Question

fill in the blank.
for a pair of sample x- and y-values, the _________ is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.

for a pair of sample x- and y-values, the is the difference between the observed sample value of y and the y-value that is predicted by usir
options: residual, outlier, slope, explanatory variable

Explanation:

To solve this, we analyze each option:

• Residual: Defined as the difference between the observed \( y \)-value and the predicted \( y \)-value from a regression equation. This matches the description.
• Outlier: A data point that is far from other data points, not related to the difference between observed and predicted \( y \)-values.
• Slope: A measure of the steepness of a line in regression, representing the rate of change, not a difference between observed and predicted values.
• Explanatory variable: The independent variable (usually \( x \)) in a regression, not related to the difference in \( y \)-values.

Answer:

residual