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August 6th, 2015, 08:43 AM   #1
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Estimate the marketing expenditure to attain a sales target of Rs 40 crores

The following data relate to marketing expenditure in Rs lac and the corresponding sales of a product in Rs crores. Estimate the marketing expenditure to attain a sales target of Rs 40 crores.

Marketing expenditure--------------------Product sales

10-----------------------------------------------14
12-----------------------------------------------17
15-----------------------------------------------23
20-----------------------------------------------21
23-----------------------------------------------25
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August 6th, 2015, 12:08 PM   #2
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There's too little data for that to be estimated sensibly.
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August 9th, 2015, 07:14 AM   #3
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Given any n data points, it is always possible to fit a n-1 polynomial through those n points. Here, you have 5 data points so you can find a unique 4th degree polynomial, y= ax^4+ bx^3+ cx^2+ dx+ e, then try to solve the equation ax^4+ bx^3+ cx^2+ dx+ e= 40. There are many different ways to do that, the most straight forward being to put each of the 5 data points in for x and y giving 5 linear equations to solve for a, b, c, d, and e.

But there are also many different way to approximate such a function. You could, for example, find the linear or quadratic function that approximates those points in the "least squares" sense (so that the sum of the squares of the error at each point is a minimum).
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