Identify the true statements about the correlation coefficient, if two variables are negatively correlated, when one variable increases, the other variable also increases. the correlation coefficient is not affected by outliers. a correlation coefficient of zero means that no relationship exists between the two variables. the sign of describes the direction of the association between two variables. when the data points in a scatter plot are randomly scattered, the correlation between the two variables is weak. the value of ranges from negative one to positive one.

Step-by-step explanation:

Correlation coefficient is the measure of linear association between two variables.  It is the ratio of cov of two variables divided by product of std deviation of each variable.  If outliers are present std deviation would be more and hence affects the correlation value very much. The correlation coefficient ranges between -1 and 1.  If negative we say negative association and vice versa.

Hence the correct true statements are

A correlation coefficient of zero means that no relationship exists between the two variables.

The sign of  corr.coeff. describes the direction of the association between two variables

When the data points in a scatter plot are randomly scattered, the correlation between the two variables is weak.

The value of corr.coeff ranges from negative one to positive one.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1