# Interpolation and extrapolation in statistics pdf

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In the mathematical field of numerical analysis , interpolation is a type of estimation , a method of constructing new data points within the range of a discrete set of known data points. In engineering and science , one often has a number of data points, obtained by sampling or experimentation , which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate , i.

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Extrapolation is the process of taking data values at points x 1 , This is most commonly experienced when an incoming signal is sampled periodically and that data is used to approximate the next data point. For example, weather predictions take historic data and extrapolate a future weather pattern. Sensors may take the current and past voltages of an incoming signal and approximate a future value, perhaps attempting to compensate more appropriately. We have seen how to use interpolation to approximate values between points x 1 , However, if we are trying to approximate a value at a value outside the range of x values, the error increases significantly when using interpolation. However, if model information is available, for example, that the data is linear, quadratic, or exponential, we may use least-squares to find a best-fitting curve.

Extrapolation and interpolation are both used to estimate hypothetical values for a variable based on other observations. There are a variety of interpolation and extrapolation methods based on the overall trend that is observed in the data. These two methods have names that are very similar. We will examine the differences between them. For both methods, we assume a few things. We have identified an independent variable and a dependent variable. Through sampling or a collection of data, we have a number of pairings of these variables.

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Interpolation is the process of deriving a simple function from a set of discrete data points so that the function passes through all the given data points i. It is necessary because in science and engineering we often need to deal with discrete experimental data. Interpolation is also used to simplify complicated functions by sampling data points and interpolating them using a simpler function. Polynomials are commonly used for interpolation because they are easier to evaluate, differentiate, and integrate - known as polynomial interpolation. In Newton's method the interpolating function is written in Newton polynomial a. Plugging in the two data points gives us. Obviously this function passes through both data points i.

Extrapolation is a useful statistical tool used to estimate values that go beyond a set of given data or observations. In this lesson, you will learn how to estimate or predict values using this tool. It could even be said that it helps predict the future! To help us remember what it means, we should think of the part of the word 'extra' as meaning 'more' data than what we originally had. This tool is not only useful in statistics but also useful in science, business, and anytime there is a need to predict values in the future beyond the range we have measured. Let's try a basic extrapolation by finding values in a numerical sequence.

## The Difference Between Extrapolation and Interpolation

Interpolation means to calculate a point or several points between two given points. For a given sequence of points, this means to estimate a curve that passes through every single point. Linear interpolation is the simplest interpolation method. Applying linear interpolation to a sequence of points results in a polygonal line where each straight line segment connects two consecutive points of the sequence. Therefore, every segment P; Q is interpolated independently as follows:.

Question 1. Define Interpolation. Answer: It is the technique of estimating the value of the dependent variable Y for any intermediate value of the independent variable X.

In this page you can download an Excel Add-in useful to linear, quadratic and cubical interpolation and extrapolation. The functions of this Add-in are very simple to use and they have context help, through a chm file.

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#### COMMENT 1

• Abstract. —Interpolation is the process of calculating the unknown value from known given values whereas extrapolation is the process of calculating unknown values beyond the given data points. Liane B. - 21.05.2021 at 00:47