Description
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) Save the data to excel or CSV file and read into R for analysis. (1 point)
(2) 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. (3 points)
(3) Perform a simple linear regression. 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. (4 points)
(4) Calculate the least squares regression equation that predicts prestige from education, income and percentage of women. Formally test whether the set of these predictors are associated with prestige at the = 0.05 level. (4 points)
(5) 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 that were significant. Calculate 95% confidence intervals where appropriate. (4 points)
(6) Generate a residual plot showing the fitted values from the regression against the residuals. Is the fit of the model reasonable? (2 points)
(7) Are there any outliers or influence points? (2 points)
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
