Just need help with number 7. thank you.

7. (15+2 for Excel work) Consider the following data for the average cost of various fuels and electricity for a twelve year period. The data measure the following:Electricity Residential rate per kilowatt hourNatural Gas Residential natural gas per 1000 cubic feetFuel Oil Residential fuel oil per gallonGasoline Regular gasoline per gallonYour model will attempt to predict residential electricity costs using the cost of the other fuels.a) (1) State whether you would expect a positive or negative relationship between electricity costs and each of the independent variables and explain why.b) (2) Use EXCEL, to create a correlation using all independent variables provided. Discuss all aspects of the correlation matrix, as it compares to your expectations in part (a) and what it tells you about the potential results of a regression analysis.c) (3) Use EXCEL to run a multiple regression to estimate electricity costs using all independent variables provided. Test if the overall regression is significant at the 5% level.d) (3) Test for the significance of each slope coefficient at the 5% level. (Incorporate all tests intoONE five step answer as in the slides.)e) (2) Based on your correlation matrix and the results of your regression do you suspect multicollinearity? If yes, which independent variable(s) to you think could be responsible?f) (2) Explain how you test for multicollinearity but do not test.g) (2) How could you rerun the regression taking into account the issues in the first regression?Which variable or variables would you keep as an explanatory variable(s), and why?

ECON 2202 ? Statistical Methods in Economics and Business II

EXCEL ASSIGNMENT

WINTER 2016

Due: by END OF CLASS (11:30) Thursday April 7, 2016

NO LATE ASSIGNMENTS ARE ACCEPTED.

IT MUST BE SUBMITTED TO COMPLETE THE COURSE REQUIREMENTS

READ ALL INSTRUCTIONS BEFORE BEGINNING!!!!!!!!

1. Late assignments receive a grade of 0. Failure to submit this assignment leads to an FND in

the course.

2. You must use EXCEL in the questions where indicated for this assignment. Copy and paste the

tables into EXCEL from the text below. You must hand in all EXCEL output where indicated. .

3. The assignment otherwise is hand written. Please label the Excel outputs with the question

numbers.

4. Students may work together on the assignment, but each student MUST submit the

assignment independently.

5. Keep a copy of this assignment to study from, solutions will be posted.

6. All hypothesis tests MUST use the five steps. Formulae are necessary in all cases unless

otherwise noted. For this assignment ONLY you can follow these examples to keep the

document smaller and save time!! The conclusions MUST be complete IN CONTEXT as always.

F-test:

1.

Ho: regression is not significant, Ha: regression is significant

2.

?=0.05, one-tailed. F?,(k, n-k-1) = F0.05,(2,7) = 6.542

3.

Reject Ho if F0 >F?

4.

F = MSR/MSE = 43.3648

5.

Since F0 > F? (43.3648> 6.542), reject Ho. The regression equation is significant; the relationship

between apples and oranges is significant.

OR if using p-values

P-value approach

1.

Ho: regression is not significant, Ha: regression is significant

2.

?=0.05, one-tailed

3.

Reject Ho if p-value < ? = 0.05

4.

p-value = 0.0001

5.

Since p-value = 0.0001 < ? = 0.05, reject Ho. The regression equation is significant; the

relationship between apples and oranges is significant.

1

1. (16 +3 for Excel work) A company is reviewing the performance of two different suppliers of

toner ink as their intention is to compare them and possible switch to the alternate one. Using

the following data for hours of toner use before empty and alpha = 0.05 in all cases answer the

following.

CURRENT

SUPPLIER

A

486

ALTERNATE

SUPPLIER

B

489

490

491

491

494

494

496

498

498

489

491

492

492

492

492

493

493

498

502

504

505

506

507

508

510

514

515

527

494

495

496

497

497

497

498

499

502

503

505

a. (5) Determine if the standard deviation of the Alternate Supplier B is significantly less than 5.

Use alpha = 0.05. (No EXCEL)

b. (3) Determine if the variation of the hours of toner use of Current Supplier A is greater than

that of Alternate Supplier B. Use EXCEL, include printout of result and DO NOT USE p-values

in test write up.

c. (3) Determine if there is any difference in the variation of the hours of toner use between the

two suppliers. Use EXCEL, include printout of result and DO NOT USE p-values in test write

up.

d. (3) Using the findings of part (c), test to determine if Current Supplier A has higher average

hours of toner use than Alternate Supplier B. Use EXCEL, include printout of result and use pvalues in test.

e. (2) What is your recommendation to the company with respect to the supplier to select?

Explain.

2. (3+1 for Excel work) Public health in a local hospital decided to test whether the length of time

that nurses wash their hands will alter the amount of bacteria remaining on them. To ensure

2

consistency in the testing nine nurses were selected and each washed their hands, in the first

trial for 2.5 seconds and in the second for 15 seconds. The amount of remaining bacteria was

measured in each case. Test the hypothesis that longer washing leads to less bacteria

remaining. Use alpha = 0.05.

CULTURE

1

66

132

120

187

190

17

33

92

1000

CULTURE

2

78

115

93

48

77

3

12

12

146

3

3. (15+1 for Excel work) Grading assignments is a real problem, taking a great deal of time and

while many students do a poor job, many copy and gain no benefit. An instructor who taught

three sections of a course carried out a test. One section had no assignments, one had

assignments but they were not graded, and the final section had graded assignments. Grades

were reviewed after the first midterm. Assume each population is normally distributed, and

samples are independent random samples. Using EXCEL where possible perform ALL ANOVA

tests necessary to determine which approach if any led to higher grades. Use alpha = 0.05 in all

tests. Use EXCEL for the ANOVA test and use the p values in testing. For those tests for which

you cannot use EXCEL, use the standard write up as used in the practice assignments.

No Assignments

69

69

92

84

79

84

76

63

76

82

89

72

72

65

73

47

92

71

83

81

92

80

64

72

84

79

74

81

Assignments, Not Graded

73

63

68

79

57

68

72

74

49

84

79

71

80

74

71

63

88

83

89

82

69

92

79

81

76

81

81

75

Assignments, Graded

83

97

72

79

84

76

91

76

83

88

91

96

68

99

89

80

79

91

83

83

76

90

79

67

86

86

82

84

4

4. (9+1 for Excel work) The instructor in the previous example teaches the same sections of the

course four times a year and wanted to investigate if there was not only a difference in the way

assignments were treated but also in the time of year the course was given. The following data was

collected. Assume all populations are normally distributed, observations are independent, and

population variances are equal. Using EXCEL perform all remaining tests necessary to determine

whether the grades were influenced by assignment method and/or semester. Use alpha = 0.05 in

all tests. No post tests are required.

TERM

FALL

WINTER

EARLY SUMMER

LATE SUMMER

No Assignments

69

69

92

84

79

84

76

63

76

82

89

72

72

65

73

47

92

71

83

81

92

80

64

72

84

79

74

81

Assignments, Not Collected

73

63

68

79

57

68

72

74

49

84

79

71

80

74

71

63

88

83

89

82

69

92

79

81

76

81

81

75

Assignments, Collected

83

97

72

79

84

76

91

76

83

88

91

96

68

99

89

80

79

91

83

83

76

90

79

67

86

86

82

84

5

5. (16) Is the type of beverage ordered with lunch at a restaurant independent of the age of the

customer? A random sample of 309 lunch customers was taken and the results are as follows.

Using alpha = 0.01, test to determine if the two factors are related. Please show intermediate

calculation steps for part marks. (No Excel in this question.)

AGE

21-34

35-55

OVER 55

COFFEE/TE

A

26

41

24

91

SOFT

DRINK

95

40

13

148

OTHER

18

20

32

70

139

101

69

309

6. (13 +5 for Excel work) Can sales of major fast food chains be explained by the number of

individual locations the chain has? Consider the following data where sales are measured in $

billions and locations are in thousands.

MCDONALD'S

BURGER KING

TACO BELL

PIZZA HUT

WENDY'S

KFC

SUBWAY

DAIRY QUEEN

A&W

SALES

17.1

7.9

4.8

4.7

4.6

4

2.9

2.7

2.7

LOCATION

S

12.4

7.5

6.8

8.7

4.6

5.1

11.2

5.1

2.9

Use EXCEL, to create a scatter diagram, correlation matrix, and regression model. Conduct all

tests at the 5% significance level.

a) (2) Reviewing the data and the scatter diagram, does the correlation matrix result support the

relationship you would expect? Are there any other considerations or concerns that arise from

this?

b) (5) Conduct a test to determine whether the population correlation coefficient is significantly

different from zero. Do not use p values.

c) (4) Is there an observation which is impacting the relationship? Given your findings in parts (a)

and (b), explain what you might consider doing to further investigate this relationship? Rerun

the correlation matrix and the equation and compare the two models with respect to the

correlation of the variables, the fit (R2), and the significance of the slope. You do not need to

write out the tests just use the p values to explain what happens and why when comparing the

significance of the model or slope.

6

d) (2) Which model would you select to examine the relationship? Explain your choice.

7. (15+2 for Excel work) Consider the following data for the average cost of various fuels and

electricity for a twelve year period. The data measure the following:

Electricity

Natural Gas

Fuel Oil

Gasoline

Residential rate per kilowatt hour

Residential natural gas per 1000 cubic feet

Residential fuel oil per gallon

Regular gasoline per gallon

Your model will attempt to predict residential electricity costs using the cost of the other fuels.

a) (1) State whether you would expect a positive or negative relationship between electricity costs

and each of the independent variables and explain why.

b) (2) Use EXCEL, to create a correlation using all independent variables provided. Discuss all

aspects of the correlation matrix, as it compares to your expectations in part (a) and what it tells

you about the potential results of a regression analysis.

c) (3) Use EXCEL to run a multiple regression to estimate electricity costs using all independent

variables provided. Test if the overall regression is significant at the 5% level.

d) (3) Test for the significance of each slope coefficient at the 5% level. (Incorporate all tests into

ONE five step answer as in the slides.)

e) (2) Based on your correlation matrix and the results of your regression do you suspect

multicollinearity? If yes, which independent variable(s) to you think could be responsible?

f) (2) Explain how you test for multicollinearity but do not test.

g) (2) How could you rerun the regression taking into account the issues in the first regression?

Which variable or variables would you keep as an explanatory variable(s), and why?

Electricit Natural

Gasolin Fuel

y

Gas

e

Oil

2.54

1.29

0.39

0.21

3.51

1.71

0.57

0.31

4.64

2.98

0.86

0.44

5.36

3.68

1.19

0.61

6.2

4.29

1.31

0.76

6.86

5.17

1.22

0.68

7.18

6.06

1.16

0.65

7.54

6.12

1.13

0.69

7.79

6.12

1.12

0.61

7.41

5.83

0.86

0.34

7.41

5.54

0.9

0.42

7.49

4.49

0.9

0.33

7