Definition of Extrapolation Formula

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Extrapolation Formula (wallstreetmojo.com)

Calculation of Linear Extrapolation (Step by Step)

Examples

Example #1

Suppose that the value of certain variables is given below in the form of (X, Y):

  • First, one must analyze the data to determine whether the data is following the trend and whether one can forecast the same. There should be two variables: one has to be a dependent variable, and the second has to be an independent variable. The numerator of the formula starts with the previous value of a dependent variable. Then one needs to add the fraction of the independent variable while calculating for mean for class intervals. Finally, multiply the value arrived in step 3 by a difference of immediately given dependent values. Adding step 4 to the dependent variable’s value will yield the extrapolated value.

  • (4, 5)(5, 6)

Based on the above information, you must find the value of Y(6) using the extrapolation method.

Solution

Use the below-given data for calculation.

  • X1: 4.00Y2: 6.00Y1: 5.00X2: 5.00

The calculation of Y(6) using the extrapolation formula is as follows,

Extrapolation Y(x) =  Y(1) + (x) – (x1) / (x2) – (x1) x {Y(2) – Y(1)}

Y(6) = 5 + 6 – 4 / 5 – 4 x (6 – 5)

The answer will be –

  • Y3 =  7

Hence, the value for Y when the value of X is 6 will be 7.

Example #2

Mr. M and Mr. N are students of the 5th standard, and they are currently analyzing the data given to them by their math teacher. The teacher has asked them to compute the weight of students whose height will be 5.90 and informed them that the below data set follows linear extrapolation.

Assuming that this data follows a linear series, you must calculate the weight, which would be the dependent variable Y in this example when the independent variable x (height) is 5.90.

In this example, we now need to find out the value, or in other words, we need to forecast the value of students whose height is 5.90 based on the trend given in the example. Then, we can use the below extrapolation formula in Excel to calculate the weight, which is a dependent variable for a given height and an independent variable.

The calculation of Y(5.90) is as follows,

  • Extrapolation Y(5.90) = Y(8) + (x) – (x8) /(x9) – (x8)   x [Y(9) – Y(8)]Y(5.90) = 59 + 5.90 – 5.70 / 5.80 – 5.70 x (62 – 59)

  • = 65

Hence, the value for Y when the value of X is 5.90 will be 65.

Example #3

Mr. W is the executive director of the company ABC. He was concerned with the company’s sales following a downward trend. Therefore, he has asked his research department to produce a new product that shall follow increasing demand as and when the production increases. After 2 years, they developed a product that faced increasing demand.

Below are the details of the last few months:

They observed that since this was a new and cheap product initially, this would follow linear demand until a certain point.

Hence moving forward, they would first forecast the demand and then compare them with actual and produce accordingly as this has demanded huge costs for them.

The marketing manager wants to know what one would demand if they produced 100 units. Based on the above information, you must calculate the demand in units when they produce 100 units.

We can use the below formula to calculate the demands in units, which is the dependent variable for given units produced, which is an independent variable.

The calculation of Y(100) is as follows,

  • Extrapolation Y(100) = Y(8) + (x)- (x8) / (x9) – (x8) x [ Y(9) – Y(8)]Y(100)   =  90 + 100 – 80 / 90 – 80 x (100 – 90)

  • = 110

Hence, the value for Y when the value of X is 100 will be 110.

Relevance and Uses

Mostly used to forecast data that is out of the current range of data. In this case, one assumes that the trend shall continue for given data and even outside that range, which is not always the case. Hence, one should use extrapolation cautiously. Instead, the interpolationInterpolationInterpolation is the mathematical procedure applied to derive value in between two points having a prescribed value. It approximates the value of a given function at a given set of discrete points. It can be applied in estimating varied concepts of cost, mathematics, statistics.read more method is a better method to do the same.

This article has been a guide to the Extrapolation Formula. Here, we discuss the formula to calculate the dependent variable’s value for an independent variable, along with practical examples and a downloadable Excel template. You can learn more about Economics from the following articles:-

  • Revenue Run RateRevenue Run RateCompanies use revenue run rate to forecast the annual revenue generation based on current revenue levels, growth rate, market demand, and other relevant factors, assuming that current earnings are free from any seasonality or outlier effect and the market conditions will remain constant.read moreVelocity of Money FormulaExcel Trend LineExcel Trend LineA trend line, often known as the best-fit line, depicts the data’s trend. It shows the overall trend, pattern, or direction based on the data points available.read moreFormula of Multiple RegressionFormula Of Multiple RegressionMultiple regression formula is used in the analysis of the relationship between dependent and numerous independent variables. Formula = y = mx1 + mx2+ mx3+ bread moreEffective Annual RateEffective Annual RateEffective annual rate (EAR) is the rate actually earned on investment or paid on the loan after compounding over a given period of time and is used to compare financial products with different compounding periods i.e. weekly, monthly, annually, etc. As the compounding periods are increased, the EAR increases. Effective Annual Rate = (1 + i/n)n – 1read more