Scatterplots and Linear Regression

Front

What is a scatterplot?

Back

A scatterplot is a graph that displays values for typically two variables for a set of data. Each point represents an observation in the dataset.

Front

What does the line of best fit represent in a scatterplot?

Back

The line of best fit represents the trend in the data, showing the relationship between the two variables.

Front

How do you determine the line of best fit?

Back

The line of best fit can be determined using methods such as least squares regression, which minimizes the distance between the data points and the line.

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 formula for a linear equation?

Back

The formula for a linear equation is typically written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line indicate in a scatterplot?

Back

The slope indicates the rate of change of the dependent variable as the independent variable changes. A positive slope means an increase, while a negative slope indicates a decrease.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero.

Front

How can you predict values using a linear regression equation?

Back

You can predict values by substituting the independent variable into the linear regression equation to find the corresponding dependent variable.

Front

What does it mean if a scatterplot shows no relationship?

Back

If a scatterplot shows no relationship, the data points are scattered randomly, indicating that changes in one variable do not affect the other.

Front

What is the significance of the correlation coefficient in linear regression?

Back

The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.