Show That the Correlation Coefficient Between Y and X Is

question 47

Essay

Show that the correlation coefficient between Y and X is unaffected if you use a linear transformation in both variables. That is, show that corr(X,Y)= corr(X^*, Y^*), where X^* = a + bX and Y^* = c + dY, and where a, b, c, and d are arbitrary non-zero constants.

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Definitions:

Oil Shale

Oil shale is a type of sedimentary rock that contains kerogen, a solid mix of organic chemical compounds from which liquid hydrocarbons can be produced, like shale oil.

Methane

A colorless, odorless flammable gas that is the simplest member of the alkane hydrocarbons, with a chemical formula of CH4.

Coal Deposits

Coal Deposits are accumulations of coal found in the Earth’s crust, originating from the decayed plant material under high pressure and heat over millions of years, primarily used as a fossil fuel.

Uranium Deposits

Concentrations of uranium minerals within the earth's crust, typically exploitable for nuclear fuel.