Question

The accompanying data show the number of people working and the sales for a small bookstore. The regression line is given below. The bookstore decides to have a gala event in an attempt to drum up business. They hire 103 employees for the day and bring in a total of $ 41,000.

Sales = 7.873 + 0.946(Number of Salespeople Working)

Number of Salespeople Working // Sales

2 // 9

3 // 12

7 // 14

9 // 14

10 // 17

10 // 20

12 // 20

16 // 23

16 // 22

22 // 29

x (overline) = 10.7

y (overline) = 18.0

SD(x) = 6.13

SD(y) = 5.96

Complete parts a through d below.

a) Find the regression line predicting Sales from Number of people working with the new point added.

b) What has changed from the original regression​ equation? ​

c) Is the new point a high leverage point or an influential​ point? ​

d) Does the new point have a large​ residual? .

Answer 1

x	y
2	9
3	12
7	14
9	14
10	17
10	20
12	20
16	23
16	22
22	29
103	41

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.884279408
R Square	0.781950071
Adjusted R Square	0.757722301
Standard Error	4.405024534
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	626.2709206	626.2709206	32.2749504	0.000301444
Residual	9	174.6381703	19.40424115
Total	10	800.9090909
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	14.77688051	1.624490632	9.096316238	7.82534E-06	11.10202739
x	0.278353878	0.048996435	5.681104681	0.000301444	0.167516241

a)
y^ = 14.777 + 0.278 x
b)
both coefficients have changed
c)

It seems like a leverage point it does not lie in same line as the rest of points
d)

RESIDUAL OUTPUT
Observation	Predicted y	Residuals	Standard Residuals
1	15.3336	-6.3336	-1.5156
2	15.6119	-3.6119	-0.8643
3	16.7254	-2.7254	-0.6522
4	17.2821	-3.2821	-0.7854
5	17.5604	-0.5604	-0.1341
6	17.5604	2.4396	0.5838
7	18.1171	1.8829	0.4506
8	19.2305	3.7695	0.9020
9	19.2305	2.7695	0.6627
10	20.9007	8.0993	1.9381
11	43.4473	-2.4473	-0.5856

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