WEEK 8: REGRESSIONS AND

REPORTING RESULTS

Predictive Modeling

DATA 5400

WEEK 8 HOMEWORK DUE SUNDAY

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â€¢ 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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â€¢ 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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â€¢ Using Cars dataset, create linear model in R

CREATING A LINEAR MODEL

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PLOT CARS DATASET

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â€¢ The lm() command is used to fit linear models

â€¢ Use lm() function to create a Single Linear Regression model on

the cars dataset

â€¢ Reminder ?lm to get to the help documentation on the function

â€¢ Run the model to see the information and extract that as part of

results interpretation

L M () FUNCTION

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â€¢ 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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â€¢ What factors lead to increases in percentage of alumni who

donate?

â€¢ 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

â€¢ 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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â€¢ Variables/Features

â€¢ University

â€¢ State

â€¢ Graduation Rate

â€¢ % of Class Under 20

â€¢ Student-Faculty Ratio

â€¢ Alumni Giving Rate

MINI PROJECT

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ALUMNI GIVING DATA SUMMARY

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â€¢ 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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