Question

1. A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons.

Salesperson		Years of Experience		Annual Sales ($1000)
1		1		84
2		1		81
3		2		87
4		4		101
5		5		104
6		7		118
7		8		119
8		9		120
9		10		127
10		11		134

a. Compute the residuals and choose a residual plot for this problem.

2.

The following data were used in a regression study.

Observation	x		y			Observation	x		y
1	1		5			6	4		3
2	2		4			7	5		9
3	2		5			8	5		3
4	3		6			9	5		10
5	3		7

a. Develop an estimated regression equation for these data. If necessary enter negative value as negative number.

      (to 2 decimals)

3.

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons.

Salesperson		Years of Experience		Annual Sales ($1000s)
1		1		80
2		1		97
3		1		101
4		2		96
5		3		96
6		4		112
7		6		131
8		6		133
9		8		148
10		9		149

The data on  annual sales ($1000s) for new customer accounts and x= number of years of experience for a sample of 10 salespersons provided the estimated regression equation y=82.44+7.77x. For these data x=4.1 ,(xi - x)^2 = 80.90 , and s=7.1613.

a. Develop the 95% confidence interval for the mean annual sales for all salespersons with seven years of experience.

b. The company is considering hiring Tom Smart, a salesperson with seven years of experience. Develop a 95% prediction interval of annual sales for Tom Smart.

( ,  ) (to 2 decimals)

4.

Given are five observations for two variables, x and y.

x	4	8	11	15	20
y	7	18	8	22	20

Develop the  confidence and prediction intervals when x=9. Explain why these two intervals are different.

s	(to 4 decimals)
t-value	(to 3 decimals)
s y *	(to 4 decimals)
spred	(to 4 decimals)

Confidence Interval for the Mean Value:

( ,  ) (to 2 decimals)

Prediction Interval for an Individual Value: (Enter negative values as negative number.)

( ,  ) (to 2 decimals)

( ,  ) (to 2 decimals)

b. The company is considering hiring Tom Smart, a salesperson with seven years of experience. Develop a  prediction interval of annual sales for Tom Smart.

( ,  ) (to 2 decimals)

5.

In the table below ratings data on x= the quality of the speed of execution and overall satisfaction with electronic trades provided the estimated regression equation. y = 0.4261 + 0.8947x

Brokerage	Speed	Satisfaction
Scottrade, Inc.	3.1	3.4
Charles Schwab	3.7	3.6
Fidelity Brokerage Services	3.0	3.1
TD Ameritrade	3.8	3.7
E*Trade Financial	2.9	3.0
Vanguard Brokerage Services	2.9	3.4
USAA Brokerage Services	3.6	4.0
Thinkorswim	3.0	3.5
Wells Fargo Investments	3.0	2.6
Interactive Brokers	3.0	2.9
Zecco.com	3.0	2.8

At the 0.05 level of significance, test whether speed of execution and overall satisfaction are related. Show the ANOVA table. What is your conclusion?

Source of Variation	Sum of Squares (to 4 decimals)	Degrees of Freedom	Mean Square (to 4 decimals)	F (to 2 decimals)
Regression
Error
Total

6.

Given are five observations for two variables, x and y.

x	2	8	11	15	18
y	58	53	49	19	11

The estimated regression equation for these data is y = 72.19 - 3.17x

a. Compute SSE, SST and SSR .

SSE	(to 2 decimals)
SST	(to 2 decimals)
SSR	(to 2 decimals)

b. Compute the coefficient of determination r^2. Comment on the goodness of fit.

(to 3 decimals)

The least squares line provided an  - Select your answer -goodbadItem 5 fit; % of the variability in y has been explained by the estimated regression equation (to 1 decimal).

c. Compute the sample correlation coefficient. Enter negative value as negative number.

(to 3 decimals)

Answer 1

Minitab is uded to solve the problems

1) Residual plot

The residuals are:

Years of experience	Sales	RESI
1	84	0.576433
1	81	-2.42357
2	87	-1.43949
4	101	2.528662
5	104	0.512739
7	118	4.480892
8	119	0.464968
9	120	-3.55096
10	127	-1.56688
11	134	0.417197

2a)

Regression Analysis: y versus x

Regression Equation

y = 3.80 + 0.593 x

3)