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=SLOPE()

Returns the slope of the linear regression line through data points in known_y's and known_x's. The slope is the vertical distance divided by the horizontal distance between any two points on the line, which is the rate of change along the regression line.

Applies To: Excel for Microsoft 365Excel for Microsoft 365 for MacExcel 2024Excel 2024 for MacExcel 2021Excel 2021 for MacExcel 2019Excel 2016
=SLOPE(known_y's, known_x's)
Hover argument names in the table for details.
Output typeNumber
Popularity25 / 100
VolatileNo
Dynamic ArrayNo
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◧ Arguments

ArgumentTypeRequiredDescription
known_y's Range Required An array or cell range of numeric dependent data points.
known_x's Range Required The set of independent data points.

▣ Examples

▦ Data
CellValue
A2 Known y
B2 Known x
A3 1/2/1900
B3 6
A4 1/3/1900
B4 5
A5 1/9/1900
B5 11
A6 1/1/1900
B6 7
A7 1/8/1900
B7 5
A8 1/7/1900
B8 4
A9 1/5/1900
B9 4
A10 Known y
B10 Known x
A11 1/2/1900
B11 6
A12 1/3/1900
B12 5
A13 1/9/1900
B13 11
A14 1/1/1900
B14 7
A15 1/8/1900
B15 5
A16 1/7/1900
B16 4
A17 1/5/1900
B17 4
Slope of the linear regression line through the data points in A3:A9 and B3:B9. =SLOPE(A3:A9,B3:B9)
Result: 0.305556

§ Remarks

  • The arguments must be either numbers or names, arrays, or references that contain numbers.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
  • If known_y's and known_x's are empty or have a different number of data points, SLOPE returns the #N/A error value.
  • The equation for the slope of the regression line is: where x and y are the sample means AVERAGE(known_x’s) and AVERAGE(known_y’s).
  • The underlying algorithm used in the SLOPE and INTERCEPT functions is different than the underlying algorithm used in the LINEST function. The difference between these algorithms can lead to different results when data is undetermined and collinear. For example, if the data points of the known_y's argument are 0 and the data points of the known_x's argument are 1: SLOPE and INTERCEPT return a #DIV/0! error. The SLOPE and INTERCEPT algorithm is designed to look for one and only one answer, and in this case there can be more than one answer. LINEST returns a value of 0. The LINEST algorithm is designed to return reasonable results for collinear data, and in this case at least one answer can be found.

✦ Tips

  • The arguments must be either numbers or names, arrays, or references that contain numbers.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
  • The equation for the slope of the regression line is: where x and y are the sample means AVERAGE(known_x’s) and AVERAGE(known_y’s).

⚠ Common Errors

#N/A If known_y's and known_x's are empty or have a different number of data points, SLOPE returns the #N/A error value.
Fix: Make the two ranges the same size
#DIV/0! For example, if the data points of the known_y's argument are 0 and the data points of the known_x's argument are 1: SLOPE and INTERCEPT return a #DIV/0! error.
Fix: داده‌های ورودی را بررسی کنید که هم‌خط و نامعین نباشند؛ از تابع LINEST برای داده‌های هم‌خط استفاده کنید.

⇄ Related Functions

=INTERCEPT() Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values. The intercept point is based on a best-fit regression line plotted through the known x-values and known y-values. Use the INTERCEPT function when you want to determine the value of the dependent variable when the independent variable is 0 (zero). For example, you can use the INTERCEPT function to predict a metal's electrical resistance at 0°C when your data points were taken at room temperature and higher. =FORECAST.LINEAR() Predicts a future value based on the linear trend of past data =RSQ() Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's. For more information, see the PEARSON function. The r-squared value can be interpreted as the proportion of the variance in y attributable to the variance in x. =LINEST() The LINEST function calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data, and then returns an array that describes the line. You can also combine LINEST with other functions to calculate the statistics for other types of models that are linear in the unknown parameters, including polynomial, logarithmic, exponential, and power series. Because this function returns an array of values, it must be entered as an array formula. Instructions follow the examples in this article. The equation for the line is: y = mx + b –or– y = m1x1 + m2x2 + ... + b if there are multiple ranges of x-values, where the dependent y-values are a function of the independent x-values. The m-values are coefficients corresponding to each x-value, and b is a constant value. Note that y, x, and m can be vectors. The array that the LINEST function returns is {mn,mn-1,...,m1,b}. LINEST can also return additional regression statistics.

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