trend

(noun)

the long-term movement in time series data after other components have been accounted for

Examples of trend 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.
    • This graph will be used in our example for drawing a trend line.
    • Illustrate the method of drawing a trend line and what it represents.

  • Describing linear relationships with correlation

    • The correlation is intended to quantify the strength of a linear trend.
    • Nonlinear trends, even when strong, sometimes produce correlations that do not reflect the strength of the relationship; see three such examples in Figure 7.11.
    • In general, the lines you draw should be close to most points and reflect overall trends in the data.
    • The first row shows variables with a positive relationship, represented by the trend up and to the right.
    • The second row shows variables with a negative trend, where a large value in one variable is associated with a low value in the other.

  • Conditions for the least squares line

    • The data should show a linear trend.
    • If there is a nonlinear trend (e.g. left panel of Figure 7.13), an advanced regression method from another book or later course should be applied.
    • 7.11: The trend appears to be linear, the data fall around the line with no obvious outliers, the variance is roughly constant.

  • Beginning with straight lines

    • If data show a nonlinear trend, like that in the right panel of Figure 7.6, more advanced techniques should be used.

  • Plotting Lines

    • 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.
    • In statistics, charts often include an overlaid mathematical function depicting the best-fit trend of the scattered data.
    • 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.

  • Introduction to line fitting, residuals, and correlation

    • The first plot shows a relatively strong downward linear trend, where the remaining variability in the data around the line is minor relative to the strength of the relationship between x and y.
    • The second plot shows an upward trend that, while evident, is not as strong as the first.
    • The last plot shows a very weak downward trend in the data, so slight we can hardly notice it.
    • One such case is shown in Figure 7.3 where there is a very strong relationship between the variables even though the trend is not linear.
    • We will discuss nonlinear trends in this chapter and the next, but the details of fitting nonlinear models are saved for a later course.

  • Displaying Data

    • Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly.

  • Types of outliers in linear regression

    • (5) There is no obvious trend in the main cloud of points and the outlier on the right appears to largely control the slope of the least squares line. (6) There is one outlier far from the cloud, however, it falls quite close to the least squares line and does not appear to be very influential.
    • You will probably find that there is some trend in the main clouds of (3) and (4).
    • In (5), data with no clear trend were assigned a line with a large trend simply due to one outlier (!).

  • Introduction to fitting a line by least squares regression

    • The lines follow a negative trend in the data; students who have higher family incomes tended to have lower gift aid from the university.

  • Extrapolation is treacherous

    • But in an alarming trend, temperatures this spring have risen.