Exercise 1 A large mail-order house believes that there is an association between the weight of the mail it receives and the number of orders to be filled. It would like to investigate the relationship, in order to be able to predict the number of orders based on the weight of the mail. From an operational perspective, knowledge of the number of orders will help in the planning of the order- fulfillment process. A sample of 25 mail shipments is selected within a range of 200 to 700 pounds. The results were as follows: Weight of Weight of Mail Orders Mail Orders (pounds) (thousands) (pounds) (thousands) 216 6.1 432 13.6 283 9.1 409 12.8 237 7.2 553 16.5 203 7.5 572 17.1 259 6.9 506 15 374 11.5 528 16.2 342 10.3 501 15.8 301 9.5 628 19 365 9.2 677 19.4 384 10.6 602 19.1 404 12.5 630 18 426 12.9 652 20.2 482 14.5 a) Set up a scatter plot and explain what you see. (this is to be done by hand.) b) Calculate the value of Pearson's correlation coefficient and interpret your value. c) Calculate the least squares regression line. d) Interpret the estimates of the y-intercept and slope in the words of the problem. e) Predict the number of orders to be filled when the weight of the mail is 315 pounds. Predict the number of orders to be filled when the weight of the mail is 680 pounds. f) What proportion of observed variation in the number of orders to be filled can be explained by the approximate linear relationship between the two variables?9) Calculate the residuals of this data using Microsoft Excel {or by hand) and plot your results [by hand). h) Predict the average number of orders when the weight of the moi] is 500 pounds. Exercise 2 The following summary statistics were obtained from a study that used regression analysis to investigate the relationship between pavement deflection and surface temperature of the pavement at various locations on a state highway. Here x = temperature ("F} and y = deflection adjustment factor 0:20): 11:15 Ex] =1425 2y, =10.68, Ex} =139.o3125 Ex}: =981645. ny=18518 a) Compute the least squares estimates a and b. What is the equation of the estimated regression line? b) What is the estimate of expected change in the deflection adjustment factor when temperature is increased by l F? c] Suppose temperature were measured in 1: rather than in \"F. What would be the estimated regression line? [Hint 'F = (9/5) *'C + 32: now substitute for the "old x" in terms of the new x."] d] What is the estimate of expected change in the deflection adjustment factor when temperature is increased by 5" C? e] If a 200'F surface temperature were within the realm of possibility, would you use the estimated line of Question 2a) to predict deflection factor for this temperature? Why or why not? Exercise 3 Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularty consume at least one of these two types of drinks. a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products? c] What is the probability that a randomly selected adult regularly consumes coffee but does not regularly consume soda