Exam 3 SampleDecision Trees

Cluster AnalysisAssociation RulesData Visualization

SAS

SAS• When to Use Which Analysis (D, C or A)?

– When someone gets an A in this class, what other classes do they get an A in?

– What predicts whether a company will go bankrupt?– If someone upgrades to an iPhone, do they also buy

a new case?– Which party will win the election?– Can we group our website visitors into types based

on their online behaviors?– Which customers will purchase our product?– Can we identify different product markets based on

customer demographics?

SAS• When to Use Which Analysis (D, C or A)?

– When someone gets an A in this class, what other classes do they get an A in?

– What predicts whether a company will go bankrupt?– If someone upgrades to an iPhone, do they also buy

a new case?– Which party will win the election?– Can we group our website visitors into types based

on their online behaviors?– Which customers will purchase our product?– Can we identify different product markets based on

customer demographics?

Decision Trees• Which is the Root Node?• # Leafs Nodes?

Decision Trees

2 5

3 4

• Which is the Root Node?• # Leafs Nodes?

1

• Probability of Purchase?i) Female, 130 lbs, 12 ft? ii) 120 lbs, 5 feet, male?

• Best predictor variable?

Outcome Data

062%

138%

n350

Outcome Data

055%

145%

n250

Outcome Data

040%

160%

n150

Outcome Data

060%

140%

n250

Outcome Data

045%

155%

n75

Outcome Data

035%

165%

n75

Height

Weight<150 >=150

Weight

Gender

<170 >=170

Male Female

<6’ >=6’

• Probability of Purchase?i) Female, 130 lbs, 12 ft? ii) 120 lbs, 5 feet, male?

• Best predictor variable?

Outcome Data

062%

138%

n350

Outcome Data

055%

145%

n250

Outcome Data

040%

160%

n150

Outcome Data

060%

140%

n250

Outcome Data

045%

155%

n75

Outcome Data

035%

165%

n75

Height

Weight<150 >=150

Weight

Gender

<170 >=170

Male Female

<6’ >=6’

• Probability of Purchase?i) 5 ft 5 inches?

ii) 6 ft 5 inches 190 lbs?

Outcome Data

062%

138%

n350

Outcome Data

055%

145%

n250

Outcome Data

040%

160%

n150

Outcome Data

060%

140%

n250

Outcome Data

045%

155%

n75

Outcome Data

035%

165%

n75

Height

Weight<150 >=150

Weight

Gender

<170 >=170

Male Female

<6’ >=6’

Decision Trees• What does it mean that Gender is

only on the right side of the tree? Why is it not on both sides?

• Based on the tree, which demographic is MOST likely to buy the product? Least likely to buy the product?

Decision Trees• What does it mean that Gender is only on the right side

of the tree? Why is it not on both sides?– Gender only has predictive/explanatory power for customers

who are greater than or equal to 6 feet and below 170lbs.– That is, in other subsets of the population, it does no better

than chance at predicting behavior.• Based on the tree, which demographic is MOST likely to

buy the product? Least likely to buy the product?– Biggest Leaf Node Probability (1): Over 6 ft, below 170 lbs,

female (1 = 65% probability)

– Biggest Leaf Node Null Probability (0): below 6 ft, below 150 lbs (0 = 62% probability)

Decision Trees• What Statistics are Used to Determine Splits for Decision

Trees?– Gini Coefficient, Chi-Square Statistics (p-value)

• What does it mean when the Gini = 1?

• What does it mean when the Chi-square is bigger?

• What happens to the p-value as the Chi-square gets bigger?

–

Decision Trees• What Statistics are Used to Determine Splits for Decision

Trees?– Gini Coefficient, Chi-Square Statistics (p-value)

• What does it mean when the Gini = 1? – The predictor is no better than flipping a coin (you want a small

Gini)• What does it mean when the Chi-square is bigger?

– The variable is better at predicting the outcome (you want a big Chi-square)

• What happens to the p-value as the Chi-square gets bigger?– The p-value gets smaller as the Chi-square gets bigger (you want

a small p-value)

Clustering• What statistics do we care about in

cluster analysis? What do they represent?

• What happens to these statistics as the number of clusters is increased?

• Why do we standardize data? Why do we eliminate outliers?

Clustering• What statistic do we care about in cluster analysis?

What does it represent?– Sum of Squared Errors – SSE (or Root Mean Square Std Dev.) – Within SSE = cohesion, Between SSE = distinctiveness

• What happens to these statistics as the number of clusters is increased?– SEE goes down (both within and between)– More cohesive clusters, less distinct though

• Why do we standardize data? Why do we eliminate outliers?– Standardize else variables with bigger values will have

greater weighting– Elimination outliers because they can skew results

Clustering• What are the pros and cons of having

only a few clusters (compared to having many clusters)?

• What is bad about the below cluster analysis result? How would you improve it?

• What are the pros and cons of having only a few clusters (compared to having many clusters)?– Easier to interpret/analyze, but they may be

less informative• What is bad about the below cluster

analysis result? How would you improve it?– Clusters should be fairly round!– Add more clusters.

Clustering

Association Rules• How would you describe the following association

rule?– {Meat, Dairy} {Vegetables}

• How many items are in this item set?

• What is (are) the antecedents? What are the consequents?

• What are the statistics we care about when evaluating an association rule?

Association Rules• How would you describe the following association rule?– {Meat, Dairy} {Vegetables}– When someone eats meat and dairy they also eat vegetables.

• How many items are in this item set?– This is a 3 item set.

• What is (are) the antecedents? What are the consequents?– Meat and Dairy are the antecedents, vegetables is the

consequent.• What are the statistics we care about when evaluating an

association rule?– Support count, Support Percent, Confidence and Lift

Association Rules• Do the following two rules have to have the

same Confidence? The same Support? The same Lift?– {Meat, Dairy} {Vegetables}– {Vegetables} {Meat, Dairy}

• What does Lift > 1 mean? Would you take action on such a rule?–What about Lift < 1?–What about Lift = 1?

Association Rules• Do the following two rules have to have the same

Confidence (NO) ? The same Support (Yes)? The same Lift (Yes)?– {Meat, Dairy} {Vegetables}– {Vegetables} {Meat, Dairy}

• What does Lift > 1 mean? Would you take action on such a rule?– More co-purchase observed than chance would predict (+

association)– What about Lift < 1? Less than chance predicts (- association)– What about Lift = 1? Chance explains the observed co-purchase

(no apparent association)

Association Rules• What might you do as a manager if

you saw a very high Lift and Confidence for the following rule about product purchase? Why would you do this?– {Pasta} {Orange Juice}

Association Rules• What might you do as a manager if you saw a

very high Lift and Confidence for the following rule about product purchase? Why would you do this?– {Pasta} {Orange Juice}

• Encourage pasta buyers to see OJ (placement)• Get them in and milk ‘em (discount pasta,

premium OJ)• Target market (advertise new OJ to Pasta

customers)

Association Rules• What is the most reliable association

rule below?

Association Rules• What is the most reliable association

rule below?– Rule 2 – Tied for best Lift (3.60), but has

Better confidence!

Data Visualization• Look at In-Class Exercise Answers...