Question

Use the data in the table below to complete parts (a) through (c).

X: 5 5 6 9 13 16 18 48

Y: 30 27 18 23 25 20 21 10

A.) Construct a scatterplot of the data.

B.) Indentify any possible outliners.

A.) The point (18,21) may be an outliner.

B.) The point (48,10) may be an outliner

C.) The point (5,27) may be an outliner.

D.) The point (5,30) may be an outliner

E.) There are no outliners.

C.) Determine if the point is influential. The change in slope or intercept is significant if it larger than 10%

The point is/is not an influential point because the slopes with the point included and without the point included are/are not signficatly different, and the intercepts are/ are not significantly different.

Answer 1

a)

B)

The point (48,10) may be an outliner

C)

with outlier slope is

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
5	30	100.000	68.063	-82.500
5	27	100.000	27.563	-52.500
6	18	81.000	14.063	33.750
9	23	36.000	1.563	-7.500
13	25	4.000	10.563	-6.500
16	20	1.000	3.063	-1.750
18	21	9.000	0.563	-2.250
48	10	1089.000	138.063	-387.750

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	120	174	1420.000	263.5	-507
mean	15.00	21.75	SSxx	SSyy	SSxy

estimated slope , ß1 = SSxy/SSxx =   -507.0   /   1420.000   =   -0.3570

intercept,   ß0 = y̅-ß1* x̄ =   27.1056

--------------------------

without outlier slope is,

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
5	30	27.939	43.184	-34.735
5	27	27.939	12.755	-18.878
6	18	18.367	29.469	23.265
9	23	1.653	0.184	0.551
13	25	7.367	2.469	4.265
16	20	32.653	11.755	-19.592
18	21	59.510	5.898	-18.735

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	72	164	175.429	105.7	-63.8571429
mean	10.29	23.43	SSxx	SSyy	SSxy

estimated slope , ß1 = SSxy/SSxx =   -63.9   /   175.429   =   -0.3640

intercept,   ß0 = y̅-ß1* x̄ =   27.1726

Change in slope = (-0.364+0.357)/-0.357 = 1.96%

change in intercept = (27.1726-27.1056)/27.1056 = 0.2%

The point is not an influential point because the slopes with the point included and without the point included are not signficatly different, and the intercepts are not significantly different.