Operations

Adding and Subtracting a Constant  Select (Data, Univariate Prototypes, Continuous Variable) to place variable X [1 2 3 4 5] on the vector display to demonstrate that adding or subtracting a constant from a variable does not change the variance of a variable. Adding a constant to the variable X (Operations, Add a Constant)

does not change the variance of the X + c variable. Subtracting a constant from the variable X (Operations, Subtract a Constant) does not change the variance of the X - c variable either.

Multiplying and Dividing by a Constant  Multiplication or division of a variable by a constant increments or decrements variance of a variable by the square of the constant. Thus, multiplying variable X by a constant (Operations, Multiply by a Constant)

changes variance of the variable X to 18 [3 (2 * 3^3 = 18)]. Dividing variable by a constant (Operations, Divide by a Constant) changes variance of variable X  to .222  [3 (2 / 3^3 = .222)].

Adding and Subtracting Variables  Variance of a sum of two variables is calculated as the sum of variances of the variables, plus two times their covariance. Variance of a difference of two variables is calculated as the sum of variances of the variables, minus two times their covariance. This can be demonstrated by entering variables X [1 2 3 4 5] and Y [3 2 1 5 4] (Data, Bivariate Prototypes) and by calculating their sums (Operations, Add Variables) and differences (Operations, Subtract Variables)

Select (Analysis I, Variance, Variance of a Variable), check Variable X, click on the True Variance and on the Accept command. Select (Analysis I, Variance, Variance of a Variable), check Variable Y, click on the True Variance and on the Accept command. Select (Analysis I, Covariance), check Variable X and Variable Y, click the Accept command and store the covariance (1.00) it in Cell 3 of the scalar module. Add variances of the variables X (2.00) and Y (2.00) and the two times the covariance component (2 * 1).

Repeating these steps you can demonstrate that variance of a difference equals the sum of the variances of its component variables minus two times their covariance, for the example 2 + 2 - (2 * 1).

Exponentiation of Variables and Constants

Select (Arguments, -3z - + 3z)

click the Display the Sequence command and rename the variable on the vector display X.

Exponentiate Variables

Select (Operations, Exponentiate Variables)

click the Append command.

and plot the function as (Graphs, Spline Graphs)

Exponentiate Constants

Select (Operations, Exponentiate Constants)

click the Append command

 

and plot the function as (Graphs, Spline Graphs)

Complemental Variables

Select (Operations, Complemental Variables)

and plot the obtained function by the (Graphs, Spline Graphs) commands.

Reciprocal Variables

Select (Operations, Reciprocal Variables)

and plot the function by the (Graphs, Spline Graphs) commands.