Module 3 Homework Assignment.

Please analyze the following problems in JMP and answer the questions below.

1. Finger Dexterity, the ability to make precisely coordinated finger movements to grasp or assemble very small objects, is important in jewelry making. Subsequently, the manufacturing manager at Gemco, a manufacturer of high-quality watches, wants to develop a regression model to predict the productivity (in watches per shift) of new employees based on dexterity. He has subjected a sample of 20 current employees to the O'Connor dexterity test in which the time required to place 3 pins in each of 100 small holes using tweezers is measured. The data is shown in the following table. Use simple linear regression analysis in JMP to see if there is a relationship between Time and Watches per shift.

Time (seconds)	Watches per shift
513	23
608	19
915	10
314	30
896	15
694	18
514	22
450	26
922	11
388	28
494	23
566	20
705	18
383	28
937	12
921	14
476	20
556	21
825	14
437	20

1. Construct a scatterplot of the data with the regression equation drawn through the data.

1. Using JMP, compute the estimated regression equation.Write out the equation.

1. Interpret the sample intercept, sample slope, and coefficient of determination.

1. At the 0.05 level of significance, is there a significant linear relationship between the number of watches produced per shift and time to complete the O'Conner test? Write your answer in a sentence and report the p-value.

1. Explain why the y-intercept makes no practical sense in this particular problem.

1. Predict how many watches per shift would yield from an employee who (1) completes the O'Connor test in 750 seconds and (2) completes the O'Connor test in 1100 seconds.

1. A manager at an ice cream store is trying to determine how many customers to expect on any given day. Overall business has been relatively steady over the past several years, but the customer count seems to have its ups and downs. He collects data over 30 days and records the number of customers, the high temperature that day, whether the day fell on a weekend/weekday and whether or not an employee stands outside the store's entrance and hands out free samples.

Customers	Temperature	Day of Week	Free Samples
376	75	Weekday	Yes
433	78	Weekday	Yes
524	80	Weekday	No
360	70	Weekday	No
500	80	Weekday	No
645	78	Weekend	No
667	80	Weekend	Yes
542	85	Weekday	No
412	70	Weekday	No
435	72	Weekday	Yes
396	69	Weekday	Yes
425	70	Weekday	Yes
702	90	Weekend	Yes
725	85	Weekend	No
509	80	Weekday	Yes
450	74	Weekday	No
378	70	Weekday	Yes
433	69	Weekday	No
467	71	Weekday	Yes
679	82	Weekend	No
701	80	Weekend	Yes
529	83	Weekday	Yes
599	92	Weekday	Yes
543	90	Weekday	No
432	80	Weekday	Yes
375	70	Weekday	Yes
690	70	Weekend	No
734	85	Weekend	Yes
465	74	Weekday	Yes
401	68	Weekday	No

1. Which variable is the response ?

1. Define two dummy variables to recode the "Day of the week" and "Free Samples" columns.

1. Fit an MLR equation to the data (). Write out the "full" model.

1. Is the overall model significant? Justify with ANOVA hypotheses and p-value

1. Are the individual variables significant? If not, remove the insignificant variables stepwise, until all remaining variables are significant. Also, check if there are any interactions between temperature and significant dummy variables.

1. Write the "best" model you've come up with.

1. Predict the number of customers the manager should expect on a Saturday with a forecasted high temperature of 80 degrees and an employee scheduled to hand out free samples.

1. What is the slope term in the equation for "Temperature" when "Day of the Week" = Weekend? Interpret the meaning of this value in terms of the problem. What is the slope for "Temperature" when "Day of the Week" = Weekday? Interpret the meaning of this value in terms of the problem.

1. Is it worth it, for the manager, to pay an employee to stand outside the entrance and give out free samples?