Chart Trend Line Principle

1.Trend Line Function:

Trend lines are graphical representations of data trends which can be used for data analysis and forecast. The analysis is also known as regression analysis, by which you can predict future values and analyze past values following trend lines in charts based on real data.

2. Introduction to R-squared values:

The reliability of trend line data analysis depends on the R-squared value of the trend line. In a trend line of a chart, the R-squared value is a number between 0 and 1.

The closer the R-squared value is to 1, the more reliable the trend line will be. The trend line is most reliable when its R-squared value is 1. If you use a trend line to fit the data, FineReport will automatically calculate its R-squared value based on the formula.

Note:

Specific types of data need to be matched with specific trend lines, and you should choose the most appropriate trend line for your data to get the most accurate forecasts. 

3. R-squared Value Calculation: 

The formula for the R-squared value is as follows where SSE and SST are calculated by using the principle of least squares:

The expression for the least squares is shown below, and you can use it to calculate the constants in the equations for various trend lines (a0 and a1 correspond to the constants appearing in the equations):

1. Linear Trend Line 

It can calculate the line with minimum variance represented by the following formula:

In the formula, m represents the slope and b represents the intercept.

2. Polynomial Trend Line

It can calculate the minimum variance of the data points by using the following formula:

In the formula, b and c represent constants.

3. Logarithmic Trend Line

It can calculate the minimum variance of the data points by using the following formula:

In the formula, c and b represents constants, and the function ln is a natural logarithm.

Note: 

For algorithmic reasons, data points with negative values on the x-axis are ignored when the fitted equation is a logarithmic.

4. Exponential Trend Line 

It can calculate the minimum variance of the data points by using the following formula:

In the formula, c and b are constants and e is the base of the natural logarithm.

Note:

 For algorithmic reasons, data points with negative values on the y-axis are ignored when the fitted equation is exponential.

1. Linear Trend line: Linear trend lines are the best-fitting straight lines for simple linear datasets. Linear trend lines usually indicate that the data is increasing or decreasing at a constant rate.

2. Logarithmic Trend line: If data increases or decreases rapidly at the beginning, but then levels off quickly, logarithmic trend lines are the best fitting curves.

3. Polynomial Trend lines: Polynomial trend lines are curves used when data fluctuates widely.

4. Exponential Trend lines: Exponential Trend lines are applied to datasets where the data is increasing or decreasing at an increasingly rapid rate. If there are zero or negative numbers in the data, an exponential trend line cannot be created.