for this question, x is a qualitative variable and y is a quantitative variable. the mean of y for the group coded 0 is 8.88 and the mean of y for the group coded 1 is 12.3, and the variance of x is 0.27. what is the covariance between x and y?

Variables that are not measurement variables. Their values do not result from measuring or counting. Designator - Values that are used to identify individuals in a table. Designator values usually do not repeat in a table, but variable values often do repeat.

Quantitative Variables:

Variables whose values result from counting or measuring something. Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting. Designator - Values that are used to identify individuals in a table.

Given that,

x is a qualitative variable

y is a quantitative variable

Mean of y for the group coded 0 = 8.88

Mean of y for the group coded 1 = 12.3

The variance of x is = 0.27

Then the covariance between x and y

IF x and Y are independent then Cov(x,y)= 0

Var(x + y) = Var X + Var y + 2cov(x,y)

Var(x + y) = 8.88 + 12.3 + 0

Var(x + y) = 21.18

Z1= X - E (X)/ √Var (X) and

Z2 = Y - E(Y)/ √Var Y

Var (z1+z2) = Var (z1) + Var(z2) + 2Cov (z1,z2)

Cov (z1,z2)= E(z1,z2) - E(z1) E(z2)

= E(z1,z2) [as E(z1) E(z2)= 0]

= E {[ X-E(X)] [Y-E(Y)]/ √Var(X) Var(y)}

= E{[ X- 0.27][Y- 0.27]/√8.88(12.3)}

= E{[ XY - 0.27X - 0.27Y + 0.072]/√109.224

= E{[ XY - 0.27X - 0.27Y + 0.072]/ 10.45

= [8.88 * 12.3 - 0.27 * 8.88 - 0.27 * 12.3 + 0.072]/ 10.45

= [109.224 - 2.39 - 3.321 + 0.072]/ 10.45

= 103.585/ 10.45

= 9.91

Var (z1+z2) = Var (z1) + Var(z2)

= {E (X)/ √Var (X)} +{ Y - E(Y)/ √Var Y}

= {8.88/√8.88 } + {12.3/√12.3}

= {8.88/2.97} + {12.3/3.5}

= 2.989 + 3.51

= 6.499

Therefore,

x is a qualitative variable and y is a quantitative variable then the covariance between x and y = 6.499

To learn more about Covariance visit :

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