a linear regression analysis. Here’s how it’s done:

  1. We calculate the slope mm and intercept bb using the least-squares method.
  2. The slope mm and intercept bb 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:

y=1.05x+3.21y = 1.05x + 3.21

Here, m=1.05m = 1.05 and b=3.21b = 3.21, 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:

  1. How is the least-squares method used in linear regression?
  2. What is the significance of the slope and intercept in a linear model?
  3. How can we measure the goodness of fit for a regression line?
  4. What are some applications of linear regression in real-world data analysis?
  5. 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