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. A confidence interval can be determined for the mean value of Y for a given value of X.
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 statements are based on principles of regression analysis and statistical prediction. Statement i correctly applies the empirical rule (68-95-99.7 rule) for normal distributions to the context of prediction errors. Statement ii is accurate because confidence intervals can indeed be calculated for predicted values of Y given X in regression analysis. Statement iii correctly interprets the rule of thumb that approximately 95% of observations fall within two standard deviations (errors) from the mean (or regression line in this context).

I Trying to Predict Weekly Sales with a Standard Error