best fit line

(noun)

A line on a graph showing the general direction that a group of points seem to be heading.

Related Terms

Examples of best fit line in the following topics:

  • Least-Squares Regression

    • The process of fitting the best- fit line is called linear regression.
    • Finding the best fit line is based on the assumption that the data are scattered about a straight line.
    • Any other potential line would have a higher SSE than the best fit line.
    • Therefore, this best fit line is called the least squares regression line.
    • The following figure shows how a best fit line can be drawn through the scatter plot graph: .

  • Optional Collaborative Classroom Activity

    • We will plot a regression line that best "fits" the data.
    • It turns out that the line of best fit has the equation:
    • The best fit line always passes through the point .
    • The process of fitting the best fit line is called linear regression.
    • This best fit line is called the least squares regression line.

  • Assumptions in Testing the Significance of the Correlation Coefficient

    • The regression line equation that we calculate from the sample data gives the best fit line for our particular sample.
    • We want to use this best fit line for the sample as an estimate of the best fit line for the population.
    • (We do not know the equation for the line for the population.
    • Our regression line from the sample is our best estimate of this line in the population. )
    • Assumption (1) above implies that these normal distributions are centered on the line: the means of these normal distributions of y values lie on the line.

  • The Coefficient of Determination

    • r2 , when expressed as a percent, represents the percent of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression (best fit) line.
    • This can be seen as the scattering of the observed data points about the regression line.
    • Approximately 44% of the variation (0.4397 is approximately 0.44) in the final exam grades can be ex- plained by the variation in the grades on the third exam, using the best fit regression line.
    • Therefore approximately 56% of the variation (1 - 0.44 = 0.56) in the final exam grades can NOT be explained by the variation in the grades on the third exam, using the best fit regression line.
    • (This is seen as the scattering of the points about the line. )

  • Line of Best Fit

    • The trend line (line of best fit) is a line that can be drawn on a scatter diagram representing a trend in the data.
    • The trend line, or line of best fit, is a line that can be drawn on a scatter diagram representing a trend in the data.
    • The mathematical process which determines the unique line of best fit is based on what is called the method of least squares - which explains why this line is sometimes called the least squares line.
    • draw the scatterplot on a grid and draw the line of best fit;
    • This graph shows what happens when we draw the line of best fit from the first data to the last data.

  • Outliers

    • We could guess at outliers by looking at a graph of the scatter plot and best fit line.
    • where $\hat{y}$=-173.5+4.83x is the line of best fit.
    • Y2 and Y3 have the same slope as the line of best fit.
    • The next step is to compute a new best-fit line using the 10 remaining points.
    • Using the new line of best fit, $\hat{y}$= −355.19+7.39(73) = 184.28.

  • Summary

    • Line of Best Fit or Least Squares Line (LSL): $\hat{y}$= a+bx x = independent variable; y = dependent variable
    • Used to determine whether a line of best fit is good for prediction.
    • The closer r is to 1 or -1, the closer the original points are to a straight line.
    • Sum of Squared Errors (SSE): The smaller the SSE, the better the original set of points fits the line of best fit.
    • Outlier: A point that does not seem to fit the rest of the data.

  • Student Learning Outcomes

  • Plotting Lines

    • In statistics, charts often include an overlaid mathematical function depicting the best-fit trend of the scattered data.
    • This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line graph.
    • It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
    • In either case, the best-fit layer can reveal trends in the data.
    • Best-fit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves.

  • Fitting a Curve

    • Curve fitting with a line attempts to draw a line so that it "best fits" all of the data.
    • Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
    • With linear regression, a line in slope-intercept form, $y=mx+b$ is found that "best fits" the data.
    • To find the slope of the line of best fit, calculate in the following steps:
    • Example:  Write the least squares fit line and then graph the line that best fits the data