Using a Line of Fit to Make Predictions
A line of fit (trend line) drawn through a scatter plot enables predictions about data values both within and beyond the known data range, as studied in Grade 11 enVision Algebra 1 (Chapter 3: Linear Functions). Students substitute x-values into the trend line equation to estimate unknown outputs. Interpolation (predictions within the data range) is generally more reliable than extrapolation (predictions beyond the range), which becomes increasingly uncertain. The line of fit equation is written in slope-intercept form for easy substitution.
Key Concepts
We can use a line of fit (trend line) drawn through a scatter plot to make predictions about data values.
We can estimate values between known data points or predict values beyond the range of our data using the trend line equation.
Common Questions
What is a line of fit (trend line)?
A line of fit is a straight line drawn through a scatter plot that approximates the linear trend in the data. It is used to make predictions from the data.
How do you use a line of fit to make a prediction?
Substitute the desired x-value into the trend line equation and solve for the predicted y-value.
What is the difference between interpolation and extrapolation?
Interpolation predicts values between known data points (within the data range). Extrapolation predicts values outside the data range and is generally less reliable.
Why are extrapolations less reliable?
The trend observed in the data may not continue indefinitely beyond the range. Conditions may change, making far-range predictions increasingly uncertain.
How do you find the equation of a line of fit?
Identify two representative points on the trend line, calculate the slope using the slope formula, then use point-slope form to write the equation.
Can a line of fit pass through every data point?
Usually not. A line of fit minimizes overall error across all points — a line through every point (interpolation curve) would not be linear.