The data on the next two pages is from a Canadian 1970 census which collected information about specific occupations.Data collected was used to develop a regression model to predict prestige for all occupations.Use R to calculate the quantities and generate the visual summaries requested below.

(1) To get a sense of the data, generate a scatterplot to examine the association between prestige score and years of education.Briefly describe the form, direction, and strength of the association between the variables.Calculate the correlation coefficient.(3 points )

(2) Perform a simple linear regression with prestige score and years of education, and briefly summarize your conclusions (no need to do the 5-step procedure here).Generate a residual plot.Assess whether the model assumptions are met.Are there any outliers or influence points?If so, identify them by ID and comment on the effect of each on the regression. (5 points)

(3) Calculate the least squares regression equation that predicts prestige score from education, income, and percentage of women.Formally test (using the 5-step procedure) whether the set of these predictors are associated with prestige score at the = 0.05 level (Hint: You should be performing the global test).(5 points)

(4) If the overall model was significant, summarize the information about the contribution of each variable separately at the same significance level as used for the overall model (no need to do a formal 5-step procedure for each one, just comment on the results of the tests).Provide interpretations for any estimates (of the slopes) that are significant.Calculate 95% confidence intervals for any estimates that are significant. (4 points)

(5) Generate a residual plot showing the fitted values from the regression against the residuals.Is the fit of the model reasonable?Are there any outliers or influence points? (3 points)

Data Set for Assignment 4

Occupational Title

Education Level (years)

Income ($)

Percent of Workforce that are Women

Prestige Score

GOV_ADMINISTRATORS

13.11

12351

11.16

68.8

GENERAL_MANAGERS

12.26

25879

4.02

69.1

ACCOUNTANTS

12.77

9271

15.7

63.4

PURCHASING_OFFICERS

11.42

8865

9.11

56.8

CHEMISTS

14.62

8403

11.68

73.5

PHYSICISTS

15.64

11030

5.13

77.6

BIOLOGISTS

15.09

8258

25.65

72.6

ARCHITECTS

15.44

14163

2.69

78.1

CIVIL_ENGINEERS

14.52

11377

1.03

73.1

MINING_ENGINEERS

14.64

11023

0.94

68.8

SURVEYORS

12.39

5902

1.91

62

DRAUGHTSMEN

12.3

7059

7.83

60

COMPUTER_PROGRAMERS

13.83

8425

15.33

53.8

ECONOMISTS

14.44

8049

57.31

62.2

PSYCHOLOGISTS

14.36

7405

48.28

74.9

SOCIAL_WORKERS

14.21

6336

54.77

55.1

LAWYERS

15.77

19263

5.13

82.3

LIBRARIANS

14.15

6112

77.1

58.1

VOCATIONAL_COUNSELLORS

15.22

9593

34.89

58.3

MINISTERS

14.5

4686

4.14

72.8

UNIVERSITY_TEACHERS

15.97

12480

19.59

84.6

PRIMARY_SCHOOL_TEACHERS

13.62

5648

83.78

59.6

SECONDARY_SCHOOL_TEACHERS

15.08

8034

46.8

66.1

PHYSICIANS

15.96

25308

10.56

87.2

VETERINARIANS

15.94

14558

4.32

66.7

OSTEOPATHS_CHIROPRACTORS

14.71

17498

6.91

68.4

NURSES

12.46

4614

96.12

64.7

NURSING_AIDES

9.45

3485

76.14

34.9

PHYSIO_THERAPSTS

13.62

5092

82.66

72.1

PHARMACISTS

15.21

10432

24.71

69.3

MEDICAL_TECHNICIANS

12.79

5180

76.04

67.5

COMMERCIAL_ARTISTS

11.09

6197

21.03

57.2

RADIO_TV_ANNOUNCERS

12.71

7562

11.15

57.6

ATHLETES

11.44

8206

8.13

54.1

SECRETARIES

11.59

4036

97.51

46

TYPISTS

11.49

3148

95.97

41.9

BOOKKEEPERS

11.32

4348

68.24

49.4

TELLERS_CASHIERS

10.64

2448

91.76

42.3

COMPUTER_OPERATORS

11.36

4330

75.92

47.7

SHIPPING_CLERKS

9.17

4761

11.37

30.9

FILE_CLERKS

12.09

3016

83.19

32.7

RECEPTIONSTS

11.04

2901

92.86

38.7

MAIL_CARRIERS

9.22

5511

7.62

36.1

POSTAL_CLERKS

10.07

3739

52.27

37.2

TELEPHONE_OPERATORS

10.51

3161

96.14

38.1

COLLECTORS

11.2

4741

47.06

29.4

CLAIM_ADJUSTORS

11.13

5052

56.1

51.1

TRAVEL_CLERKS

11.43

6259

39.17

35.7

OFFICE_CLERKS

11

4075

63.23

35.6

SALES_SUPERVISORS

9.84

7482

17.04

41.5

COMMERCIAL_TRAVELLERS

11.13

8780

3.16

40.2

SALES_CLERKS

10.05

2594

67.82

26.5

NEWSBOYS

9.62

918

7

14.8

SERVICE_STATION_ATTENDANT

9.93

2370

3.69

23.3

INSURANCE__AGENTS

11.6

8131

13.09

47.3

REAL_ESTATE_SALESMEN

11.09

6992

24.44

47.1

BUYERS

11.03

7956

23.88

51.1

FIREFIGHTERS

9.47

8895

0

43.5

POLICEMEN

10.93

8891

1.65

51.6

COOKS

7.74

3116

52

29.7

BARTENDERS

8.5

3930

15.51

20.2

FUNERAL_DIRECTORS

10.57

7869

6.01

54.9

BABYSITTERS

9.46

611

96.53

25.9

LAUNDERERS

7.33

3000

69.31

20.8

JANITORS

7.11

3472

33.57

17.3

ELEVATOR_OPERATORS

7.58

3582

30.08

20.1

FARMERS

6.84

3643

3.6

44.1

FARM_WORKERS

8.6

1656

27.75

21.5

ROTARY_WELL_DRILLERS

8.88

6860

0

35.3

BAKERS

7.54

4199

33.3

38.9

SLAUGHTERERS_1

7.64

5134

17.26

25.2

SLAUGHTERERS_2

7.64

5134

17.26

34.8

CANNERS

7.42

1890

72.24

23.2

TEXTILE_WEAVERS

6.69

4443

31.36

33.3

TEXTILE_LABOURERS

6.74

3485

39.48

28.8

TOOL_DIE_MAKERS

10.09

8043

1.5

42.5

MACHINISTS

8.81

6686

4.28

44.2

SHEET_METAL_WORKERS

8.4

6565

2.3

35.9

WELDERS

7.92

6477

5.17

41.8

AUTO_WORKERS

8.43

5811

13.62

35.9

AIRCRAFT_WORKERS

8.78

6573

5.78

43.7

ELECTRONIC_WORKERS

8.76

3942

74.54

50.8

RADIO_TV_REPAIRMEN

10.29

5449

2.92

37.2

SEWING_MACH_OPERATORS

6.38

2847

90.67

28.2

AUTO_REPAIRMEN

8.1

5795

0.81

38.1

AIRCRAFT_REPAIRMEN

10.1

7716

0.78

50.3

RAILWAY_SECTIONMEN

6.67

4696

0

27.3

ELECTRICAL_LINEMEN

9.05

8316

1.34

40.9

ELECTRICIANS

9.93

7147

0.99

50.2

CONSTRUCTION_FOREMEN

8.24

8880

0.65

51.1

CARPENTERS

6.92

5299

0.56

38.9

MASONS

6.6

5959

0.52

36.2

HOUSE_PAINTERS

7.81

4549

2.46

29.9

PLUMBERS

8.33

6928

0.61

42.9

CONSTRUCTION_LABOURERS

7.52

3910

1.09

26.5

PILOTS

12.27

14032

0.58

66.1

TRAIN_ENGINEERS

8.49

8845

0

48.9

BUS_DRIVERS

7.58

5562

9.47

35.9

TAXI_DRIVERS

7.93

4224

3.59

25.1

LONGSHOREMEN

8.37

4753

0

26.1

TYPESETTERS

10

6462

13.58

42.2

BOOKBINDERS

8.55

3617

70.87

35.2