Correlation & Linear Regression

Front

What is correlation?

Back

Correlation is a statistical measure that describes the extent to which two variables change together. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.

Front

What does a correlation coefficient of r = 1 indicate?

Back

A correlation coefficient of r = 1 indicates a perfect positive correlation between two variables, meaning they move in the same direction.

Front

What does a correlation coefficient of r = -1 indicate?

Back

A correlation coefficient of r = -1 indicates a perfect negative correlation between two variables, meaning they move in opposite directions.

Front

What does a correlation coefficient of r = 0 indicate?

Back

A correlation coefficient of r = 0 indicates no correlation between the two variables, meaning changes in one variable do not affect the other.

Front

What is linear regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What is the purpose of the line of best fit in linear regression?

Back

The line of best fit minimizes the distance between the line and all the data points, providing the best estimate of the relationship between the variables.

Front

What does it mean if a scatter plot shows no correlation?

Back

If a scatter plot shows no correlation, it means that there is no discernible pattern or relationship between the two variables being plotted.

Front

How can you visually identify a positive correlation in a scatter plot?

Back

A positive correlation in a scatter plot is identified by points that trend upwards from left to right, indicating that as one variable increases, the other also increases.

Front

How can you visually identify a negative correlation in a scatter plot?

Back

A negative correlation in a scatter plot is identified by points that trend downwards from left to right, indicating that as one variable increases, the other decreases.

Front

What is the formula for the correlation coefficient (r)?

Back

The formula for the correlation coefficient (r) is r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)], where n is the number of pairs, Σxy is the sum of the product of paired scores, Σx is the sum of x scores, and Σy is the sum of y scores.