Regression and Correlation Coefficient

Front

What is the formula for exponential regression?

Back

The formula for exponential regression is typically expressed as y = ab^x, where 'a' is the initial value, 'b' is the growth factor, and 'x' is the independent variable.

Front

How do you interpret the correlation coefficient (r)?

Back

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. Values range from -1 to 1, where r = 1 indicates a perfect positive correlation, r = -1 indicates a perfect negative correlation, and r = 0 indicates no correlation.

Front

What does a correlation coefficient of r = 0 indicate?

Back

A correlation coefficient of r = 0 indicates that there is no linear relationship between the two variables.

Front

What does a correlation coefficient of r ≈ -0.8 suggest about the relationship between x and y?

Back

A correlation coefficient of r ≈ -0.8 suggests a strong negative linear relationship between x and y.

Front

What is the significance of a strong positive correlation (e.g., r = 0.99)?

Back

A strong positive correlation (e.g., r = 0.99) indicates that as one variable increases, the other variable also tends to increase, and the relationship is very close to a straight line.

Front

What is the difference between linear and exponential models?

Back

Linear models represent a constant rate of change, while exponential models represent a variable rate of change that increases or decreases multiplicatively.

Front

What is the general form of a linear regression equation?

Back

The general form of a linear regression equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How can you determine if a relationship is linear or non-linear from a graph?

Back

A relationship is linear if the data points form a straight line or close to a straight line on a graph. Non-linear relationships will show curves or other patterns.

Front

What does it mean if the correlation coefficient is close to -1?

Back

If the correlation coefficient is close to -1, it indicates a strong negative linear relationship, meaning that as one variable increases, the other variable tends to decrease.

Front

What is the purpose of regression analysis?

Back

The purpose of regression analysis is to model the relationship between a dependent variable and one or more independent variables, allowing for predictions and insights into the data.