Correlation and Coefficient of Determination

Correlation analysis is

• univariate analysis.

• bivariate analysis.

• multivariate analysis.

• both bivariate and multivariate analysis.

Answer explanation

Correlation analysis requires more than one variable.

Which one is NOT appropriate to use to study the association between variables?

• Scatterplot.

• Pie chart.

• Correlation.

• Regression.

Answer explanation

Pie chart is suitable to illustrate the percentage distribution.

Describe the relationship.

• Positive linear relationship.

• Negative linear relationship.

• Positive curvilinear relationship.

• Negative curvilinear relationship.

Answer explanation

As x increases, y decreases.

Two variables have a positive association when

• the value of one variable tends to increase as the other variable increases.

• the value of one variable tends to increase as the other variable decreases.

• the value of one variable tends to increase regardless how the other variable change.

• the values of both variables are always positive.

Answer explanation

Both variables move in the same direction although the numbers are negative.

The correlation coefficient, r is used to determine

• y values given values of x.

• x values given values of y.

• the strength and direction of relationship between x and y.

• none of these.

If there is a strong correlation, the value of r must be

• any value larger than 1.

• closer to -1 if the correlation is negative.

• closer to 0 if the correlation is positive.

• none of these.

Answer explanation

The closer to 1 and -1, the stronger the relationship.

The correlation coefficient

• is the same as r².

• can never be negative.

• is the square of coefficient of determination.

• is the square root of coefficient of determination.

Answer explanation

We use the r² to get the coefficient of determination!

Tags

CCSS.HSS.ID.C.8

Coefficient of correlation lies between

• 0 and +1

• 0 and -1

• -1 and +1

• -5 and +5

Answer explanation

The value of r must be between -1 and +1

Tags

CCSS.HSS.ID.C.8

If two variables, x and y, have a very strong linear relationship, then

• there is evidence that x causes a change in y.

• there is evidence that y causes a change in x.

• there might not be any causal relationship between x and y.

• None of these alternatives is correct.

Answer explanation

Correlation does not imply causation.

Tags

CCSS.HSS.ID.C.9

If the coefficient of determination is 0.81, the correlation of coefficient is

• 0.6561.

• must be positive.

• must be negative.

• could be either +0.9 or -0.9.

Answer explanation

Correlation of coefficient is the square root of coefficient of determination.

Tags

CCSS.HSS.ID.C.8