Practice: Linear Regression

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 does the slope in a linear regression equation represent?

Back

The slope indicates the rate of change of the dependent variable for each unit increase in the independent variable.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret the y-intercept in a linear regression equation?

Back

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

Front

What is the purpose of the line of best fit?

Back

The line of best fit minimizes the distance between the line and all the data points in a scatter plot, providing the best approximation of the relationship between variables.

Front

What is a scatter plot?

Back

A scatter plot is a graphical representation of two variables, showing the relationship between them using points on a Cartesian plane.

Front

How can you determine the line of best fit from a scatter plot?

Back

You can determine the line of best fit by visually inspecting the scatter plot or using statistical methods like least squares regression.

Front

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

Back

A correlation coefficient close to 1 indicates a strong positive linear relationship between the two variables.

Front

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

Back

The correlation coefficient (r) is calculated using the formula: r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)], where n is the number of data points.

Front

What is the significance of residuals in linear regression?

Back

Residuals are the differences between observed values and predicted values; they help assess the accuracy of the regression model.