How to use the FORECAST.LINEAR function
What is the FORECAST.LINEAR function?
The FORECAST.LINEAR function calculates a value based on existing x and y values using linear regression. Use this function to predict linear trends.
FORECAST.LINEAR replaced the FORECAST function in Excel 2016.
Table of Contents
1. Introduction
When to predict linear trends?
The data shows an approximately linear relationship between the variables. A scatterplot can be used to visualize this.
The FORECAST.LINEAR function is great for extrapolating a trend beyond the observed data. A linear equation provides a simple method for predicting linear trends.
What is a linear equation?
A linear equation is a type of equation that can be written in the form ax + b = 0, where a and b are constants and x is a variable. A linear equation represents a relationship between two quantities that are proportional to each other.
For example, if you have a linear equation that says y = 3x + 4, it means that for every unit increase in x, the value of y increases by 3 units and when x is zero y is 4.
The graph of a linear equation is always a straight line, a linear equation does not involve powers of variables.
Related functions to linear trends
| Function | Description |
|---|---|
| LINEST(known_y's, [known_x's], [const], [stats]) | Returns statistics for a linear trend line fit to data |
| GROWTH(known_y's, [known_x's], [new_x's], [const]) | Returns predicted y-values for exponential growth trend |
| TREND(known_y's, [known_x's], [new_x's], [const]) | Calculates values along a linear trend |
2. Syntax
FORECAST.LINEAR(x, known_y's, known_x's)
3. Arguments
| x | Required. The data point for which you want to predict a value. |
| known_y's | Required. Known y points. |
| known_x's | Required. Known x points. |
4. Example 1
You have monthly sales data for the past three years and want to forecast the sales for the next six months. Use the FORECAST.LINEAR function to predict the future sales based on the historical data?
The image above shows the sales data for the last three years in cell range C17:E28, here is the data:
| # | Year | Date | Sales |
| 1 | 1 | Q1 | 130 |
| 2 | 1 | Q2 | 110 |
| 3 | 1 | Q3 | 105 |
| 4 | 1 | Q4 | 155 |
| 5 | 2 | Q1 | 135 |
| 6 | 2 | Q2 | 115 |
| 7 | 2 | Q3 | 100 |
| 8 | 2 | Q4 | 175 |
| 9 | 3 | Q1 | 130 |
| 10 | 3 | Q2 | 125 |
| 11 | 3 | Q3 | 130 |
| 12 | 3 | Q4 | 194 |
The arguments for the FORECAST.LINEAR function are:
FORECAST.LINEAR(x, known_y's, known_x's)
- x - B29
- known_y's - $E$17:$E$28
The dollar signs lets you lock the cell reference to E17:E28. This means that when we copy cell F29 to cells below this cell reference stays the same. This makes sure that the same historical data is used for each new future value we calculate.
- known_x's - $B$17:$B$28
The dollar signs lets you lock the cell reference to B17:B28. This means that when we copy cell F29 to cells below this cell reference stays the same. This makes sure that the same historical data is used for each new future value we calculate.
The formula in cell F29 calculates the future sales value for quarter 1 based on the historical data in $E$17:$E$28 and $B$17:$B$28
Formula in cell F29:
Cell F29 is copied to cells below as far as needed. The chart above shows the future values as a orange line, the blue line represents historical sales data specified in cell range E17:E28 and B17:B28.
The chart above is a line chart with two different series, the first serie is in $E$17:$E$33 and the second serie is in $F$17:$F$33. Both series share the same x values.
Sales data often show non-linear patterns due to various factors such as seasonality, market trends, economic conditions, and consumer behavior etc. A linear function assumes a constant rate of change, which may not accurately capture the underlying patterns and dynamics of sales data.
5. Example 2
A geologist has collected geological data for the past decade and wants to forecast the next years. Use the FORECAST.LINEAR function to estimate future data based on the given data?
The image above shows the sales data for the last decade in cell range C17:C26, here is the data:
| Year | Historical data |
| 1 | 1055 |
| 2 | 956 |
| 3 | 963 |
| 4 | 902 |
| 5 | 1012 |
| 6 | 958 |
| 7 | 1097 |
| 8 | 1058 |
| 9 | 955 |
| 10 | 1025 |
The arguments for the FORECAST.LINEAR function are:
FORECAST.LINEAR(x, known_y's, known_x's)
- x - B27
- known_y's - $C$17:$C$26
The dollar signs lets you lock the cell reference to C17:C26. This means that when we copy cell D27 to cells below this cell reference stays the same. This makes sure that the same historical data is used for each new future value we calculate.
- known_x's - $B$17:$B$26
The dollar signs lets you lock the cell reference to B17:B26. This means that when we copy cell D27 to cells below this cell reference stays the same. This makes sure that the same historical data is used for each new future value we calculate.
The formula in cell F29 calculates the future geological value for year 11 based on the historical data in C17:C26 and B17:B26. The orange line displaying the future values in the image appears as a straight line reflecting the linear nature of the regression model used for the prediction.
Formula in cell D27:
Cell D27 is copied to cells below as far as needed.
6. Function not working
FORECAST.LINEAR function returns a
- #VALUE error if x is not numeric.
- #N/A error if known_y's or known_x's is left out.
- #DIV/0! error value if the variance of known_x's evaluates to zero.
6.1 Troubleshooting the error value
When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.
- The first line describes the error if you press with left mouse button on it.
- The second line opens a pane that explains the error in greater detail.
- The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
- This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
- The fifth line lets you edit the formula in the Formula bar.
- The sixth line opens the Excel settings so you can adjust the Error Checking Options.
Here are a few of the most common Excel errors you may encounter.
#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.
#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.
#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.
#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.
#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.
#NAME error - The #NAME error happens if you misspelled a function or a named range.
#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.
#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.
#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.
6.2 The formula returns an unexpected value
To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:
- Select the cell containing the formula you want to examine in detail.
- Go to tab “Formulas” on the ribbon.
- Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control. - Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
- Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
- Press "Close" button to dismiss the dialog box.
There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..
- Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
- Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
- Press F9: This will calculate and display the result of just that selected portion.
- Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
- Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.
The image above shows cell reference B29 converted to hard-coded value using the F9 key. The FORECAST.LINEAR function requires numerical values which is not the case in this example. We have found what is wrong with the formula.
Tips!
- View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
- Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
- Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.
Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button
6.3 Other errors
Floating-point arithmetic may give inaccurate results in Excel - Article
Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.
7. What is the math formula behind the function
a = ȳ - bx̄
The expression a = ȳ - bx̄ represents the equation for the y-intercept (a) of the linear regression line, where:
- ȳ is the mean or average value of the dependent variable y.
- b is the slope of the linear regression line.
- x̄ is the mean or average value of the independent variable x.
b = Σ(x - x̄)(y - ȳ)/Σ(x - x̄)2
Formula b represents the slope of the linear regression line which is used to model the linear relationship between two variables, x and y.
Σ(x - x̄)(y - ȳ) calculates the sum of the products of the deviations of x from its mean (x̄) and the deviations of y from its mean (ȳ) for each data point (x, y). It measures the covariance between the variables x and y.
Σ(x - x̄)2 calculates the sum of the squared deviations of x from its mean (x̄). It represents the variance of the x values.
Dividing Σ(x - x̄)(y - ȳ) by Σ(x - x̄)2 gives the slope of the linear regression line, which describes the change in the mean value of y for a unit change in x.
Functions in 'Statistical' category
The FORECAST.LINEAR function function is one of 73 functions in the 'Statistical' category.
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