Trend lines can be fitted to collect data plotted on x-y axes, and scholars can assign mathematical functions on the basis of their shape. This can be done mathematically using numerical analysis techniques or automatically using computer spreadsheets or other software. Scholars can then extrapolate these trend lines to estimate past and future values of the data or interpolated to estimate data values between collected points. Six types of trend lines see the most common use: linear, logarithmic, power, exponential, polynomial and moving average.
If the plotted data points follow a straight or nearly straight line, then a linear type of trend line best fits them. With a spreadsheet such as Microsoft Excel, you select the plotted data set and select the linear trend line to be fitted to it. With numerical analysis, a linear trend line tracks a mathematical function of the form f(x) = axe + b, where a and b are constants determined by numerical analysis and x is the variable representing the data points.
If the plotted data increases or decreases steeply and then begins to level out, the logarithmic trend line tends to work best. On a spreadsheet, select the logarithmic trend line. If you are using numerical analysis, determine the constant in the logarithmic function.
If the plotted data points appear in the form of an arc curving either upward or downward, then choose a power trend line. With a spreadsheet, select the power trend line to be fitted to it. With numerical analysis, determine the value of the exponent and the constants of the function that fits the curve.
An exponential trend line is similar in shape to a power trend line, but where a power trend line creates a symmetric arc; the exponential trend line turns more sharply on one end than the other. Like the power trend line, the direction can be either up or down. On a spreadsheet, select the exponential trend line. With numerical analysis, determine the constant multiplier of the natural logarithmic base e, and the constant multiplier of the multiplier of the exponent, which in this case would be the variable representing the data points.
If the plotted data points change direction more than once, then the type of trend line chosen should be the polynomial trend line. With a spreadsheet, select the polynomial trend line to be fitted to it. For numerical analysis, determine the degree of the polynomial and the value of the constants by analysis.
If the plotted data fluctuates up and down, then a moving average makes the best choice. A moving average takes an average of a specified number of points and uses that average as the next point. It produces a smooth curve that makes it easier to identify trends in the data. Using a spreadsheet, select the moving average trend line and specify the number of points to be used in each average. Numerical analysis isn't necessary for a moving average trend line; you need to specify the most effective number of points to be included in an average.
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