Question

I need help on the last 3 columns on the right hand side and on the bottom as well.

Answer 1

Step-by-step explanation:

Given;

We are given a table of x and y values in order to calculate the correlation coefficient.

Required;

We are required to calculate and populate the tables for the values;

`\begin{gathered} (i)\frac{X-\bar{X}\text{ }}{S_x} \\ (ii)\frac{Y-\bar{Y}}{S_y} \\ (iii)\frac{(X-\bar{X})(Y-\bar{Y})\text{ }}{S_xS_y} \end{gathered}`

The variables here are;

`\begin{gathered} \bar{X}=mean\text{ }value\text{ }of\text{ }x \\ \bar{Y}=mean\text{ }value\text{ }of\text{ }y \\ S_x=standard\text{ }deviation\text{ }of\text{ }x \\ S_y=standard\text{ }deviation\text{ }of\text{ }y \end{gathered}`

With the use of a calculator the mean and standrd deeviations are as follows;

`\begin{gathered} \bar{X}=31 \\ \bar{Y}=10.77 \\ S_x=10.68 \\ S_(y=2.17) \end{gathered}`

The values that goes in the column;

`\begin{gathered} \frac{X-\bar{X}}{S_x} \\ (i)(18-31)/(10.68)=-1.2172 \\ (ii)(20-31)/(10.68)=-1.0299 \\ (iii)(22-31)/(10.68)=-0.8427 \\ (iv)(25-31)/(10.68)=-0.5618 \\ (v)(31-31)/(10.68)=0 \end{gathered}`

For the next column;

`\begin{gathered} \frac{Y-\bar{Y}}{S_y} \\ \\ (i)(14-10.77)/(2.17)=1.4885 \\ \\ (ii)(14-10.77)/(2.17)=1.4855 \\ \\ (iii)(12-10.77)/(2.17)=0.5668 \\ \\ (iv)(11-10.77)/(2.17)=0.1059 \\ \\ (iv)(10-10.77)/(2.17)=-0.3548 \end{gathered}`

For the last column;

`\begin{gathered} \frac{(X-\bar{X})(Y-\bar{Y})}{S_xS_y} \\ \\ (i)((-1.2127)(1.4885))/((10.68)(2.17))=-0.0779 \\ \\ (ii)((-1.0299)(1.4885))/((10.68)(2.17))=-0.0661 \\ \\ (iii)((-0.8427)(0.5668))/((10.68)(2.17))=-0.0206 \\ \\ (iv)((-0.5618)(0.1059))/((10.68)(2.17))=-0.0026 \\ \\ (v)((0)(-0.3548))/((10.68)(2.17))=0 \end{gathered}`