A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in
square feet) of 135 homes. A regression was done to predict the amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear model is appropriate. The model is usage = 1254 + 0.7 size. What would a negative residual mean for people living in a house that is 2284 square feet? (A) They are using more electricity than expected.
(B) Their house is smaller than expected.
(C) Their house is bigger than expected.
(D) They are using the least amount of electricity of all of the houses sampled.
(E) They are using less electricity than expected.
The residual mean value is the observed value minus the predicted or expected value. If it is negative it means that the expected value of electricity usage is higher than the observed electricity usage value, so they are using less electricity than expected.
A theorem states that, given a circle with center C and a point P on the circumference, the tangent line through P and the radius CP are perpendicular.
As the sample size n increases, the sample mean (μy) becomes a more accurate estimate of the parametric mean, so the standard error of the mean becomes smaller. Therefore, the variance of y decreases and the distribution of y becomes highly concentrated around μy.
