Correlation and Regression Concepts

What is the primary purpose of a scatter plot in statistics?

• To display the frequency distribution of a single variable.

• To show the relationship between two continuous variables.

• To compare parts of a whole.

• To illustrate changes in data over time.

In the linear regression equation y = mx + b, what does 'm' represent?

• The y-intercept, where the line crosses the y-axis.

• The value of y when x is zero.

• The change in y for every one-unit increase in x.

• The overall strength of the relationship between x and y.

If two variables have a negative correlation, how do they tend to move relative to each other?

• They move in the same direction; as one increases, the other increases.

• They move in opposite directions; as one increases, the other decreases.

• They show no clear pattern of movement.

• Their movement is random and unpredictable.

What does the correlation coefficient 'r' indicate about the relationship between two variables?

• Only the direction of the relationship.

• Only the strength of the relationship.

• Both the direction and the strength of the relationship.

• The causal link between the variables.

What does a correlation coefficient (r) of 0 signify between two variables?

• A perfect positive linear relationship.

• A perfect negative linear relationship.

• No linear relationship.

• A strong non-linear relationship.

What does the squared correlation coefficient (r²) measure?

• The direction of the linear relationship.

• The steepness of the regression line.

• The proportion of variance in one variable that is predictable from the other.

• The total number of data points in a scatter plot.

If the squared correlation coefficient (r²) between two variables is 0.7, what can be concluded?

• There is a 70% chance that one variable causes the other.

• 70% of the variation in one variable can be predicted by the other.

• The linear relationship between the variables is weak.

• The correlation coefficient (r) is exactly 0.7.

What is the primary lesson learned from the example of the "Cool-Cage Act" and its proposed solutions to reduce drownings?

• Strong correlations always indicate a direct cause-and-effect relationship.

• Variables that appear correlated are always causally linked.

• Correlation does not necessarily imply causation.

• Only linear relationships are important for making policy decisions.