MET CS 555 Assignment 4 solution

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)