Question

A legal researcher wanted to measure the effect of the length of a criminal trial on the length of jury deliberation. He observed in a sample of 10 randomly selected courtroom trials the following data on length of trial (in days) and length of jury deliberation (in hours). Using the table below, complete the followiwng steps: I have to work the problem out. no exel Step 1: Calculate the regression and Y-intercept by calculating N, the sum of X, the sum of Y, the sum of X-squared, the sum of Y-squared, and the sum of XY. Step 2: Calculate the mean of X and the mean of Y. Step 3: Calculate SSx, SSy, and SP Step 4: Determine the regression line Step 5: Predict the length of jury deliberation for a recently completed trial that lasts six days. Step 6: Find the coefficient of determination and nondetermination. What do they mean? Step 7: Construct and analysis of variance table. X (Days) Y(Hours) 2 4 7 12 4 6 1 4 1 1 3 4 2 7 5 2 2 4 3 6

Answer 1

	X (Days)	Y(Hours)	X2	Y2	XY
	2	4	4	16	8
	7	12	49	144	84
	4	6	16	36	24
	1	4	1	16	4
	1	1	1	1	1
	3	4	9	16	12
	2	7	4	49	14
	5	2	25	4	10
	2	4	4	16	8
	3	6	9	36	18
Sum	30	50	122	334	183

Here

n = 10

The formula for regression is

The formula for slope is

The formula for y-intercept is

The equation for regression line is

To predict the length of jury deliberation for a recently completed trial that lasts six days.

Given X = 6

The equation for regression line is

So,

The length of jury deliberation for a recently completed trial that lasts six days is 8 hours.

Here

r = 0.6365

The coefficient of determination = r2 = (0.6365)2 = 0.4051

and the coefficient of nondetermination = 1 - r2 = 1 - 0.4051 = 0.5949

Coefficient of determination gives you the percentage variation in y explained by x-variables.It gives you an idea of how many data points fall within the results of the line formed by the regression equation. The higher the coefficient, the higher percentage of points the line passes through when the data points and line are plotted.

Here, the coefficient is 0.4051, so 40.51% of the points should fall within the regression line.

The coefficient of nondetermination indicates percent of variation which is unexplained by the regression equation.

For construction ANOVA

	X (Days)	Y(Hours)
	2	4	3.969	1.062961	0.000961	1
	7	12	9.124	17.007376	8.271376	49
	4	6	6.031	1.062961	0.000961	1
	1	4	2.938	4.251844	1.127844	1
	1	1	2.938	4.251844	3.755844	16
	3	4	5	0	1	1
	2	7	3.969	1.062961	9.186961	4
	5	2	7.062	4.251844	25.623844	9
	2	4	3.969	1.062961	0.000961	1
	3	6	5	0	1	1
Sum	30	50		34.0148	49.9688	84
mean	3	5

n= 10

ANOVA
	df	SS	MS	F
Regression	1		34.0148	5.45
Residual	n-2 = 8		6.2461
Total	n-1=9

Note:

Mean sum of square due to Regression = 34.0148 / 1 = 34.0148

Mean sum of square due to Residual = 49.9688 / 8 = 6.2461

F = 34.0148 / 6.2461 = 5.45