i. Trying to predict weekly sales with a standard error of estimate of $1,955, we would conclude that 68 percent of the predictions would not be off more than $1,955, 95 percent would not be off by more $3,910, and 99.7 percent would not be off by more than $5,865. ii. The smaller the sample, the smaller the possible error as measured by the standard error of estimate.
iii. Approximately 95% of the values lie within two standard errors of the regression line.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

The first statement is correct as it accurately describes the empirical rule (or 68-95-99.7 rule) which applies to normal distributions, indicating that approximately 68%, 95%, and 99.7% of the observations fall within one, two, and three standard deviations from the mean, respectively. The third statement is also correct, as it is a general principle in statistics that approximately 95% of observations fall within two standard deviations (or standard errors, in the context of regression) from the mean (or regression line). The second statement is incorrect because the smaller the sample size, the larger the standard error of estimate tends to be, reflecting greater uncertainty in predictions.

I Trying to Predict Weekly Sales with a Standard Error