line

(noun)

a path through two or more points (compare ‘segment'); a continuous mark, including as made by a pen; any path, curved or straight

Related Terms

Examples of line in the following topics:

  • 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.
    • Trend lines typically are straight lines, although some variations use higher degree polynomials depending on the degree of curvature desired in the line.
    • 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.
    • having the same number of data points on each side of the line - i.e., the line is in the median position;

  • 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.

  • Line Graphs

    • Judge whether a line graph would be appropriate for a given data set
    • A line graph is a bar graph with the tops of the bars represented by points joined by lines (the rest of the bar is suppressed).
    • A line graph of these same data is shown in Figure 2.
    • A line graph of the percent change in the CPI over time.
    • A line graph of the percent change in five components of the CPI over time.

  • Optional Collaborative Classroom Activity

    • For your line, pick two convenient points and use them to find the slope of the line.
    • Find the y-intercept of the line by extending your lines so they cross the y-axis.
    • If each of you were to fit a line "by eye", you would draw different lines.
    • Any other line you might choose would have a higher SSE than the best fit line.
    • This best fit line is called the least squares regression line.

  • Plotting Lines

    • A line graph is a type of chart which displays information as a series of data points connected by straight line segments.
    • A line graph is a type of chart which displays information as a series of data points connected by straight line segments.
    • A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.
    • A line chart is typically drawn bordered by two perpendicular lines, called axes.
    • If lines are drawn parallel to both axes, the resulting lattice is called a grid.

  • A Graph of Averages

    • This can be done by drawing a line through the scatterplot.
    • In most cases, a line will not pass through all points in the data.
    • A good line of regression makes the distances from the points to the line as small as possible.
    • The points on a graph of averages do not usually line up in a straight line, making it different from the least-squares regression line.
    • The graph of averages plots a typical $y$ value in each interval: some of the points fall above the least-squares regression line, and some of the points fall below that line.

  • Introduction to Linear Regression

    • The best-fitting line is called a regression line.
    • The vertical lines from the points to the regression line represent the errors of prediction.
    • The equation for the line in Figure 2 is
    • This makes the regression line:
    • The black line consists of the predictions, the points are the actual data, and the vertical lines between the points and the black line represent errors of prediction.

  • An objective measure for finding the best line

    • Mathematically, we want a line that has small residuals.
    • The resulting dashed line shown in Figure 7.12 demonstrates this fit can be quite reasonable.
    • However, a more common practice is to choose the line that minimizes the sum of the squared residuals:
    • The line that minimizes this least squares criterion is represented as the solid line in Figure 7.12.
    • This is commonly called the least squares line.

  • The Equation of a Line

    • Simple linear regression fits a straight line through the set of $n$ points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible.
    • The intercept of the fitted line is such that it passes through the center of mass $(x, y)$ of the data points.
    • The origin of the name "linear" comes from the fact that the set of solutions of such an equation forms a straight line in the plane.
    • In this particular equation, the constant $m$ determines the slope or gradient of that line, and the constant term $b$ determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
    • Three lines — the red and blue lines have the same slope, while the red and green ones have same y-intercept.

  • 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.