In linear regression, the slope corresponds to which type of error?

In linear regression, the slope corresponds to which type of error?

• A. Proportional error
• B. Constant error
• C. Random error
• D. Systematic error

Answer: (A)

In linear regression, the line captures the predictable part of the relationship between x and y, while the deviations of observed y from that line are regarded as random measurement noise, the residuals. The slope is estimated to explain how much y changes on average for a unit change in x, given these random residuals. The model assumes these errors are random (unbiased and with roughly constant variance across x); if errors were systematic, they would bias the slope, and if errors were proportional to the size of the data, the variance would change with x, requiring transformation or different modeling. So the residuals—the unexplained part of y—are best described as random error.

In linear regression, the line captures the predictable part of the relationship between x and y, while the deviations of observed y from that line are regarded as random measurement noise, the residuals. The slope is estimated to explain how much y changes on average for a unit change in x, given these random residuals. The model assumes these errors are random (unbiased and with roughly constant variance across x); if errors were systematic, they would bias the slope, and if errors were proportional to the size of the data, the variance would change with x, requiring transformation or different modeling. So the residuals—the unexplained part of y—are best described as random error.