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 Mail	Orders		Weight of 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

1. Set up a scatter plot and explain what you see.(this is to be done by hand.)
2. Calculate the value of Pearson's correlation coefficient and interpret your value.
3. Calculate the least squares regression line.
4. Interpret the estimates of the y-intercept and slope in the words of the problem.
5. 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.
6. 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?
7. Calculate the residuals of this data using Microsoft Excel (or by hand) and plot your results (by hand).
8. Predict the average number of orders when the weight of the mail 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(y = 0): See image for equation: