Question

Which statements about residuals are true for the least-squares regression line? I. A random scattering of residuals indicates that the relationship is linear. II. The sum of the residuals is always 0. III. Residuals are plotted against the original x-values.

Answer 1

The true statements about residuals for the least-squares regression line are: a random scattering of residuals indicates a linear relationship, the sum of residuals is always zero, and residuals are plotted against the x-values.

Step-by-step explanation:

The statements about residuals that are true for the least-squares regression line are:

1. A random scattering of residuals indicates that the relationship is linear. When the residuals are randomly scattered around the line of best fit, it suggests that the relationship between the variables is linear.
2. The sum of the residuals is always 0. The sum of the residuals is always zero, which means that the line of best fit passes through the mean of the data points.
3. Residuals are plotted against the original x-values. The residuals, which represent the distance between the actual y-values and the predicted y-values, are plotted against the corresponding x-values to analyze the pattern and assess the accuracy of the regression line.