91影视

A scatterplot is constructed for the pairs of measurements for women and men.

a.

Since the points on the lower-left corner do not seem to follow an increasing straight-line trend or a decreasing straight-line trend, there seems to be no linear correlation among x and y for women.

b.

Similarly, the points on the upper right corner neither follow an increasing straight-line trend or a decreasing straight-line trend, there seems to be no linear correlation among x and y for men.

c.

To calculate the correlation coefficient between x and y for women, the following computations are made:

The formula to calculate correlation coefficient r is given by

\(\begin{aligned} r &= \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{\sqrt {n\left( {\sum {x^2}} \right) - {{\left( {\sum x} \right)}^2}} \sqrt {n\left( {\sum {y^2}} \right) - {{\left( {\sum y} \right)}^2}} }}\\ &= \frac{{4\left( 9 \right) - \left( 6 \right)\left( 6 \right)}}{{\sqrt {4\left( {10} \right) - {{\left( 6 \right)}^2}} \sqrt {4\left( {10} \right) - {{\left( 6 \right)}^2}} }}\\ &= 0\end{aligned}\)

Thus, the correlation coefficient between x and y for women is 0.

To calculate the correlation coefficient between x and y for men, consider the following calculations:

The formula to calculate correlation coefficient r is given by

\(\begin{aligned} r &= \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{\sqrt {n\left( {\sum {x^2}} \right) - {{\left( {\sum x} \right)}^2}} \sqrt {n\left( {\sum {y^2}} \right) - {{\left( {\sum y} \right)}^2}} }}\\ &= \frac{{4\left( {361} \right) - \left( {38} \right)\left( {38} \right)}}{{\sqrt {4\left( {362} \right) - {{\left( {38} \right)}^2}} \sqrt {4\left( {362} \right) - {{\left( {38} \right)}^2}} }}\\ &= 0\end{aligned}\)

Thus, the correlation coefficient between x and y for men is 0.

d.

To compute the correlation between all the 8 points, consider the following calculations:

The correlation coefficient is equal to:

\(\begin{aligned} r &= \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{\sqrt {n\left( {\sum {x^2}} \right) - {{\left( {\sum x} \right)}^2}} \sqrt {n\left( {\sum {y^2}} \right) - {{\left( {\sum y} \right)}^2}} }}\\ &= \frac{{8\left( {370} \right) - \left( {44} \right)\left( {44} \right)}}{{\sqrt {8\left( {372} \right) - {{\left( {44} \right)}^2}} \sqrt {8\left( {372} \right) - {{\left( {44} \right)}^2}} }}\\ &= 0.985\end{aligned}\)

Thus, the correlation between x and y when all the 8 points are taken into account is equal to 0.985.

e.

All of the points corresponding to women lie on the lower-left corner while all of the points corresponding to men lie on the upper-right corner.

There seems to be no association/mix-up of the two sets of values.

Therefore, the points corresponding to women and menappear to represent two different and distinct populations and should be analyzed separately.