Correlation and Linear Regression Quiz

According to the guide, what is the definition of correlation?

• A measure of the linear relationship between two quantitative (numerical) variables

• A method for predicting the value of one variable based on another

• A test to compare the averages of two or more groups

• A visual representation of data using a bell curve

What is the best way to initially visualize a potential relationship between two quantitative variables?

• A bar chart

• A line graph connecting the points

• A scatter plot

• A box plot

In a scatter plot, what does each individual dot represent?

• One variable

• The average of the data

• The correlation coefficient

• One single observation or data point

If a scatter plot shows a pattern of dots going from the bottom-left to the top-right, what kind of relationship does this suggest?

• A negative relationship

• A positive relationship

• No relationship

• A causal relationship

What is the primary question that correlation analysis seeks to answer?

• Does one variable cause a change in another variable?

• As one numerical variable changes, does the other change in a predictable way?

• Are the means of the two variables significantly different?

• How can we predict the value of Y from X?

The correlation coefficient (r) provides a precise number that measures what two aspects of a linear relationship?

• Cause and effect

• Mean and standard deviation

• Strength and direction

• Slope and intercept

If the correlation coefficient (r) is a negative value (e.g., -0.85), what does this indicate about the relationship?

• It is a weak relationship

• It is a direct relationship where both variables increase together

• It is an inverse relationship where one variable tends to decrease as the other increases

• There is no relationship between the variables

Which of the following correlation coefficient (r) values indicates the strongest linear relationship?

• +0.75

• -0.20

• +1.0

• 0.0

What is the most critical point to remember about the relationship between correlation and causation?

• Strong correlation proves causation

• Correlation does not equal causation

• Causation is only possible with a negative correlation

• If there is no correlation, there can be no causation

In the classic analogy, ice cream sales are positively correlated with drowning incidents. What is the 'third variable' that likely causes both?

• The price of ice cream

• The number of swimming pools

• Hot weather

• The availability of lifeguards