Question

Liam used a statistical software to fit a linear model to his environmental science project data. The residuals he calculated were −0.12,−0.45,−0.33
, and −0.27
. What can Liam conclude about the appropriateness of the linear model based on these residuals?(1 point)
Responses

The linear model does not accurately represent the data because all of the residuals are negative.
The linear model does not accurately represent the data because all of the residuals are negative.

The linear model is appropriate because the residual values are close to 0.
The linear model is appropriate because the residual values are close to 0.

The residuals indicate a perfect fit.
The residuals indicate a perfect fit.

The residuals are too small to make any conclusion.
The residuals are too small to make any conclusion.

Answer 1

The linear model is appropriate because the residual values are close to 0.

Explanation: the residuals (−0.12, −0.45, −0.33, −0.27) are small in magnitude (not near large errors), so the model fits the data reasonably well. They aren’t zero (so not a perfect fit) and being all negative only indicates a small consistent overestimate by the model, not that the model is inappropriate.