# What percentage of the variation in the times required to prepare an order for shipping is…

A distribution center for a chain of electronics supply stores fills and ships orders to retail outlets. A random sample of orders is selected as they are received and the dollar amount of the order (in thousands of dollars) is recorded, and then the time (in hours) required to fill the order and have it ready for shipping is determined.

A scatterplot showing the times as the response variable and the dollar amounts (in thousands of dollars) as the predictor shows a linear trend. The least squares regression line is determined to be: yˆ=0.76+1.8x

A plot of the residuals versus the dollar amounts showed no pattern, and the following values were reported:?Correlation r=0.92; r2=0.846;standard deviation of the residuals se=0.48.

**1.** What percentage of the variation in the times required to prepare an order for shipping is accounted for by the fitted line?

(a) 92% (b) 48% (c) 84.6% (d) 1.8% (e) 68%

**2.** The histogram summarizing the residuals is reasonably symmetric around zero and bell-shaped. Which of the following conclusions can be drawn based on the Empirical Rule?

(a) Approximately 68% of the times to prepare an order are within .48 hours of the regression line.?

(b) Approximately 95% of the times to prepare an order are within 1.692 hours of the regression line.?

(c) 84.6% of the times to prepare an order vary from the regression line by less than 1 hour.?

(d) 92% of the times to prepare an order can be predicted accurately based on the dollar amount of the order.?

(e) 84.6% of the variation in the times to prepare an order is due to factors other than the dollar amount of the order.?

**3.**Which of the following statements is an appropriate interpretation and use of the regression line provided?

(a) If the dollar amount of an order from one store is $1000 more than the dollar amount of an order from?another store, the larger order would be predicted to require 1.8 more hours to prepare than smaller order. (b) The units on the slope b1=1.8 are: hours per thousands of dollars.?

(c) The predicted time to prepare an order for shipping that has an absolute dollar amount of $2500 would be 5.26 hours.?

(d) Not all of the residuals computed for the fitted values would be equal to zero.?

(e) All of (a) – (d) are appropriate.?

**4.**Using the fitted line, calculate the residual for an order costing 3000$ and requiring 7 hours to be ready for shipment.