WEEK 8: REGRESSIONS AND
REPORTING RESULTS
Predictive Modeling
DATA 5400
WEEK 8 HOMEWORK DUE SUNDAY
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• U N D E R S TA N D I N G Y O U R R E S U LT S I N T E R P R E T I N
G & R E P O R T I N G Y O U R F I N D I N G S
LINEAR REGRESSION:
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• U N D E R S TA N D I N G Y O U R R E S U LT S I N T E R P R E T I N
G & R E P O R T I N G Y O U R F I N D I N G S
MULTIPLE REGRESSION:
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• Using Cars dataset, create linear model in R
CREATING A LINEAR MODEL
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PLOT CARS DATASET
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• The lm() command is used to fit linear models
• Use lm() function to create a Single Linear Regression model on
the cars dataset
• Reminder ?lm to get to the help documentation on the function
• Run the model to see the information and extract that as part of
results interpretation
L M () FUNCTION
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• Output shows coefficients and intercept, can manually check that
calculations compare to the linear regression formula
INTERPRET RESULTS
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ADD FITTED LINE TO SCATTER PLOT
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ULEARN DATASET | L M WITH MULTIPLE FEATURES
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CREATE MODEL ON HEIGHT AND AGE
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REPORTING STATISTICS FROM YOUR MODEL
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1. Variable Coefficients
2. P values
3. Model Statistics
CREATE MODEL WITH MULTIPLE RESULTS
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SUPPORTING YOUR HYPOTHESIS
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R E P O RT I N G R E G R E S S I O N R E S U LT S
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REPORTING YOUR RESULTS
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FORMATTING AND REFERENCING A TABLE
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• What factors lead to increases in percentage of alumni who
donate?
• Research shows students who are more satisfied with their contact
with teachers are more likely to graduate, one might suspect
smaller classes + low student-faculty ratio -> satisfied graduates
• Look at the giving model data for 48 Universities to determine
which factors are those that lead to higher giving outcomes
PROBLEM STATEMENT
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1. Use the methods of the descriptive statistics summarize the data.
2. Write a directional hypothesis to explain the relationship between graduation rate and alumni giving.
3. Test your hypothesis using a simple linear regression model that can be used to predict the alumni giving
rate, given the graduation rate. Report and discuss your findings using appropriate model statistics.
4. Write directional hypotheses to explain the relationship between the other variables in the database and
alumni giving.
5. Develop a multiple linear regression model that could be used to predict the alumni giving rate using
Graduate Rate, % of Classes Under 20, and Student/Faculty Ratio as independent variables. Report and
discuss your findings using appropriate model statistics.
6. What conclusions and recommendations can you derive from your analysis?
7. Which universities are achieving a substantially higher alumni giving rate than would be expected, given
their Graduate Rate, % of Classes Under 20, and Student/Faculty Ratio?
8. Discuss any limitations of your current model and make recommendations for future research (e.g. ways
to improve the model, inclusion of other independent variables to improve the explanatory strength of
your model.)
MANAGERIAL REPORT
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• Variables/Features
• University
• State
• Graduation Rate
• % of Class Under 20
• Student-Faculty Ratio
• Alumni Giving Rate
MINI PROJECT
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ALUMNI GIVING DATA SUMMARY
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• We believe that students at colleges with smaller classes are more
likely to give back to the college and therefore the college will
have a higher giving rate
EXAMPLE HYPOTHESIS
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CREATE MODEL AND VIEW INITIAL RESULTS
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