Exercise no 49 page 496

The National Highway Association is studying the relationship between the number of bidders on a highway project and the winning (lowest) bid for the project. Of particular interest is wether the number of bidders increase or dercrease the amount of the winning bid.

Project Wiining Bid

Num of Bid

($ millions) Project Wiining Bid

Num of Bid

($ millions)

Y X Y X

1 5.1 9 9 10.3 6

2 8 9 10 8 6

3 9.7 3 11 8.8 4

4 7.8 10 12 9.4 7

5 7.7 5 13 8.6 7

6 5.5 10 14 8.1 7

7 8.3 7 15 7.8 6

8 5.5 11

a. Determine the regression equation

�� � � � �� � � ��.���� � 1.516 �� � ��.���� � 2.299 (see Table below)

� � ���.����������.������.���� � ���.����.��� � �0.705 � � � "#"$ � �0.705 �.����.��� � �0.46 � � �& � ��& � 7.91 � �0.46�7.13 � 11.19

The Regression equation is �() � 11.19 � 0.46�

Project

Wiining

Bid

Num of

Bid

Y X

1 5.1 9 -2.81 7.88 1.87 3.48 -5.24

2 8 9 0.09 0.01 1.87 3.48 0.17

3 9.7 3 1.79 3.22 -4.13 17.08 -7.41

4 7.8 10 -0.11 0.01 2.87 8.22 -0.31

5 7.7 5 -0.21 0.04 -2.13 4.55 0.44

6 5.5 10 -2.41 5.79 2.87 8.22 -6.90

7 8.3 7 0.39 0.15 -0.13 0.02 -0.05

8 5.5 11 -2.41 5.79 3.87 14.95 -9.31

9 10.3 6 2.39 5.73 -1.13 1.28 -2.71

10 8 6 0.09 0.01 -1.13 1.28 -0.11

11 8.8 4 0.89 0.80 -3.13 9.82 -2.80

12 9.4 7 1.49 2.23 -0.13 0.02 -0.20

13 8.6 7 0.69 0.48 -0.13 0.02 -0.09

14 8.1 7 0.19 0.04 -0.13 0.02 -0.03

15 7.8 6 -0.11 0.01 -1.13333 1.28 0.12

Jumlah 118.6 107 0.00 32.19 0.00 73.73 -34.41

Rata-

Rata 7.91 7.13

b) Estimate the amount of the winning bid if there were seven bidders

�( � 11.19 � 0.46 �7� � 7.97

c) A New Entrance is to be contructed on the ohio Turnpike. There are seven bidders on the project. Develop 1 95 percent prediction interval for the wininnging bid

Confidence Interval � + ,�.-. �/ � �-0�-&�1∑�-0�-&�1

�3� � ∑����1/�� �3� � ��.���� � 1.11 (see table below) For α = 0.05, ,4/� � 2.145

Prediction interval for the winning bid if there are seven bidder,

7.97 + 2.145 �1.11� 6�7 � 7.13��16.13

)( YY −2

)( YY − )( XX −2

)( XX − ))(( YYXX −−

7.97 + 2.145 �1.11��0.015� 7.97 + 0.077

Project

Wiining

Bid

Num of

Bid

Y X

1 5.1 9 7.05 -1.95 3.80

2 8 9 7.05 0.95 0.90

3 9.7 3 9.81 -0.11 0.01

4 7.8 10 6.59 1.21 1.46

5 7.7 5 8.89 -1.19 1.42

6 5.5 10 6.59 -1.09 1.19

7 8.3 7 7.97 0.33 0.11

8 5.5 11 6.13 -0.63 0.40

9 10.3 6 8.43 1.87 3.50

10 8 6 8.43 -0.43 0.18

11 8.8 4 9.35 -0.55 0.30

12 9.4 7 7.97 1.43 2.04

13 8.6 7 7.97 0.63 0.40

14 8.1 7 7.97 0.13 0.02

15 7.8 6 8.43 -0.63 0.40

Jumlah 118.6 107 -0.03 16.13

Rata-

Rata 7.91 7.13

d) Deteremine the coefficient of determination �� � �0.705� � 0.4970 � 49.70%

)( Yestest

YY −2

)(est

YY −

Exercise no 50 page 496-497

Mr William profit is studying companies going public for the first time. He is

particularly interested in the relationship between size of the offering and the price

per share. A Sampel of 15 companioes that recently went public revealed the

following information

Company Price/Share Size

Company Price/Share Size

Y X Y X

1 10.8 9 9 11.3 160.7

2 11.3 94.4 10 10.6 96.5

3 11.2 27.3 11 10.5 83

4 11.1 179.2 12 10.3 23.5

5 11.1 71.9 13 10.7 58.7

6 11.2 97.9 14 11 93.8

7 11 93.5 15 10.8 34.4

8 10.7 70

a. Determine the regression equation

�� � � � �� � � �.������ � 0.31 �� � ��.���,������ � 47.23 (see table below) Coeffisient of correlation � � ��.���������9.������.��� � ��.���9�.���� � 0.46 � � � ":"; � 0.46 9.����.�� � 0.003 � � �& � ��& � 10.91 � �0.003�79.59 � 10.67 �� � 10.67 � 0.003�

Compan

y

Price/Shar

e Size

Y X

1 10.8 9 -0.11 0.01 -70.59 4,982.48 7.53

2 11.3 94.4 0.39 0.15 14.81 219.43 5.83

3 11.2 27.3 0.29 0.09 -52.29 2,733.90 -15.34

4 11.1 179.2 0.19 0.04 99.61 9,922.82 19.26

5 11.1 71.9 0.19 0.04 -7.69 59.08 -1.49

6 11.2 97.9 0.29 0.09 18.31 335.38 5.37

7 11 93.5 0.09 0.01 13.91 193.58 1.30

8 10.7 70 -0.21 0.04 -9.59 91.90 1.98

9 11.3 160.7 0.39 0.15 81.11 6,579.37 31.90

10 10.6 96.5 -0.31 0.09 16.91 286.06 -5.19

11 10.5 83 -0.41 0.17 3.41 11.65 -1.39

12 10.3 23.5 -0.61 0.37 -56.09 3,145.71 34.03

13 10.7 58.7 -0.21 0.04 -20.89 436.25 4.32

14 11 93.8 0.09 0.01 14.21 202.02 1.33

15 10.8 34.4 -0.11 0.01 -45.1867 2,041.83 4.82

Jumlah 163.6 1193.8 0.00 1.31 0.00

31,241.4

8 94.26

Rata-

Rata 10.91 79.59

)( YY −2

)( YY − )( XX −2

)( XX − ))(( YYXX −−

b) Determine the coefficient of determination

�� � 0.4663� � 0.2174 � 21.74%

Exercise no 51 page 497

Bardi Trucking co., located in Cleveland, ohio, makes deliveries in the great lakes

region, the southwest, and the northeast. Jim bardi, the president is studying the

relationship between the distance a shipment must travel and the length of time, in

days, it takes the shipment to arrive the destination. To investigate,Mr Bardi selected

a random sample of 20 shipments made last month. Shipping distance is the

independent variable and shipping is the dependent variable. The result as follow

Shipment Shipp.time Distance

Shipment Shipp.time Distance

Y X Y X

1 5 656 11 7 862

2 14 853 12 5 679

3 6 646 13 13 835

4 11 783 14 3 607

5 8 610 15 8 665

6 10 841 16 7 647

7 9 785 17 10 685

8 9 639 18 8 720

9 10 762 19 6 652

10 9 762 20 10 828

b) Determine the coefficient of correlation. Can we conclude that there is a

positive correlation between distance and time ? use the 0.05 significant level

� � ���.�9�9�� � 2.70 �� � ���.�9�,���9�� � 87.45 (see table below) Coeffisient of correlation between room occupied and income is

� � �.�9�,�9��9�����,�9����,��� � �.�9�,�9����.��� � 0.692 (strong positive correlation) =>: @ � > =A: @ B > C � >. >D EFGH � +I. A>A EJKLMNO � P√R � I√A � PI � >. ST√AU√A � >. STI � I. TV>. WI � X. >SU EJKLMNO Y EFGH we coclude to reject Hipothesis null

Shipmen

t

Shipp.tim

e

Distanc

e

Y X

1 5 656 -3.4 11.56 -69.85 4,879.02 237.49

2 14 853 5.6 31.36 127.15 16,167.12 712.04

3 6 646 -2.4 5.76 -79.85 6,376.02 191.64

4 11 783 2.6 6.76 57.15 3,266.12 148.59

5 8 610 -0.4 0.16 -115.85 13,421.22 46.34

6 10 841 1.6 2.56 115.15 13,259.52 184.24

7 9 785 0.6 0.36 59.15 3,498.72 35.49

8 9 639 0.6 0.36 -86.85 7,542.92 -52.11

9 10 762 1.6 2.56 36.15 1,306.82 57.84

10 9 762 0.6 0.36 36.15 1,306.82 21.69

11 7 862 -1.4 1.96 136.15 18,536.82 -190.61

12 5 679 -3.4 11.56 -46.85 2,194.92 159.29

13 13 835 4.6 21.16 109.15 11,913.72 502.09

14 3 607 -5.4 29.16 -118.85 14,125.32 641.79

15 8 665 -0.4 0.16 -60.85 3,702.72 24.34

16 7 647 -1.4 1.96 -78.85 6,217.32 110.39

17 10 685 1.6 2.56 -40.85 1,668.72 -65.36

18 8 720 -0.4 0.16 -5.85 34.22 2.34

19 6 652 -2.4 5.76 -73.85 5,453.82 177.24

20 10 828 1.6 2.56 102.15 10,434.62 163.44

Jumlah 168 14517 0.00 138.80 0.00

145,306.5

5 3,108.20

Rata-

Rata 8.4 725.85

c) Determine the cooffient of determination

�� � 0.692� � 0.4788 � 47.88% d) Determine the standar error of estimate �� � � � ��

� � � ":"; � 0.692 �.�9��.�� � 0.021 � � 8.4 � 0.021�725.85� � �6.84

�� � �6.84 � 0.021 �

)( YY −2

)( YY − )( XX −2

)( XX − ))(( YYXX −−

Shipment Shipp.time Distance

Y X

1 5 656 6.94 -1.94 3.75

2 14 853 11.07 2.93 8.57

3 6 646 6.73 -0.73 0.53

4 11 783 9.60 1.40 1.95

5 8 610 5.97 2.03 4.12

6 10 841 10.82 -0.82 0.67

7 9 785 9.65 -0.65 0.42

8 9 639 6.58 2.42 5.86

9 10 762 9.16 0.84 0.70

10 9 762 9.16 -0.16 0.03

11 7 862 11.26 -4.26 18.16

12 5 679 7.42 -2.42 5.85

13 13 835 10.70 2.31 5.31

14 3 607 5.91 -2.91 8.45

15 8 665 7.13 0.87 0.77

16 7 647 6.75 0.25 0.06

17 10 685 7.55 2.46 6.03

18 8 720 8.28 -0.28 0.08

19 6 652 6.85 -0.85 0.73

20 10 828 10.55 -0.55 0.30

Jumlah 168 14517 168.06 -0.06 72.34

Rata-

Rata 8.4 725.85

Z� �- � 6∑�� � ����[ � 2 � 672.3418 � 2.005

)( Yestest

YY − 2)(est

YY −

Exercise no 56 page 499

The following table shows the mean annual percent return on capital (profitability)

and the mean annual percentage sales growth for eight aerospace and defense

companies

Company Profitability

Sales

growth

Y X

1 23.1 8

2 13.2 15.6

3 24.2 31.2

4 11.1 2.5

5 10.1 35.4

6 10.8 6

7 27.3 8.7

8 20.1 3.2

a. Compute the coefficient of correlation. Conduct a test of hypotehesis to

determine if it is reasonable to conclude that the population correlation is greater

than zero. Use tha 0.05 significance level

� � ���.����� � 6.95 �� � �.���,�9��� � 12.72 Coeffisient of correlation between room occupied and income is

� � ���.���������.������.��� � ���.�����.�� � �0.058 (weak negative correlation)

Company Profitability

Sales

growth

Y X

1 23.1 8 5.61 31.50 -5.83 33.93 -32.69

2 13.2 15.6 -4.29 18.38 1.78 3.15 -7.61

3 24.2 31.2 6.71 45.06 17.38 301.89 116.63

4 11.1 2.5 -6.39 40.80 -11.33 128.26 72.34

5 10.1 35.4 -7.39 54.58 21.58 465.48 -159.39

6 10.8 6 -6.69 44.72 -7.83 61.23 52.33

7 27.3 8.7 9.81 96.29 -5.13 26.27 -50.29

8 20.1 3.2 2.61 6.83 -10.63 112.89 -27.76

Jumlah 139.9 110.6 0.00 338.15 0.00 1,133.10 -36.44

Rata-

Rata 17.49 13.83

\9: ] Y 0 \�: ] ^ 0 _ � 0.05 ,`ab � 1.895 ,cdefgh � �√[ � 2√1 � �� � 0.058√6√1 � 0.058� � 0.14210.998 � 0.1423 ,cdefgh Y ,`ab we coclude to accept Hipothesis null or no positive correlation

b. Develop the regression equation for profitability based on growth. �� � � � �� � � � ":"; � �0.058 �.����.�� � �0.03

)( YY −2

)( YY − )( XX −2

)( XX − ))(( YYXX −−

� � �i � ��i � 17.49 � ��0.03j 13.83� � 17.90 �k � 17.90 � 0.03�