stats 2 week 5

1)       The following sample observations were randomly selected.

   X :    4        5         3         6      10
   Y:    4        6          5         7      7

(1)

Fill in the blanks below: (Round your answers to 2 decimal places.)

correlation between X and Y.

(3)

Fill in the blanks. (Round your answer to the nearest whole number.)

  The coefficient of determination obtained here indicates X accounts for approximately  relationship between X and Y. The coefficient of determination is is the dependent variable.

(c)

Determine the correlation coefficient. (Round your answer to 2 decimal places.)

  Coefficient of correlation

correlation between the variables.

4)       The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

Number of
Assemblers

One-Hour
Production (units)

2

15

4

25

1

10

5

40

3

30

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

(b)

A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production?

  , as the number of assemblers, so does the production.

(c)

Compute the coefficient of correlation. (Negative amounts should be indicated by a minus sign. Round s_x, s_y and r  to 3 decimal places.)

X

Y

(

(

(

2  

15  

 is the independent variable and is the dependent variable.

(b-1)

Determine the coefficient of correlation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

X

Y

(

(

(

9.0  

8.1  

correlation between age of car and selling price. So, H_o. Weconclude that the correlation in the population is
   greater than zero.

7)       The following hypotheses are given.

A random sample of 15 paired observations have a correlation of −.46. Can we conclude that the correlation in the population is less than zero? Use the .05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

  Reject H₀ if t < −1.771

t

=

  H_o. 

8)       The following sample observations were randomly selected.

X:

 5

 3

6

 3

 4

 4

6

8

Y:

13

15

7

12

13

11

9

5

(a)

Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

X

Y

(

(

(

5  

13   

[removed]  

2.375  

[removed]  

5.641  

[removed]    

3  

15   

−1.875  

[removed]  

3.516  

[removed]  

−8.203    

6  

7   

[removed]  

[removed]  

[removed]  

13.141  

−4.078    

3  

12   

−1.875  

1.375  

[removed]  

[removed]  

[removed]    

4  

13   

−0.875  

[removed]  

0.766  

[removed]  

−2.078    

4  

11   

[removed]  

0.375  

[removed]  

0.141  

[removed]   

6  

9   

1.125  

−1.625  

[removed]  

[removed]  

[removed]   

8  

5   

[removed]  

[removed]  

[removed]  

31.641  

−17.578    

[removed] 

[removed]  

[removed]  

[removed]  

[removed]    

=

[removed]

=

[removed]

  s_x

=

[removed]

s_y

=

[removed]

r

=

[removed]

b

=

[removed]

a

=

[removed]

  Y' = [removed]+ [removed]X

(b)

Determine the value of

[removed]

9)       Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following.

Number of Rooms

Kilowatt-Hours (thousands)

Number of Rooms

Kilowatt-Hours (thousands)

12

9

8

6

9

7

10

8

14

10

10

10

6

5

5

4

10

8

7

7

(a)

Determine the regression equation. (Round your answers to 3 decimal places.)

(b)

Determine the number of kilowatt-hours, in thousands, for a six-room house.(Round your answer to 3 decimal places.)

 Number of kilowatt-hours

[removed] 

10)   Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.

Number of
Contacts,
X

Sales
($ thousands),
Y

Number of
Contacts,
X

Sales
($ thousands),
Y

14  

24  

23  

30  

12  

14  

48  

90  

20  

28  

50  

85  

16  

30  

55  

120  

46  

80  

50  

110  

(a)

Determine the regression equation. (Negative amounts should be indicated by a minus sign.Do not round intermediate calculations. Round final answers to 2 decimal places.)

X

Y

(

(

(

14  

[removed] 

[removed] 

[removed] 

376.36  

1376.41  

719.74  

12  

14  

−21.4  

−47.1  

[removed] 

[removed] 

[removed] 

20  

[removed] 

−13.4  

[removed] 

179.56  

[removed] 

443.54  

16  

30  

[removed] 

−31.1  

[removed] 

967.21  

[removed] 

46  

[removed] 

12.6  

[removed] 

[removed] 

357.21  

[removed] 

23  

[removed] 

−10.4  

[removed] 

[removed] 

967.21  

[removed] 

48  

90  

[removed] 

28.9  

213.16  

[removed] 

421.94  

50  

85  

[removed] 

23.9  

275.56  

[removed] 

396.74  

55  

[removed] 

[removed] 

[removed] 

466.56  

3469.21  

1,272.24  

50  

110.0  

16.6  

48.9  

[removed] 

[removed] 

[removed] 

[removed] 

[removed] 

[removed] 

[removed] 

[removed] 

=

[removed]

=

[removed]

  s_x

=

[removed]

s_y

=

[removed]    

r

=

[removed]   

   b =[removed]

   a  = [removed]

  Y' = [removed]+ [removed]X

(b)

Determine the estimated sales if 40 contacts are made.(Do not round intermediate calculations. Round final answers to 2 decimal places.)

[removed]