What is a best fit line in excel

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In statistics, a line of best fit is the line that best “fits” or describes the relationship between a predictor variable and a response variable.

The following step-by-step example shows how to create a line of best fit in Excel.

Step 1: Enter the Data

First, let’s enter the following dataset that shows the number of hours spent practicing and the total points scored by eight different basketball players:

 

Step 2: Create a Scatter Plot

Next, let’s create a scatter plot to visualize the relationship between the two variables.

To do so, highlight the cells in the range A2:B9, then click the Insert tab along the top ribbon, then click the option titled Scatter in the Charts group:

The following scatter plot will automatically be created:

Step 3: Add the Line of Best Fit

To add a line of best fit to the scatter plot, click anywhere on the chart, then click the green plus (+) sign that appears in the top right corner of the chart.

Then click the arrow next to Trendline, then click More Options:

In the Format Trendline panel that appears, click the button next to Linear as the trendline option, then check the box next to Display Equation on chart:

The line of best fit along with the equation for the line will appear on the chart:

Step 4: Interpret the Line of Best Fit

From the chart we can see that the line of best fit has the following equation:

y = 2.3095x – 0.8929

Here is how to interpret this equation:

• For each additional hour spent practicing, average points scored increases by 2.3095.
• For a player who practices zero hours, average points scored is expected to be -0.8929.

Note that it doesn’t always make sense to interpret the intercept value in a regression equation.

For example, it’s not possible for a player to score negative points.

In this particular example, we’re mostly interested in the value for the slope of the regression line which is 2.3095.

Additional Resources

The following tutorials explain how to perform other common tasks in Excel:

How to Perform Simple Linear Regression in Excel
How to Perform Multiple Linear Regression in Excel
How to Calculate R-Squared in Excel

How To Do A Linear Fit In Excel?

We can chart a regression in Excel by highlighting the data and charting it as a scatter plot. To add a regression line, choose “Layout” from the “Chart Tools” menu. In the dialog box, select “Trendline” and then “Linear Trendline”. To add the R 2 value, select “More Trendline Options” from the “Trendline menu.

How do you find linear fit?

The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0). This calculator will determine the values of b and a for a set of data comprising two variables, and estimate the value of Y for any specified value of X.

How do you use ya bX?

You might also recognize the equation as the slope formula. The equation has the form Y= a + bX, where Y is the dependent variable (that’s the variable that goes on the Y axis), X is the independent variable (i.e. it is plotted on the X axis), b is the slope of the line and a is the y-intercept.

How do you find r2 on Excel?

Double-click on the trendline, choose the Options tab in the Format Trendlines dialogue box, and check the Display r-squared value on chart box.

What is the line of best fit?

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.A straight line will result from a simple linear regression analysis of two or more independent variables.

What is Y BX A?

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

How do you find regression on Excel?

Click on the “Data” menu, and then choose the “Data Analysis” tab. You will now see a window listing the various statistical tests that Excel can perform. Scroll down to find the regression option and click “OK”.

What is BX in statistics?

In Statistics, the preferred equation of a line is represented by y = a + bx, where b is the slope and a is the y-intercept. (The preferred form is actually y = b₀ + b₁x.) Thus, statisticians prefer to maintain this format by using the form LinReg(a + bx), where a is the y-intercept and b is the slope.

How do you find L1 and l2 on TI 84?

Press 2nd and 1 to obtain L1 and press 2nd and 2 to obtain L2.

What is R2 in Excel Trendline?

When adding a trendline in Excel, you have 6 different options to choose from.Trendline equation is a formula that finds a line that best fits the data points. R-squared value measures the trendline reliability – the nearer R 2 is to 1, the better the trendline fits the data.

How does Trend function work in Excel?

Trend function in Excel is a Statistical Function that computes the linear trend line based on the given linear set of data. It calculates the predictive values of Y for given array values of X and uses the least square method based on the given two data series.

How do you make a best fit column in Excel?

Select the column or columns that you want to change. On the Home tab, in the Cells group, click Format. Under Cell Size, click AutoFit Column Width. Note: To quickly autofit all columns on the worksheet, click the Select All button, and then double-click any boundary between two column headings.

How do you do a line of best fit on Excel 2021?

Add a trendline

1. Select a chart.
2. Select the + to the top right of the chart.
3. Select Trendline. Note: Excel displays the Trendline option only if you select a chart that has more than one data series without selecting a data series.
4. In the Add Trendline dialog box, select any data series options you want, and click OK.

How do you make a line of best fit on Excel Online?

How to add Trendline in Excel

1. STEP 1:Highlight your table of data, including the column headings:
2. STEP 2: Select All Charts > Line > OK (Excel 2013 & 2016)
3. STEP 3: Right-click on the line of your Line Chart and Select Add Trendline.
4. STEP 4: Ensure Linear is selected and close the Format Trendline Window.

How do you find the line of best fit for linear regression?

The least Sum of Squares of Errors is used as the cost function for Linear Regression. For all possible lines, calculate the sum of squares of errors. The line which has the least sum of squares of errors is the best fit line.

What does a linear best fit line mean?

The line of best fit , also called a trendline or a linear regression, is a straight line that best illustrates the overall picture of what the collected data is showing. It helps us to see if there is a relationship or correlation between the two factors being studied.

Is the line of best fit the same as the regression line?

The regression line is sometimes called the “line of best fit” because it is the line that fits best when drawn through the points. It is a line that minimizes the distance of the actual scores from the predicted scores.

How do you find b0 and b1 in linear regression?

The mathematical formula of the linear regression can be written as y = b0 + b1*x + e , where: b0 and b1 are known as the regression beta coefficients or parameters: b0 is the intercept of the regression line; that is the predicted value when x = 0 . b1 is the slope of the regression line.

How do you find B in a linear equation?

In the equation y = mx + b for a straight line, the number m is called the slope of the line. Let x = 0, then y = m • 0 + b, so y = b. The number b is the coordinate on the y-axis where the graph crosses the y-axis.

How do you find a regression line?

The formula for the best-fitting line (or regression line) is y = mx + b, where m is the slope of the line and b is the y-intercept.

What is Y in Y a bx?

• y is the dependent variable. • x is the independent variable. • a is a constant. • b is the slope of the line.

Источник

LINEST function

This article describes the formula syntax and usage of the LINEST function in Microsoft Excel. Find links to more information about charting and performing a regression analysis in the See Also section.

Description

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 = 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 . LINEST can also return additional regression statistics.

Syntax

LINEST(known_y’s, [known_x’s], [const], [stats])

The LINEST function syntax has the following arguments:

Syntax

known_y’s Required. The set of y-values that you already know in the relationship y = mx + b.

If the range of known_y’s is in a single column, each column of known_x’s is interpreted as a separate variable.

If the range of known_y’s is contained in a single row, each row of known_x’s is interpreted as a separate variable.

known_x’s Optional. A set of x-values that you may already know in the relationship y = mx + b.

The range of known_x’s can include one or more sets of variables. If only one variable is used, known_y’s and known_x’s can be ranges of any shape, as long as they have equal dimensions. If more than one variable is used, known_y’s must be a vector (that is, a range with a height of one row or a width of one column).

If known_x’s is omitted, it is assumed to be the array <1,2,3. >that is the same size as known_y’s.

const Optional. A logical value specifying whether to force the constant b to equal 0.

If const is TRUE or omitted, b is calculated normally.

If const is FALSE, b is set equal to 0 and the m-values are adjusted to fit y = mx.

stats Optional. A logical value specifying whether to return additional regression statistics.

If stats is TRUE, LINEST returns the additional regression statistics; as a result, the returned array is .

If stats is FALSE or omitted, LINEST returns only the m-coefficients and the constant b.

The additional regression statistics are as follows.

The standard error values for the coefficients m1,m2. mn.

The standard error value for the constant b (seb = #N/A when const is FALSE).

The coefficient of determination. Compares estimated and actual y-values, and ranges in value from 0 to 1. If it is 1, there is a perfect correlation in the sample — there is no difference between the estimated y-value and the actual y-value. At the other extreme, if the coefficient of determination is 0, the regression equation is not helpful in predicting a y-value. For information about how r 2 is calculated, see «Remarks,» later in this topic.

The standard error for the y estimate.

The F statistic, or the F-observed value. Use the F statistic to determine whether the observed relationship between the dependent and independent variables occurs by chance.

The degrees of freedom. Use the degrees of freedom to help you find F-critical values in a statistical table. Compare the values you find in the table to the F statistic returned by LINEST to determine a confidence level for the model. For information about how df is calculated, see «Remarks,» later in this topic. Example 4 shows use of F and df.

The regression sum of squares.

The residual sum of squares. For information about how ssreg and ssresid are calculated, see «Remarks,» later in this topic.

The following illustration shows the order in which the additional regression statistics are returned.

You can describe any straight line with the slope and the y-intercept:

Slope (m):
To find the slope of a line, often written as m, take two points on the line, (x1,y1) and (x2,y2); the slope is equal to (y2 — y1)/(x2 — x1).

Y-intercept (b):
The y-intercept of a line, often written as b, is the value of y at the point where the line crosses the y-axis.

The equation of a straight line is y = mx + b. Once you know the values of m and b, you can calculate any point on the line by plugging the y- or x-value into that equation. You can also use the TREND function.

When you have only one independent x-variable, you can obtain the slope and y-intercept values directly by using the following formulas:

The accuracy of the line calculated by the LINEST function depends on the degree of scatter in your data. The more linear the data, the more accurate the LINEST model. LINEST uses the method of least squares for determining the best fit for the data. When you have only one independent x-variable, the calculations for m and b are based on the following formulas:

where x and y are sample means; that is, x = AVERAGE(known x’s) and y = AVERAGE( known_y’s ).

The line- and curve-fitting functions LINEST and LOGEST can calculate the best straight line or exponential curve that fits your data. However, you have to decide which of the two results best fits your data. You can calculate TREND( known_y’s,known_x’s ) for a straight line, or GROWTH( known_y’s , known_x’s ) for an exponential curve. These functions, without the new_x’s argument, return an array of y-values predicted along that line or curve at your actual data points. You can then compare the predicted values with the actual values. You may want to chart them both for a visual comparison.

In regression analysis, Excel calculates for each point the squared difference between the y-value estimated for that point and its actual y-value. The sum of these squared differences is called the residual sum of squares, ssresid. Excel then calculates the total sum of squares, sstotal. When the const argument = TRUE or is omitted, the total sum of squares is the sum of the squared differences between the actual y-values and the average of the y-values. When the const argument = FALSE, the total sum of squares is the sum of the squares of the actual y-values (without subtracting the average y-value from each individual y-value). Then regression sum of squares, ssreg, can be found from: ssreg = sstotal — ssresid. The smaller the residual sum of squares is, compared with the total sum of squares, the larger the value of the coefficient of determination, r 2 , which is an indicator of how well the equation resulting from the regression analysis explains the relationship among the variables. The value of r 2 equals ssreg/sstotal.

In some cases, one or more of the X columns (assume that Y’s and X’s are in columns) may have no additional predictive value in the presence of the other X columns. In other words, eliminating one or more X columns might lead to predicted Y values that are equally accurate. In that case these redundant X columns should be omitted from the regression model. This phenomenon is called “collinearity” because any redundant X column can be expressed as a sum of multiples of the non-redundant X columns. The LINEST function checks for collinearity and removes any redundant X columns from the regression model when it identifies them. Removed X columns can be recognized in LINEST output as having 0 coefficients in addition to 0 se values. If one or more columns are removed as redundant, df is affected because df depends on the number of X columns actually used for predictive purposes. For details on the computation of df, see Example 4. If df is changed because redundant X columns are removed, values of sey and F are also affected. Collinearity should be relatively rare in practice. However, one case where it is more likely to arise is when some X columns contain only 0 and 1 values as indicators of whether a subject in an experiment is or is not a member of a particular group. If const = TRUE or is omitted, the LINEST function effectively inserts an additional X column of all 1 values to model the intercept. If you have a column with a 1 for each subject if male, or 0 if not, and you also have a column with a 1 for each subject if female, or 0 if not, this latter column is redundant because entries in it can be obtained from subtracting the entry in the “male indicator” column from the entry in the additional column of all 1 values added by the LINEST function.

The value of df is calculated as follows, when no X columns are removed from the model due to collinearity: if there are k columns of known_x’s and const = TRUE or is omitted, df = n – k – 1. If const = FALSE, df = n — k. In both cases, each X column that was removed due to collinearity increases the value of df by 1.

When entering an array constant (such as known_x’s) as an argument, use commas to separate values that are contained in the same row and semicolons to separate rows. Separator characters may be different depending on your regional settings.

Note that the y-values predicted by the regression equation may not be valid if they are outside the range of the y-values you used to determine the equation.

The underlying algorithm used in the LINEST function is different than the underlying algorithm used in the SLOPE and INTERCEPT functions. 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:

LINEST returns a value of 0. The algorithm of the LINEST function is designed to return reasonable results for collinear data and, in this case, at least one answer can be found.

SLOPE and INTERCEPT return a #DIV/0! error. The algorithm of the SLOPE and INTERCEPT functions is designed to look for only one answer, and in this case there can be more than one answer.

In addition to using LOGEST to calculate statistics for other regression types, you can use LINEST to calculate a range of other regression types by entering functions of the x and y variables as the x and y series for LINEST. For example, the following formula:

works when you have a single column of y-values and a single column of x-values to calculate the cubic (polynomial of order 3) approximation of the form:

y = m1*x + m2*x^2 + m3*x^3 + b

You can adjust this formula to calculate other types of regression, but in some cases it requires the adjustment of the output values and other statistics.

The F-test value that is returned by the LINEST function differs from the F-test value that is returned by the FTEST function. LINEST returns the F statistic, whereas FTEST returns the probability.

Examples

Example 1 — Slope and Y-Intercept

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Источник

A trendline, often called “the best-fit line,” is a line that shows the trend of the data. As you have seen in many charts, it shows the overall trend or pattern, or direction from the existing data points. Excel provides the option of plotting the trend line on the chart. When we add this trend line to the chart, it looks like a line chart without any ups and downs.

How to Add and Insert Trend Line in Excel?

You can download this Trend Line Excel Template here – Trend Line Excel Template

To add a trendline in Excel, we need to insert the chart for the available data. Before adding a trend line, remember the Excel charts supporting the trendline. For example, we can add a trendline to a column chart, line chart, bar chart, scattered chart or XY chart, stock chart, or In Excel, a bubble chart is a type of scatter plot that uses bubbles to display values and comparisons. Like scatter plots, bubble charts compare data on both horizontal and vertical axes.read more.

It will add the default trend line of “Linear Trend Line.” The best-fit trend line shows whether the data is trending upwards or downwards.

We have several trend line types, below are the types of the trend line.

• Exponential Trendline
• Linear Trendline
• Logarithmic Trendline
• Polynomial Trendline
• Power Trendline
• Moving Average Trendline

All these trendlines are part of the statistics. One of the other popular trendlines is the “Moving Average” trendline.

The “Moving Average” trendline shows the trend of the average of a specific number of periods. For example, the quarterly trend of the data. Right-click on column bars to apply the moving average trendline and choose “Add Trendline.” It will open the “Format Trendline” window to the right end of the worksheet.

In the above window, choose the “Moving Average” option and set the period to 2. It will add the trendline for the average of every 2 periods.

How to Format the Trendline in Excel Chart?

The default trendline does not have any special effects on the trend line. Therefore, we need to format the trend line to make it more appealing.

Select the trend line and press Ctrl +1. Then, in the “Format Trendline” window, choose “FILL” and “LINE,” make the width 2 pt, and the color dark blue.

This Excel trendline can also forecast the sales numbers for the next months. To do this, go to “Trendline Options, “Forecast,” and make “Forward” to 3 periods.

As shown in the above image, we have added a forward trend for 3 periods, increasing the trend line for 3 months.

From this chart, our trendline shows a continuous decline in sales numbers.

Things to Remember

• A trendline is a built-in tool in Excel.
• The “Moving Average” trendline shows the average trend line of the mentioned periods.
• We must always format the default trendline to make it more appealing.

Recommended Articles

This article has been a guide to TrendLine in Excel. Here, we learn how to add and insert the trendline in Excel, examples, and a downloadable Excel template. You may learn more about Excel from the following articles: –

• Excel Rotate Pie Chart
• Plots in Excel
• Grouped Bar Chart in Excel
• How to Make Dot Plots in Excel?