Understanding Residuals and Standard Deviation in Linear Models

What is another term used for the standard deviation of residuals?

• Linear Regression Error

• Residual Mean Error

• Root Mean Square Error

• Mean Absolute Error

How is a residual calculated for a given data point?

• By dividing the predicted y-value by the actual y-value

• By multiplying the predicted y-value with the actual y-value

• By adding the predicted y-value to the actual y-value

• By subtracting the predicted y-value from the actual y-value

What does a positive residual indicate about a data point?

• The data point is below the model

• The data point is above the model

• The data point is an outlier

• The data point is on the model

What is the residual when the actual value is equal to the predicted value?

• Positive

• Negative

• Undefined

• Zero

What is the first step in calculating the standard deviation of residuals?

• Finding the mean of residuals

• Subtracting residuals from the mean

• Squaring each residual

• Adding all residuals

How do you calculate the mean of squared residuals?

• Divide the sum of squared residuals by one less than the number of residuals

• Divide the sum of squared residuals by the number of residuals

• Multiply the sum of squared residuals by the number of residuals

• Subtract the sum of squared residuals from the number of residuals

What is the final step in calculating the standard deviation of residuals?

• Adding the mean of squared residuals

• Subtracting the mean of squared residuals

• Taking the square root of the mean of squared residuals

• Multiplying the mean of squared residuals

What is the approximate value of the standard deviation of residuals calculated in the video?

• 1.000

• 0.707

• 0.500

• 1.500

Why might someone choose to calculate the mean of absolute residuals instead?

• To simplify the calculation

• To reduce the impact of outliers

• To give more weight to outliers

• To increase the complexity of the model

What does a lower standard deviation of residuals indicate about a model?

• The model fits the data poorly

• The model fits the data well

• The model is too complex

• The model is too simple