Question

Question 10

Please answer the following set of questions, based on the information provided below.

The data listed below give information for 10 middle-level managers at a particular company. The first column is years of experience [X] and the second column is annual salary (in thousands) [Y]. We are going to examine the relationship between salary in thousands [Y] and years of experience[X]. Below is the regression output.

Manager#	(X)	(Y)
1	xx	66
2	xx	69
3	23	78
4	xx	41
5	19	xx
6	15	xx
7	24	xx
8	xx	33
9	2	28
10	xx	32

SUMMARY OUTPUT
Regression Statistics
Multiple R	xxx
R Square	0.789
Adjusted R Square	0.740
Standard Error	8.376
Observations	10

ANOVA
	df	SS	MS	F	SignificanceF
Regression	1.000	1503.75	1503.75	xxxx	xxxx
Residual	8.000	561.25	70.156
Total	xxx	xxx
	Coefficients	Standard Error	t Stat	P value
Intercept	16.586	7.201	2.303	0.050
Yrs Exp (X)	2.892	0.625	xxx	0.003

RESIDUALOUTPUT
Observation	Standardized Residuals
1	-0.956
2	2.129
3	-0.567
4	-1.307
5	1.381
6	-0.417
7	-2.780
8	-0.962
9	1.734
10	1.377

Based on the cut-off of 2.5 standard deviations, how many potential outliers are there?

Answer 1

To examine the relationship between salary in thousands [Y] and years of experience[X],

i.e. to test against

Now,

and n = 10

The value of test statistic

P-value = 0.003

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is significant relationship between salary in thousands [Y] and years of experience[X].

For observation 7, residual is outside the bound ( 0 - .2.5*1, 0 + 2.5*1) = (-2.5, 2.5), so we can consider it as potential outlier.

Hence, number of potential outliers = 1