correlation

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 is the range of correlation coefficients (r)?

Back

The correlation coefficient (r) ranges from -1 to 1. An r value of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 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 is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot. It minimizes the distance between the line and all the data points.

Front

How do you determine the equation of the line of best fit?

Back

The equation of the line of best fit can be determined using statistical methods such as least squares regression, which calculates the slope and y-intercept that minimize the sum of the squares of the vertical distances of the points from the line.

Front

What is the slope in the equation of a line?

Back

The slope in the equation of a line (y = mx + b) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What does a positive slope indicate about the relationship between two variables?

Back

A positive slope indicates that there is a positive correlation between the two variables, meaning that as one variable increases, the other variable also tends to increase.

Front

What does a negative slope indicate about the relationship between two variables?

Back

A negative slope indicates that there is a negative correlation between the two variables, meaning that as one variable increases, the other variable tends to decrease.

Front

What is a scatter plot?

Back

A scatter plot is a graphical representation of two variables where each point represents an observation. It is used to visualize the relationship between the variables.

Front

What is the purpose of the line of best fit in a scatter plot?

Back

The purpose of the line of best fit in a scatter plot is to summarize the relationship between the two variables and to make predictions based on that relationship.