Question

Assume that we apply a square root transformation to a ratio attribute x to obtain the new attribute x*. As part of your analysis, you identify an interval (a, b) in which x* has a linear relationship to another attributey.
a) What is the corresponding interval (A, B) in terms of x ?

b) Give an equation that relates y to x.

Answer 1

Answer:

(a) The corresponding interval is  $(a^2\;,\;b^2)$

(b) Equation:        y = m.(x)^$^{\frac{1}{2}$ + c

Explanation:

The transformation from x to x* is of square root. Mathematically,

      x* = √x

or    x = (x*)²

Part (a):

It means that an interval of (a , b) in x* can be transformed into x by taking square of each term of the interval value.

Therefore, interval in x will be (a² , b²).

Part (b):

It is given that x* and y are linearly related. Therefore, we can use linear equation to equate them.

y = m.(x*) + c

Substituting  x* = √x in above equation, we get

y = m.(x)^$^{\frac{1}{2}$ + c

This equation relates y to x.