Question

Here is data with y as the response variable.

x	y
23.3	102.1
43.8	48.9
14.7	60.3
12.2	104.3
208	-239.7
44.3	11.6
48.6	30
34.9	100.1
55.7	21.4
32.4	56.3
36.3	82.3

Make a scatter plot of this data. Which point is an outlier?

Enter as an ordered pair. For example (a,b) - with parenthesis.


Find the regression equation for the data set without the outlier.

Enter as an equation of the form y=a+bxy=a+bx. Rounded to three decimal places. For WAMAP questions, do not include the hat in y-hat.


Find the regression equation for the data set with the outlier.

Enter as an equation of the form y=a+bxy=a+bx. Rounded to three decimal places. For WAMAP questions, do not include the hat in y-hat.

Is this outlier an influential point?

• No, the outlier does not appear to be an influential point.
• Yes, the outlier appears to be an influential point.

Answer 1

Solution

1.Make a scatter plot of this data. Which point is an outlier?

Scatter plot 150 100 50 0 -500 50 100 150 200 250 -100 -150 -200 -250 -300 X

The outlier points is (X =208, Y= -239.7)

Find the regression equation for the data set without the outlier.
Will will use excel to find regression equation without outlier

The output of regreesion is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.7243
R Square	0.5246
Adjusted R Square	0.4652
Standard Error	25.1913
Observations	10.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	5602.9700	5602.9700	8.8291	0.0178
Residual	8.0000	5076.8110	634.6014
Total	9.0000	10679.7810
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	121.9268	21.7688	5.6010	0.0005	71.7278	172.1257	71.7278	172.1257
x	-1.7388	0.5852	-2.9714	0.0178	-3.0882	-0.3894	-3.0882	-0.3894

So the regression equation is

y = 121.927 - 1.739*x

Find the regression equation for the data set with the outlier.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.972
R Square	0.946
Adjusted R Square	0.940
Standard Error	23.751
Observations	11.000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.000	88203.011	88203.011	156.363	0.000
Residual	9.000	5076.811	564.090
Total	10.000	93279.822
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	121.919	10.017	12.171	0.000	99.258	144.580	99.258	144.580
x	-1.739	0.139	-12.505	0.000	-2.053	-1.424	-2.053	-1.424

y = 121.919 - 1.739*y

Is this outlier an influential point

Yes, the outlier appears to be an influential point

Since the value for R -square when outlier is included is 0.946 and when outlier is removed = 0.5246.

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