Line of Best Fit

Definition

The line of best fit, also known as the regression line, is a straight line that best represents the relationship between two variables in a scatter plot. It is used to make predictions and estimate the value of one variable based on the value of the other variable.

5 Must Know Facts For Your Next Test

1. The line of best fit is determined by minimizing the sum of the squared vertical distances between the data points and the line.
2. The slope of the line of best fit represents the rate of change between the two variables, indicating how much one variable changes for every one-unit change in the other variable.
3. The y-intercept of the line of best fit represents the predicted value of the dependent variable when the independent variable is zero.
4. The strength of the relationship between the two variables is measured by the correlation coefficient, which ranges from -1 to 1.
5. The line of best fit can be used to make predictions about the value of the dependent variable for a given value of the independent variable.

Review Questions

• Explain how the line of best fit is determined in the context of a scatter plot.
  • The line of best fit is determined by minimizing the sum of the squared vertical distances between the data points and the line. This is done using a statistical technique called linear regression, which calculates the slope and y-intercept of the line that best represents the relationship between the two variables. The goal is to find the line that minimizes the overall distance between the data points and the line, making it the best fit for the data.
• Describe the relationship between the line of best fit and the correlation coefficient.
  • The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. The line of best fit is directly related to the correlation coefficient, as the slope of the line of best fit is equal to the correlation coefficient multiplied by the ratio of the standard deviations of the two variables. The closer the correlation coefficient is to 1 or -1, the stronger the linear relationship, and the more accurate the line of best fit will be in representing the data.
• Explain how the line of best fit can be used to make predictions in the context of fuel efficiency (12.9 Regression).
  • In the context of fuel efficiency (12.9 Regression), the line of best fit can be used to make predictions about the fuel efficiency of a vehicle based on its characteristics, such as engine size, weight, or other relevant variables. The regression equation, which describes the line of best fit, can be used to estimate the fuel efficiency of a vehicle by inputting the values of the independent variables. This allows for making informed predictions about the fuel efficiency of a vehicle, which can be useful for decision-making, such as purchasing a new vehicle or evaluating the efficiency of existing ones.

Related terms

Scatter Plot: A scatter plot is a graphical representation of the relationship between two variables, where each data point is plotted as a point on a coordinate plane.

Correlation:

Correlation is a statistical measure that describes the strength and direction of the linear relationship between two variables.

Regression Equation:

The regression equation is the mathematical formula that describes the line of best fit, allowing you to predict the value of one variable based on the value of the other variable.