AP Stats - Linear Regression MCQ Practice

Front

What is the Least Squares Regression Line (LSRL)?

Back

The LSRL is a straight line that minimizes the sum of the squares of the vertical distances (residuals) of the points from the line. It is used to predict the value of a dependent variable based on the value of an independent variable.

Front

How do you calculate the residual for a given point?

Back

The residual is calculated as the difference between the observed value and the predicted value from the regression line. Formula: Residual = Observed value - Predicted value.

Front

What does a residual plot indicate?

Back

A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps to assess the fit of the regression model; a random pattern suggests a good fit, while a pattern indicates a poor fit.

Front

What is the slope of the least squares regression line?

Back

The slope indicates the change in the dependent variable for a one-unit change in the independent variable. It is calculated as the ratio of the covariance of x and y to the variance of x.

Front

What is the y-intercept of the least squares regression line?

Back

The y-intercept is the predicted value of the dependent variable when the independent variable is zero. It represents the starting point of the regression line on the y-axis.

Front

What does a correlation coefficient of -1.08 indicate?

Back

A correlation coefficient must be between -1 and 1. A value of -1.08 suggests a calculation error, as it is not a valid correlation coefficient.

Front

What is the formula for the slope of the regression line given standard deviations and correlation?

Back

The slope (b) can be calculated using the formula: b = r * (s_y / s_x), where r is the correlation coefficient, s_y is the standard deviation of y, and s_x is the standard deviation of x.

Front

What does it mean if a residual plot shows no pattern?

Back

If a residual plot shows no pattern, it indicates that the linear regression model is appropriate for the data, and the assumptions of linear regression are likely met.

Front

What is the significance of the y-intercept in a regression analysis?

Back

The y-intercept provides context for the regression line, indicating the expected value of the dependent variable when the independent variable is zero, which can be meaningful in certain contexts.

Front

What is the interpretation of a positive slope in a regression line?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also tends to increase.