How to use Excel to calculate least squares

Let yi=a+bxi

List the known yi and xi in columns A and B of Excel sheet.

For example, if yi is located in a1:a10 and xi is located in b1:b10, you can use Function Compute:

Slope = slope(a1:a10,b1:b10) intercept. intercept(a1:a10,b1:b10)

1. Input the equation into Excel, 12x+4y-7z=403-5x+12y+9z=store the coefficients before x, y, and z in the 3 equations into the cell area in order to form a 3*3 array, and then input the values on the right side of the equation equal sign into the cell in turn to form a longitudinal column.

2. Select the inverse matrix region in the figure below.

3. Enter the formula =minverse(c15:e17) in the function box.

4. Press Ctrl+Shift+Enter at the same time to get the inverse matrix of the equation coefficient matrix.

5. Finally, select the region h15:h17 corresponding to xyz on the surface of the equation solution.

6. Enter the formula =mmult(c15:e17,h9:h11) in the function box, and press ctrl+shift+enter at the same time to get the result.

The method of calculating the multivariate least squares method with excel is as follows:

The methods of using Excel to achieve least squares calculation include: using Excel functions, using data analysis tools, adding trend lines, etc.

** with formulas.

The least squares method is used to complete the calculation step by step and the result is obtained.

Apply the statistical functions of Excel.

a、linest（）

Use least squares to best fit a straight line to a known data, and then return an array describing this straight line. It is also possible to combine linest with other functions to compute statistics for other types of linear models in unknown parameters, including polynomials, logarithms, exponents, and power series. Because this function returns an array of values, it must be entered as an array formula.

b、slope（）

Return according to known y's and known x'The slope of the linear regression line fitted by the data points in s. The slope is the ratio of the re-straightening distance to the horizontal distance of any two points on the line, which is the rate of change of the regression line.

c、intercept（）

The intercept of the line and the y-axis is calculated using the existing x-value and y-value. The intercept is through known known X'S and known y'The intersection of the linear regression line of the s data point with the y-axis. When the independent variable is 0 (zero), the intercept function can be used to determine the value of the dependent variable.

d、correl（）

Returns the correlation coefficient between array1 and array2 for the cell range. Use the correlation coefficient to determine the relationship between the two attributes.

Add a trend line.

The application of adding trend lines is more intuitive than other methods and can be used to complete both linear and nonlinear regression. The specific method will not be repeated.

Data analysis tools.

The Regression analysis tool performs linear regression analysis by using a "least squares" straight line fit for a set of observations. This tool can be used to analyze how a single dependent variable is affected by the value of one or several independent variables.

Regression Analysis dialog box.

y-value input area Enter a reference to the dependent variable data region here. The area must consist of a single column of data.

x-value input area Enter a reference to the argument data area here. Microsoft Office Excel sorts the arguments in this area in ascending order from left to right. The maximum number of independent variables is 16.

Flag Select this check box if the first row or column of the data source region contains a flag item. If there are no flags in the data source area, clear this check box and Excel will generate the appropriate data flags in the output table.

Confidence Check this option if you need to include additional confidence levels in the summary output table. In the box, enter the confidence level you want to use. The default value is 95%.

Dev Tools tab - Add-ons - Tick the Analytics Tools Library and then the Data tab. Select Data Analysis.

The Data Analysis dialog box is displayed, select Regression, and OK.

Use the function trend

This command is based on the functional relationship of the curve of the known data, and the corresponding y value of the existing x-array, for example, is **; First, select the region where the y value is generated, such as d1 d9. There are three sets of data, namely x, y and new x, which are placed in the three columns of a1 a9, b1 b9, c1 c9, after selecting d1 d9, click the fx icon to open the function parameter dialog box, known y'Select the button on the right of the blank box at the S point, then select B1 B9, which is the known Y value, and select the known X (known X) as well's) and new x's; The last const is generally not specified, it is used to specify whether the b value of the fitting line is 0 (assuming that the analytical formula of the fitting line is y=mx+b), and if you don't fill it, you don't force b=0;Finally, click OK, this is the only value in the selected area, then you need to press the F2 key, and finally press Ctrl+Shift+Enter, and the result will appear in the selected area. Hope it helps.

Excel has special functions that can be used directly:

linest、trend

1. Set yi=a+bxi

2. List the known yi and xi in the Excel table A and B columns 3, for example, Yi is located in A1:A5 and Xi is located in B1:B54, then you can use the function to calculate:

slope = slope(a1:a5,b1:b5) intercept = intercept(a1:

a5,b1:b5) The least squares formula is a mathematical formula, mathematically called curve fitting, least squares, which refers specifically to linear regression equations! The formula for least squares is b=y(average)-a*x(average).

We don't understand that, you can do your own research.

Example 1 Slope and y-intercept.

a b1 Known.

y Known. x 2 1 0

Formula Description (result).

linest(a2:a5,b2:b5,,false) returns slope (2).

index(linest(a2:a5,b2:b5,,false),2) returns intercept (1).

Tip: The inner formula in the example can also be entered as an array formula. After copying the formula to the A7 cell of a blank worksheet, select the region A7:B7 that starts with the formula cell.

Press F2, then Ctrl+Shift+Enter.

Please refer to the method described in the library.