udledning

Let two data sets (x,y) and (x?,y?) be related by x? = c1 +c2x and y? = c3 +c4y for all i = 1, …, n. This means that the only differences between the two data sets are the location and the scale of measurements. Such data transformations are often applied in economic studies. For example y may be the total variable production costs in dollars of a firm in month i and y? the total production costs in millions of dollars. Then c3 are the total fixed costs (in millions of dollars) and c4 = 106.

a) Derive the relation y? = α? + β?x? between y? and x? if y and x satisfy the linear relation y = α+βx. Hint: Start by finding the expressions for x and y. Then you can insert these into the above equations and isolate. In order to arrive at the final result, you must define something like β? and α?

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