AP Stats 3.2 Residuals, r squared and LSRL

How do you calculate residuals in least squares regression?

• By adding the predicted values to the actual values of the response variable.

• By multiplying the predicted values with the actual values of the response variable.

• By dividing the predicted values by the actual values of the response variable.

• By subtracting the predicted values from the actual values of the response variable.

Tags

CCSS.HSS.ID.B.6

Why are residuals important in statistics?

• Residuals are not important in statistics.

• Residuals are only important in certain types of statistical analysis.

• Residuals are used to measure the accuracy of a statistical model.

• Residuals are important in statistics because they measure the difference between the actual and predicted values in a regression model.

Tags

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

What does a positive residual indicate in least squares regression?

• The actual value is lower than the predicted value.

• The actual value is higher than the predicted value.

• The actual value is equal to the predicted value.

• The actual value is unrelated to the predicted value.

Tags

CCSS.HSS.ID.B.6

What does a negative residual indicate in least squares regression?

• The actual value is lower than the predicted value.

• The actual value is higher than the predicted value.

• The actual value is equal to the predicted value.

• The actual value is unrelated to the predicted value.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

How do you interpret residuals in least squares regression?

• Residuals are the independent variables in the regression equation.

• Residuals represent the error in the regression model.

• Residuals indicate the strength of the relationship between the dependent and independent variables.

• Residuals represent the difference between observed and predicted values in regression.

What is the least squares regression line?

• The least squares regression line is a line that minimizes the sum of the squared differences between the actual and predicted values.

• The least squares regression line is a line that is determined by randomly selecting points from the data set.

• The least squares regression line is a line that connects all the actual values.

• The least squares regression line is a line that maximizes the sum of the squared differences between the actual and predicted values.

Tags

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

How do you find the equation of the least squares regression line?

• y = a + bx

• y = bx + m

• y = ax + c

• y = ax + b

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

How does the least squares regression line minimize the sum of squared residuals?

• By finding the line that has the smallest sum of the squared vertical distances between the observed data points and the predicted values on the line.

• By finding the line that has the smallest sum of the squared horizontal distances between the observed data points and the predicted values on the line.

• By finding the line that has the largest sum of the squared vertical distances between the observed data points and the predicted values on the line.

• By finding the line that has the smallest sum of the absolute vertical distances between the observed data points and the predicted values on the line.

What is the significance of the slope in least squares regression?

• The slope indicates the strength of the relationship between the variables.

• The slope represents the average value of the dependent variable.

• The slope represents the change in the dependent variable for a one-unit change in the independent variable.

• The slope is unrelated to the change in the dependent variable.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

How do you interpret the coefficient of determination in least squares regression?

• The coefficient of determination represents the correlation between the explanatory and response variables.

• The coefficient of determination represents the proportion of the variance in the response variable that can be explained by the explanatory variable(s).

• The coefficient of determination represents the average of the explanatory and response variables.

• The coefficient of determination represents the proportion of the variance in the explanatory variable that can be explained by the response variable(s).

Tags

CCSS.HSS.ID.C.8