Line of Best Fit: Apply It 3

  • Recognize when a linear regression model will fit a given data set.
  • Use technology to create scatterplots, find the line of best fit, and find the correlation coefficient.
  • Find the estimated slope and [latex]y[/latex]-intercept for a linear regression model.
  • Use the line of best fit to predict values.
We use a Least Squares Regression analysis to determine the equation of a line of best fit in order to make predictions based on an existing data set.

  • The line of best is a line that best describes a scatterplot of the data by minimizing the total vertical distances (errors) from all the data points to the line.
  • The vertical error associated with each data point (the distance from the point to the line of best fit) is called the residual of that data point. It lets us know how far off the prediction made by the line of best fit is from the actual observation.
  • The correlation coefficient [latex]r[/latex] describes the strength and direction of the linear relationship between the two quantitative variables in the data set.

Linear (Least Square) Regression Analysis

The slope-intercept form of a linear equation is commonly expressed in statistics using [latex]\hat{y}= a + bx[/latex], where [latex]b[/latex] represents the constant rate of change and [latex]a[/latex] represents the y-intercept.

Equation of the Line of Best Fit

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Choose Your Own Dataset

For this problem, you'll find and interpret the equation for the line of best fit for a data set of your choosing.