To perform linear interpolation in Excel, use the FORECAST function to interpolate between two pairs of x- and y-values directly. 5% is twice the distance between 2% vs. CountIf (rng, typeName) 'Set the Row up on the. Here’s a description of what you need to know about each of these arguments: Argument. linear(a2,c2:d2,e2:f2),na()) When I try to move the table and the interpolation cells, the results can change or be lost. Thanks in advance for your valuable suggestions. In the Insert menu, click on the Scatter icon and click on the scatter chart option with smooth lines and markers. XonGrid Interpolation Add-in (sourceforge. interp (points,a [:,0],a [:,1]) Note also that np. Sorted by: 1. There are functions to create that table very easy. 4-219)/ (220-219)) Of course, the values would be references, with 3 and 4 being received from lookup function. Extrapolation in Excel is easy: have a list of numbers (and optionally their paired "X-values"), and it can easily generate further entries in the list with the GROWTH () function. Step 1: Set up Data Model for Cubic Spline Interpolation. =B2+ (A4-A2)* (B3-B2)/ (A3-A2) In the above example, the formula’s last section, highlighted in red, calculates how much time taken changes whenever the speed of the bike changes by 1. Use Tab to toggle from the function arguments fields. If I assume that it must be done in Excel. I needed to interpolate data from a table to calculate the internal energy at a given pressure. Re: Interpolate An Array Of Numbers. . Brian's approach will interpolate any function that has function values for integer arguments. Utilizing Growth Trend Method. Polar 2D Interpolation. Fill in a series that fits a simple trend, use functions to. The online Microwave Encyclopedia has the full 6 line implementation along with a good explanation of how it works. Excel Questions . 5 psia "thermo" wrote: I was surprised that Excel doesn't have a built in linear interpolation routine. For example, you select “Canada” and “VAT”, you want to get 5% in return. 96 and speed 800 result in 50. 384 kPa. Locate where 12 bar a (A) would be. 1. Also, it calculates (or approximates) the. 2. I have a table with x,y values. In Excel, I have a table of data giving fluid densities (rho) with temperatures (T) and pressures (P) as parameters. Call the value that comes after A2. To lookup a list of values and interpolate answers between given data, I currently use a combination of MATCH and INDEX which results in a lengthy formula. Table of Contents hide. 1, (p. But i have no idea how to do it. For detailed instructions on how to do nonlinear interpolation within an Excel. In Table 2 I have several sale dates, and the same sale price for simplicity. xll and for the 64 bits version of Excel select XonGrid-w64. Interpolate the missing values y with y = m * x + c. Import Interpolation. Below this table, we want to be able to define the country in cell C11 (here: “Canada”) and the data type in cell C12 (here: “VAT”). First, the value of x will go, then add the y-axis values and finally add x-axis values in the formula and click Enter. Neville's Method uses various Lagrange interpolating polynomials of higher and higher degree for various nodes t. 210 209 151 118 98. Fill in a series that fits a simple trend, use functions to extend complex and nonlinear data, or perform regression analysis with the Analysis ToolPak Add-in. We can add another series to highlight the input data points. 4. 9 (in addition to 0<= X <=0. . Given two known values (x1, y1) and (x2,. But, since either inter-polation process just involves two data points, it will likely miss the general overall shape of the curve that the fitted curve. Since the index values in column 1 of the table are in descending order, this can be obtained with: =MATCH(vnum. In simple terms, linear interpolation is a method of estimating a value between two known data points by assuming that the relationship between the two data points is linear or straight-line. I hope you already have the LET () function, because I used it in my interpolation formula. Hi there, I have previously been able to interpolate across a table using a combination of FORECAST, OFFSET and MATCH but for a new data set I'm using, I have been unable to produce a solution with this sort of formula. 674), for 40 C in the first column. I want to interpolate for a given x1 value between the y values using the hllokup function also. Interpolating between Two Values by Joining SLOPE and INTERCEPT Functions. Designate the forecast period. It calculates the dependent variable (Y) for a given independent variable (X) by fitting a straight line to the available data. But now if the data is not in the table i want to interpolate between two sets of data. Excel has an in-built function called INTERPOLATE that you can use to perform interpolation. 3 Torque. . LINEAR Result: GROWTH Result: FORECAST Inner-linear interpolation (manual) FORECAST Inner-linear interpolation (automatic) Author: Excel Off The Grid Last modified by: Mark Proctor Created Date: 4/8/2020 7:55:27 PMIn this article, we discuss how you can interpolate missing data in Excel with elaborate explanations. The linear interpolation equation above can be implemented directly in Microsoft Excel provided the tabulated values are. 48 4Y 0. It is only tested on positive values and ten rows, so you will definitely need to adapt it to many corner cases - but it should point you in the right direction: Sub Interpolate () Dim valueToTop As Integer For Row = 1 To 10 valueToTop = -1 valueToBottom = -1 If Cells (Row, 1). Answer to Below is a portion of a steam table used in. ‘Table – The range of values with at least YCol columns ‘YCol – the column of Table used for the Y-side of the interpolation ‘Dim TableRow As Integer, Temp As Variant Dim TableRow As Long, Temp As Variant ‘see below Dim x0 As Double, x1 As Double, y0 As Double, y1 As Double Dim d As Double ‘TableRow – the row of Table that. LINEAR (x, known_y's, known_x's) to calculate the interpolated value. This video demonstrates how to use ExceLab Add-in INTERPXYZ() function to interpolate scattered (x,y,z) points onto a uniform grid and plot the data with Exc. That said: for the example in the sample set I chose a 3rd order polynomial to "match" the spline look and it found an. Enter the formula =Interpol2D (y, x) into your spreadsheet where you want the interpolation result displayed. This is a simple double interpolationThe reference table used in the video is Table 19-from IS456:2000. Excel replace value in a column using a pattern. One of: ‘linear’: Ignore the index and treat the values as equally spaced. Usually labeled Saturation Temperature and Saturation Pressure. To interpolate linearly in Excel, follow these steps: Enter your data into an Excel worksheet. Use the # of days or the date as the X value and the value for the Y value. The interpolation method is one of: "nearest". Description. The different types of this concept include linear interpolation among others which are discussed below. In the spreadsheet, insert the formula: =interpolate (X, [XRangeReference], [YRangeReference],<param>), where X is the value you wish to. Use the tablelookup function in the equations section to compute an output value by interpolating the query input value against a set of data points. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. Select the range of 12 data points for the X Function Argument field. Use INTERPXY to interpolate from a set of (x,y) data points at an arbitrary point. Based on an input value elsewhere, I want the formula to locate the two bounding values in column 1 and then to linearly interpolate the input value between the two (column 1, column 2) data points. Use the Add-in. 3D Interpolation in Excel: 4 Easy Steps. Next, let’s create a scatter plot to check if the data follows a linear trend. Transcribed image text: Below is a portion of a steam table used in thermodynamics. 1) If deemed necessary, rearrange data to simplify the lookup step. The question is, both Trend method and Vlookup method are not working for me. It gets more complicated from there. =B1+ (A2-A1)* (B3-B1)/ (A3-A1) in B2. On the Data tab, in the Forecast group, click Forecast Sheet. If I assume that it must be done in Excel. Range ("g3"). 3. 0218x3 – . 4], and the indices would be i1=1, i2=2. linear interpolation, log interpolation and harmonic interpolation, especially for statistics tables. Step 1: Create the Dataset. Data Formatted as a Table. I have found fomrulas for vlookup and xlookup but not for hlookup. Define a matching set of x values. g. Step 3: Interpret the Polynomial Curve. 96 and speed 800 result in 48. 2. tutorial for linear interpolation in Microsoft excelexcel formula: =FORECAST(B17,OFFSET(KnownY,MATCH(B17,KnownX,1)-1,0,2),OFFSET(KnownX,MATCH(B17,KnownX,1)-. Inside the file you will find the columns with values and also the graphs for easier understanding. 35m limiting distance, I would have to enter values (into green cells) into the interpolation table of 40m2 at 1. Based on audio signal frame power (in dB), I could search for appropriate gain from the table. 7 4 = o − − = − − Linear interpolation works for estimating any thermodynamic intensive property in any phase for tabulated materials. Both Kenneth's and Cringe's solutions assume the relationship is linear (which it is in the table, but not in general). If y is a matrix or an N-dimensional array, the interpolation is performed on each column of y . Since python is utilised, it is good practice to reuse existing functions already written by the community. Aug 19, 2016. Naturally, multivariate interpolation gets more complex than simple single variable interpolation. To do this, click on Chart Design > Select Data. As a result, when we apply this algorithm to the provided dataset, we receive the following interpolated y value: Interpolated value. I understand table format is good rather than a list format but what I mentioned is just an example, in actual the data could be much much bigger (usually in my case it reaches 500-600). EXC and PERCENTILE. tutorial for linear interpolation in Microsoft excelexcel formula: =FORECAST(B17,OFFSET(KnownY,MATCH(B17,KnownX,1)-1,0,2),OFFSET(KnownX,MATCH(B17,KnownX,1)-. The file here is an excel file and I have imported them into matlab and named the variable naca which is the size of 395*4. Next, select the cell where you want the interpolated value to appear and use the formula =FORECAST. forcast wants a range or an array and not numbers which is what you are passing with indexys:indexys1 You are passing the values of the index, so it would return something like 104:34 and not a range or an array. I have attached the workbook with the formula I was trying to use. Click within the result cell and enter: Table of Contents hide. 3. 4 to find the resultant. 2. The table will be placed in sheet 3 of the Excel Spreadsheet. There's no logarithmic regression or interpolation in Excel, even in the Anlaysis ToolPak. 1) a lookup function to locate the interval containing new_x (I tend to use the MATCH () function). Simple Mathematic formula Linear interpolation is the process of estimating a new value by drawing a straight line between two nearby known values. In other words, my table looks like this: D. The two time series are plotted separately below. Linear interpolation. My problem is this: I have some data from a geophysics survey in a simple xlsx sheet (Excel 2010). 6% and 520 were the results achieved, I need to figure out what the weighted average is between 11% and 12% whilst at the same time the weighted average between 500 and 550 to arrive at a final exact figure. Given two known values (x1, y1) and (x2, y2), we can estimate the y-value for some point x by using the following formula: y = y1 + (x-x1) (y2-y1)/ (x2-x1) To create a sample linear interpolation formula, follow these steps: Type the following values in a worksheet: excel Copy A1: 9 B1: = (A7-A1)/ (ROW(A7)-ROW(A1)) A2: =A1+$B$1 A3: A4: A5: A6: A7: 11 Select cells A2:A6. To create a sample linear interpolation formula, follow these steps: Type the following values in a worksheet: excel Copy A1: 9 B1: = (A7-A1)/ (ROW(A7)-ROW(A1)). Next, select the cell where you want the interpolated value to appear and use the formula =FORECAST (x, known_y's, known_x's) to calculate the interpolated value. That is because I do not know how to use the Excel table structure references to: a) get only the first row. I have one doubt regarding the linear interpolation. 24 1M 0. When the lookup is intermediate of two values in the lookup column, it returns the lesser value from the second column. Learn how to use the FORECAST function and XLOOKUP to perform linear interpolation in Excel when there are only two or more pairs of x- and y-values. INC(<column>, <k>) Parameters. known_x’s – a range of x. Limit represents the most extreme number of. my problem in interpolate it was on fixed set. xlsx. You can express trends in visual data by extrapolating a graph by a trendline. Shows how to set up a cell to automatically do linear interpolation in Microsoft Excel. 2,075. Using the Equation of the Linear Interpolation 2. You can also implement a user defined function (UDF) interpolateX. Messages. The INDEX function can find data in a 2d table if we use both the row_num and column_num arguments. 1. Converting Data to a Table. So the data looks like: 1 18 4 46 9 57 15 69 21 64 27 56 30 48 33 44. You'll need much more advanced software for that, such as MatLab. I am trying to figure out a way to interpolate data from a table to calculate a value. 226, which multiplied by 950,000 is 1,164,960. Let f(x)=e^x over the closed interval [1,2]. 2. Step 1: Finding the Value of Z. VBA doesn’t recognize these functions by themselves. e. Is there a readymade solution from MATLAB for doing so?And the formula for each cell should: Take the input of Stations (column "B") Check, for that specific Stations number, the amount of data on the other table (like make a filter on STATIONS for the specific number) Perform an VLOOKUP for checking the JPH based on the %SMALL value on row 2. I will discuss these in future articles. interpolate)# There are several general facilities available in SciPy for interpolation and smoothing for data in 1, 2, and higher dimensions. If not specified, x is taken to be the indices of y ( 1:length (y) ). Instead you should 'add trendline' choose the type of relationship the x and y data share (or you believe works best) and click 'Display Equation on chart'. interpolate. You can linearly. for univariate polynomial interpolation can be recovered from the LU factorization of a Vandermonde matrix. In conditional formatting options, selects color scales. 2 AOA, I want to find out the corresponding Cl & Cd. i hope this clarifies This message was edited by c_t on 2002-09-06 04:33 This message was edited by c_t on 2002-09-06. Read tutorial and download example Excel file here:do I have MATLAB read an Excel file, interpolate between table values, and then assign the values to variables? Follow 21 views (last 30 days). As an example, if you want to find the saturated pressure of water at a temperature of 40 C you can look in Table B. Choose the Scatter chart type and select the scatterplot. The set example is this, as shown in figure 1. value = Application. Create table rangesInter This calculate the ranges, if range is >1 day you have missing dates. So if I understand you correctly you just want to interpolate in 3D. 5 seconds by a. lookup_array is the range of cells that Excel searches through to find the lookup_value. It is easy to perform interpolation of non-linear 2D data in Excel. Interpolate in Excel Graph: 6 Ways. How to Multiply Column by a Constant in Excel. What is the best way to interpolate in such a dataset (so I have a value for every day) ?Use the XLOOKUP function to find things in a table or range by row. 1) Select an empty cell for the output. Data Interpolation within a Matrix. I would like to plot surface chart (contours). Hello all, I just wanted to stop by and share my work. Step 2. The problem is that you interpolate the data on a linear scale but expect the outcome to look smooth on a logarithmic scale. Right-click from the left side panel of the new window, then choose 'Insert' > 'Module'. 1W 0. Conclusion. The syntax and usage of the two functions are the same. Here, you can follow any method to do the task. Hello, I am trying to get an excel formula that will do linear interpolation for me. A short introduction to using linear interpolation to find intermediate values (i. Count If nR < 2 Then Exit Function If x < rX (1) Then ' x < xmin, extrapolate l1. I do a lot of spreadsheets that requires linear interpolation using arrays. The file here is an excel file and I have imported them into matlab and named the variable naca which is the size of 395*4. See below figure. 2: subtract the smaller value from your input value , subtract the smaller value from the larger value , divide the former by the latter. Re: A Formula To Lookup And Interpolate. , it linearly interpolates {x, log(y)} and then outputs the interpolated {x', y'} (in other words, it gives f(x)) by exponentiating the result rather than giving {x', log(y')}. Now we can find the missing rows, and the real rows on either side (for interpolation): DECLARE @Missing table ( x integer NOT NULL PRIMARY KEY, prev_row integer NULL, next_row integer NULL ); -- Find missing rows INSERT @Missing (x, prev_row, next_row) SELECT Missing. The worksheet is set up to interpolate a data set of up to fifty points to a new data set of up to fifty points This is an HP R8486A power sensor New X points Interpolated Y points This data is from a HP 346B noise source Noise source ENR table example This is an example of interpolating the calibration factor of a power head The data below is. 96 and speed 800 result in 48. . You can easily use the MATCH function to return the location of your unkown value. What I need is a complete set of {date, value} pairs where for each date withing the range a value is known (either measured or calculated). Assume you have the data table starting in A1 with a blank. Failing to follow. 0. As an example, if you want to find the saturated pressure of water at a temperature of 40 C you can look in Table B. I mean It might be 3 tables with B equal to: -1 0 1. There are other Excel tools that we can use to project/interpolate values, such as Analysis ToolPak or Microsoft Solver Foundation. For given points (x 0 , y 0) and (x 1, y 1) the value at y for a known x can be calculated by the following. . But the tendency between points is to visually interpolate the values, while in some cases the data is constant from one point to the next, where it jumps to a new value. Then, we will head to the Home tab and select Fill in the Editing group. A simpler option is to choose a nearby but conservative option (one that results in a slightly higher p-value), or you could just use the closest table entry. Use of Linear Trend Method. . Enter the data. In this method, we will use a VBA code for searching a value in a range, and then, get the desired result with the help of the interpolation. Surprisingly, linear interpolation is quite hard to do in Excel. Is there a formula to automatically do this? My current code is below and it's a bit clunky, especially trying to apply the formula for hundreds of row of data. Jerry. To fill in the missing qualities, we can feature the reach beginning when the missing qualities, then click Home > Editing > Fill > Series. e. An instance of this class is created by passing the 1-D vectors comprising the data. 1,500. Let's say we have two data series x_i and y_i such that for all i in [[1,N]], y_i = f(x_i) where f is a non-linear function. I. I am trying to obtain an estimate of an x and y value given a z value using a x,y,z matrix. Use INTERPXY to map a scattered (x,y) data points onto a uniform grid for easy plotting in Excel. Interpolation can be used to estimate the thermal resistance for non-tabulated values between the tabulated ones. This seems really common. Next I clicked the 'Hidden and Empty Cells. The interp1d class in the scipy. 9. 4 Torque. Using the TREND Function 4. It is considered to be the simplest of all methods to interpolate between two values when values are approximately linear. Double Interpolation is very familiar to Engineers who are using it for every Design ProblemsThose who want to do Double Interpolate in excel this Video will. The following step-by-step example shows how to use the TREND function to extrapolate data in practice in Excel. Interpolate in Excel Graph: 6 Ways. For the sake of overview, we put this into a table: x x 0 x 1::: x m y y 0 y 1::: y m For. I have also tried interp1 function to interpolate. Once the index number is returned, you can use. Example: Linear Interpolation. xls, since then it will not be available to other users of the spreadsheet. If one of the looked-up values is not in the exact range, provide the results as follows: 1- no interpolation, the lower bound/first value. . For the "Value III" I know the math formula when you interpolate r numbers between two numbers a and b then the distance d between interpolated numbers is: d = (b-a)/ (r+1) And the values of those interpolated numbers are: r1 = a + d r2 = r1 + d or r2 = a + 2*d r3 = r2 + d or r3 = a + 3*d. 674), for 40 C in the first column. First, you need to have a clean and tidy group of data to work with. If I calculate it with the data you have given: Temperature 29. The way the I measure these variables, the ammonia level are always one of these six values (on top of the table), so it works as a categorical variable. Step 2: Next, gather as many as possible historical and current data points in order to build a function. Linear interpolation. INC will interpolate when the value for the specified percentile is between two values in the array. Then you can use this actual equation to interpolate the value. Along the Y axis, is pressure altitude, each line representing a change of 1000 feet. I have a specific point of temperature and pressure and need the thermal conductivity interpolated from them. 96 at a speed of 1000 should be 54. 1. Your data seems to be pretty smooth. 96 at a speed of 1000 should be 54. Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994. , time) and another for the dependent variable (e. 4 Torque. 3. =B2+ (A4-A2)* (B3-B2)/ (A3-A2) In the above example, the formula’s last section, highlighted in red, calculates how much time taken changes whenever the speed of the bike changes by 1. To create a heat map in Excel you need to follow the below steps: First of all, select the data on which you want to apply a heat map (here you need to select all the cells where you have sales values) After that, go to Home Tab Styles Conditional Formatting. The interpolation data can be structured (defined on a grid) or unstructured (defined on a generic point cloud). Thanks so far. Things to Remember. Use INTERPXY to interpolate from a set of (x,y) data points at an arbitrary point. Rows. use this with index and index +1 to find to two values around your input. For example, look up the price of an automotive part by the part number, or find an employee name based on their employee ID. I have made an example. I have a table with many discrete sequential values down the rows of column 1, with corresponding values along each row down column 2. linear interpolation to estimate. 2 0. Step 3: Use the Interpolate Function. 9 C 263. For example, if you're using data about how sales increased as a company hired more sales professionals, the numbers of sales professionals go in column A, and the corresponding total sales go in column B. 12 KB. Examples. Method 1: Mathematical Equation for Linear Interpolation. We can mea-sure the length of the intervals a and b (simply by using a ruler). Here is an Example for a mathematical solution: Generate x-values x (we need them as array for the next 2 steps) Calculate the slope m for the given row values. ” Choose the cell where you wish the data to be pasted. Applying Trendline for Data Extrapolation in Excel. I would like to write an Excel function that linearly interpolates between data points. . Linear interpolation is a way to fill in the ``holes'' in tables. Linear interpolation is useful when looking for a value between given data points. To start, place at least two columns of data in an empty Excel worksheet. For this to work properly, the values in the lookup_array must be in ascending order. This data should contain two columns: one for the independent variable (e. . As the highest number in this table is 32, I need to generate a column with 32 cells, B1:B32. First, organize your data into two columns with known values. I need to have on X axis -90° to 90° with increment of 10° and same for Y. LINEAR formula to the cell where you want to add the interpolated value. In continuation of our discussion about "How to use the steam table" for Thermodynamics, we created this video to learn how to interpolate manually and by us. the excel file make a first linear interpolation on pressure and a second linear interpolation on temperature. Whether you're new to Microsoft Excel or simply looking to pick up a few new tips and tricks, you're sure to enjoy this free software tutorial. 8), but this number is not fixed. The task: Depending on the country and the data type you want to get the correct value from the table. Once we press ENTER, an array of coefficients will appear: Using these coefficients, we can construct the following equation to describe the relationship between x and y: y = . This help content & information General Help Center experience. We can also use this equation to calculate the expected value of y, based on the value of x. With XLOOKUP, you can look in one column for a search term and return a result from the same row in another column, regardless of which side the return column. Hello everyone! I'm a fairly basic user in excel so I'm looking for some help. data points exactly by simply using linear interpolation between the known values. The first way is plugging in the basic mathematical formula for linear interpolation. If we leave the Type as Linear, Excel will use the following formula to determine what step value to use to fill in the missing data: Step = (End – Start) / (#Missing obs + 1) For this example, it determines the. Range ("A2:A" & lastRow2) For s1Row = 2 To lastRow1 typeName = Sheets (SourceSheet1). It allows you to incorporate table-driven modeling directly in your custom block, without the need of. Implementing Weighted Moving Average Formula. Summary. Syntax PERCENTILE. 2. Unable to download your file. We will show you 2 ways. While many people can interpolate on an intuitive basis, the article below shows the formalized mathematical approach behind the intuition. To use an interpolation function, click on the fx button on the formula bar, select the XonGrid 4 interpolation category, select a function then enter your data. But some columns of my table has NaN values and the. For x1 and y1, use the input and output from the lower value, and for x2 and y2, use the input and output from the higher value. vq = interp1 (x,v,xq) returns interpolated values of a 1-D function at specific query points using linear interpolation. . Interpolate Missing Data in Excel: 4 Easy Ways. , temperature). Method 1: Mathematical Equation for Linear Interpolation. Click on the image of the example steam table to open that image in a new window in a larger size to be easier to see it clearly. 3- exact interpolated value. 3) Linear interpolation (I sometimes use the TREND () function) to return the correct y value for the new x value. I would note that I don't usually use IF() functions when I do interpolations. Step 2: Fill the formula with the desired values. This is the easiest way to interpolation by set up formula only 1 time and we can use this forever. To interpolate linearly in Excel, follow these steps: Enter your data into an Excel worksheet. 5. Use the x,y data in a X Y (Scatter) plot. Since we’ve grouped the table into cells, we can pass the column [Table Data]. With a starting value of 1. Cubic Spline Interpolation in Excel: Step-by-Step Procedure. 2 AOA, I want to find out the corresponding Cl & Cd. 2 AOA, I want to find out the corresponding Cl & Cd. Firstly, we will use the known and surrounding values to find the missing values. =iferror(forecast. The table is fairly complex as there are two axis from which I would like to interpolate. You can use the linear method if your data set creates a straight line and a calculator or software if the data set creates a more complex shape. Addendum: Advanced Solve Functionality Setup in Excel 2007 Advanced solve functionality is available in Excel, it just needs to be enabled through an Add-In. In this method, you will show two different ways for data extrapolation in Excel. Table of Contents hide. For example, you select “Canada” and “VAT”, you want to get 5% in return. Linear Interpolation in Excel: Step-by-Step Example Interpolation is the process of estimating an unknown value of a function between two known values. As there are just few points as written above, I need to interpolate the correct gain every time as the power is usually between the points. Steps. I have a table that shows me a chemical concentration value based on temperature, pH and ammonia. interp will give you linear interpolation only. More precisely, I would like the macro to account for X values <0 or >0. Linear interpolation is a way to fill in the ``holes'' in tables.