Question

Here is data with y as the response variable.

(x,y): 59.2 48.5, 64.5 46.8, 47.4 13.8, -37.3 10, 71.4 84.9, 71.6 18.3, 64.4 28.3, 71.1 89.6, 56.2 6.2, 56.7 11.7, 69.1 23.8

Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair. For example (a,b) - with parenthesis.

1. Find the regression equation for the data set without the outlier. Enter as an equation of the form y = a + b x . Rounded to three decimal places. Do not include the hat in y-hat. Find the regression equation for the data set with the outlier.

2. Enter as an equation of the form y = a + b x . Rounded to three decimal places. Do not include the hat in y-hat.

3. Is this outlier an influential point?

a. Yes, the outlier appears to be an influential point.

b. No, the outlier does not appear to be an influential point.

Answer 1

Scatter plot:

Outlier : (-37.3, 10)

Without Outlier:

X	Y	XY	X²	Y²
59.2	48.5	2871.2	3504.64	2352.25
64.5	46.8	3018.6	4160.25	2190.24
47.4	13.8	654.12	2246.76	190.44
71.4	84.9	6061.86	5097.96	7208.01
71.6	18.3	1310.28	5126.56	334.89
64.4	28.3	1822.52	4147.36	800.89
71.1	89.6	6370.56	5055.21	8028.16
56.2	6.2	348.44	3158.44	38.44
56.7	11.7	663.39	3214.89	136.89
69.1	23.8	1644.58	4774.81	566.44

Ʃx =	631.6
Ʃy =	371.9
Ʃxy =	24765.55
Ʃx² =	40486.88
Ʃy² =	21846.65
Sample size, n =	10
x̅ = Ʃx/n = 631.6/10 =	63.16
y̅ = Ʃy/n = 371.9/10 =	37.19
SSxx = Ʃx² - (Ʃx)²/n = 40486.88 - (631.6)²/10 =	595.024
SSyy = Ʃy² - (Ʃy)²/n = 21846.65 - (371.9)²/10 =	8015.689
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 24765.55 - (631.6)(371.9)/10 =	1276.346

Slope, b = SSxy/SSxx = 1276.346/595.024 =    2.145032805

y-intercept, a = y̅ -b* x̅ = 37.19 - (2.14503)*63.16 =    -98.29027199

Regression equation :   

y = -98.290 + (2.145) x  

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

With Outlier:

X	Y	XY	X²	Y²
59.2	48.5	2871.2	3504.64	2352.25
64.5	46.8	3018.6	4160.25	2190.24
47.4	13.8	654.12	2246.76	190.44
-37.3	10	-373	1391.29	100
71.4	84.9	6061.86	5097.96	7208.01
71.6	18.3	1310.28	5126.56	334.89
64.4	28.3	1822.52	4147.36	800.89
71.1	89.6	6370.56	5055.21	8028.16
56.2	6.2	348.44	3158.44	38.44
56.7	11.7	663.39	3214.89	136.89
69.1	23.8	1644.58	4774.81	566.44

Ʃx =	594.3
Ʃy =	381.9
Ʃxy =	24392.55
Ʃx² =	41878.17
Ʃy² =	21946.65
Sample size, n =	11
x̅ = Ʃx/n = 594.3/11 =	54.02727273
y̅ = Ʃy/n = 381.9/11 =	34.71818182
SSxx = Ʃx² - (Ʃx)²/n = 41878.17 - (594.3)²/11 =	9769.761818
SSyy = Ʃy² - (Ʃy)²/n = 21946.65 - (381.9)²/11 =	8687.776364
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 24392.55 - (594.3)(381.9)/11 =	3759.534545

Slope, b = SSxy/SSxx = 3759.53455/9769.76182 =    0.384813327

y-intercept, a = y̅ -b* x̅ = 34.71818 - (0.38481)*54.02727 =    13.92776727

Regression equation :   

y = 13.928 + (0.385) x

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

3. Answer: a. Yes, the outlier appears to be an influential point.