Question

Table 1: Weight Suspended in kg

		Luke	Rey	Anikin
week	1	0	10	35
week	2	10	10	41
week	3	15	20	45
week	4	20	20	48
week	5	25	40	50
week	6	30	40	53
week	7	35	80	55
week	8	40	80	61
week	9	45	160	70
week	10	50	160	74
week	11	55	320	77
week	12	60	320	80

In an alternate reality, a temporal anomoly transports Luke Skywalker, Rey and Anikin Skywalker to Yoda's home planet as 8 year olds. Yoda's people decide to train them all in the ways of the Force. As they begin their Jedi training, their progress is tracked weekly. One of the items tracked is weight of object they are able to make hover. The results of the first 12 weeks of training are shown in Table 1.

1. Examine the data in Table 1. Without doing any calculations, of the three Jedi trainees, for which kid(s) would be Simple Linear Regression be a good tool to model their progress? Why? Explain in 50 words or less.

2. Perform a simple linear regression on all three kid's progress. Hint: time is the x variable and weight of stone suspended is the y variable. Perform a simple linear regression on all three kid's progress. Show your work in the analysis tab, putting the output in the designated spaces.

What is the regression equation for Luke? For Rey? For Anikin? Put your results in the indicated space.

What is the r2 for each kid? According to the p-value, which of the regression lines is statistically significant at an alpha of 0.05?

3. Using Luke and Anikin's regression equations, make a prediction during which week Luke will catch up with Anikin.

Table 2: Number of items Suspended

	rocks	kittens	daggers	wookies
Luke	25	15	30	3
Rey	30	5	45	2
Anikin	25	25	40	5

4.  Jedi trainee can suspend in the air after 12 weeks of training. Do an ANOVA analysis - Randomized Block Design at alpha = 0.05. Put the output in the indicated area. Is there a difference in the 3 kids overall ability to suspend objects in the air (rows)? Is there a difference in the type of object that is suspended objects in the air (columns)? Put the p-factor and conclusion in the indicated space.

5. Based upon the data in Table 2, perform a Chi-square Test Of Independence to determine if the type of suspended objects is dependent upon the Jedi trainee doing the suspending.

Answer 1