Question

1. We try to study the relationship between a personality scale that measures willingness to take orders (on a scale from 0 to 20, where 20 represents eagerness to take orders) and the number of days served in county prison for misdemeanors. Here are the data from a sample of six prisoners:

Prisoner	Willing-ness	Days Served	(x-xbar)	(y-ybar)	(x-xbar)^2	(y-ybar)^2	(x-xbar)* (y-ybar)
Jake	20	4	9	-20	81	400	-180
Jason	3	65	-8	41	64	1681	-328
Sarah	10	20	-1	-4	1	16	4
Don	11	9	0	-15	0	225	0
Dean	18	7	7	-17	49	289	-119
Joan	4	39	-7	15	49	225	-105
Sum	66	144	0	0	244	2836	-728
Mean	66/6=11	144/6=24	Variance==>		244/5=48.8	2836/5=567.2
Median	10.5	14.5	Standard Deviation=>		0.9946	586.7881

Mean of the Willingness score tells us:

Median of the Days Served tells us:

Variance of the willingness score tell us:

Standard Deviation of the days served tells us:

While try to find the relationship of these two variables,

Which one is the dependent variable?

Which one is the independent variable?

What is the Sample Covariance?

What is the sample coefficient of correlation (r) and what does this tell us?

What is the Coefficient of Determination (R²) and what is this telling us?

What is the Slope coefficient (b₁) and what is this telling us?

What is the y-intercept (b₀) and what is this telling us?

From the above measures, particularly your r and R², can you say that the low scores of the willingness will cause the prisoner serving more days in Jail? Why or why not?

Answer 1