AP Statistics : Bivariate Data

Study concepts, example questions & explanations for AP Statistics

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Example Questions

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Example Question #1 : Bivariate Data

Which of the following correlation coefficients indicates the strongest relationship between variables?

Possible Answers:

Correct answer:

Explanation:

Correlation coefficients range from 1 to -1.  The closer to either extreme, the stronger the relationship.  The closer to 0, the weaker the relationship. 

Example Question #1 : How To Find Correlation

It is found that there is a correlation of exactly  between two variables. Which of the following is incorrect?

Possible Answers:

There is a strong association between the two variables.

There is enough evidence, with a correlation of , to assert that one variable causes the other

All of the answer choices are correct

The association between the two variables is positive

Correlation is measured on a scale of  to 

Correct answer:

There is enough evidence, with a correlation of , to assert that one variable causes the other

Explanation:

Under no circumstance will correlation ever equate to causation, regardless of how strong the correlation between two variables is. In this case, all other answer choices are correct. 

Example Question #1 : How To Find Correlation

In a medical school, it is found that there is a correlation of  between the amount of coffee consumed by students and the number of hours students sleep each night. Which of the following is true?

i. There is a positive association between the two variables.

ii. There is a strong correlation between the two variables.

iii. Coffee consumption in medical school students causes students to sleep less each night.

Possible Answers:

i and ii

iii only 

ii only

i and iii

i, ii, and iii

Correct answer:

ii only

Explanation:

Since the correlation is negative, there must be a negative association between the two variables (therefore statement i is incorrect). Statement ii is correct since a correlation of  to  on an absolute value scale of  to  is considered to be a strong correlation. Statement iii is incorrect since correlation does not mean causation. 

Example Question #1 : How To Find Correlation

Which of the following shows the least correlation between two variables? 

Possible Answers:

Correct answer:

Explanation:

The strength of correlation is measured on an absolute value scale of  to  with  being the least correlated and  being the most correlated. The positive or negative in front of the correlation integer simply determines whether or not there is a positive or negative correlation between the variables. 

A correlation of  means that there is no correlation at all between two variables.

Example Question #1 : How To Find Correlation

Which of the following correlation coefficients implies the strongest relationship between variables:

 

 

 

 

Possible Answers:

Correct answer:

Explanation:

A high correlation coefficient regardless of sign implies a stronger relationship. In this case  has a stronger negative relationship than the positive relationship described by a value of 

Example Question #1 : How To Find Correlation

A national study on cell phone use found the following correlations:

-The correlation between the number of texts sent each day and a person's average credit card debt is .

-The correlation between the number of texts sent each day and the number of books read each month is .

Which of the following statements are true?

i. As the number of texts sent each day increases, average credit card debt increases.

ii. Sending more texts causes people to read less.

iii. A person's average credit card debt is related more strongly to the number of texts sent each day than the number of books read each month is related to the number of texts sent each day.

 

Possible Answers:

i and ii

ii and iii

ii

i and iii

iii

Correct answer:

i and iii

Explanation:

i is correct because there is a positive correlation between the number of texts sent each day and average credit card debt. 

ii is incorrect because the word "cause" was used in the statement. Correlation does not mean causation. There is a relationship between the number of texts sent each day and the number of books that a person reads each month. However, the number of texts sent each day does not cause a person to read a certain number of books each month. 

iii is correct because the absolute values of the correlations indicate which correlation is stronger.  is a stronger correlation than .

Example Question #1 : How To Find Linearity

A basketball coach wants to determine if a player's height can predict the number of points the player scores in a season. Which statistical test should the coach conduct?

Possible Answers:

P-score

Linear regression

ANOVA

Correlation

T-test

Correct answer:

Linear regression

Explanation:

Linear regression is the best option for determining whether the value of one variable predicts the value of a second variable.  Since that is exactly what the coach is trying to do, he should use linear regression.

Example Question #1 : Bivariate Data

In a regression analysis, the y-variable should be the ___________ variable, and the x-variable should be the ___________ variable.

Possible Answers:

Greater, Lesser

First, Second

Qualified, Unqualified

Independent, Dependent

Dependent, Independent

Correct answer:

Dependent, Independent

Explanation:

Regression tests seek to determine one variable's ability to predict another variable.  In this analysis, one variable is dependent (the one predicted), and the other is independent (the variable that predicts).  Therefore, the dependent variable is the y-variable and the independent variable is the x-variable.

Example Question #2 : How To Find The Least Squares Regression Line

If a data set has a perfect negative linear correlation, has a slope of  and an explanatory variable standard deviation of , what is the standard deviation of the response variable?

Possible Answers:

Correct answer:

Explanation:

The key here is to utilize

.

"Perfect negative linear correlation" means , while the rest of the problem indicates  and . This enables us to solve for .



Example Question #3 : How To Find The Least Squares Regression Line

A least-squares regression line has equation  and a correlation of . It is also known that . What is ?

Possible Answers:

Correct answer:

Explanation:

Use the formula .

Plug in the given values for and and this becomes an algebra problem.

 

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