Exam info

Question 1

NUMERICAL VARIABLES

Answer 1

Numerical:
• Continuous (entities get a distinct score), e.g. temperature,
body length.
• Discrete (counts), e.g.: number of defects

Question 2

CATEGORICAL VARIABLES

Answer 2

Categorical (entities are divided into distinct categories):
• Binary variable (two outcomes), e.g. dead or alive.
• Ordinal variable, e.g. bad, intermediate, good.
• Nominal variable (order not important), e.g. whether someone is an omnivore,
vegetarian or vegan

Question 3

HYPOTHESIS TESTING

Answer 3

1. State the null-hypothesis H0 and the alternative Ha
2. Collect evidence (data)
3. Can H0 be maintained, given
   the evidence?
   if p-value <= 0.05 – Reject H0
   if p-value > 0.05 – Do not reject H0
4. At the a% significance level, there is(not) sufficient statistical evidence to infer …

Question 4

Types of Hypothesis errors

Answer 4

1. Type I error (α): Reject H0 when H0 is true – Jury convicts an innocent person.
2. Type II error (β): Do not reject H0 when H0 is false – Jury acquits a guilty person.
3. Correct decision: Reject H0 when H0 is false – Jury convicts a guilty person.
4. Correct decision: Do not reject H0 when H0 is true – Jury acquits an innocent person.

Question 5

Confidence interval

Answer 5

Confidence interval - consists of an interval of numbers produced
by a point estimate, and an associated confidence level specifying the probability that the interval contains the
population parameter.
• Confidence intervals have the general form:
Point Estimate +/- Margin of Error

Question 6

Statistical Inference

Answer 6

Methods for estimating/predicting and testing hypotheses about population
characteristics based on information contained in a sample.

Question 7

Population

Answer 7

A population is collection of all elements of interest for a particular study

Question 8

Parameter

Answer 8

parameter is a characteristic of a population
(e.g., such as the mean number of
customer service calls of all customers).

Question 9

Sample

Answer 9

A sample is a representative subset of the population.

Question 10

Statistic

Answer 10

A statistic is a characteristic of a sample (e.g., mean number of customer
service calls of the 5000 customers in the sample (1.563)).

Question 11

Sample Proportion

Answer 11

The sample proportion p, is the statistic used to measure the unknown value of the population proportion p.

Question 12

Point estimation

Answer 12

Use of a single known value of a statistic to estimate the associated population
parameter.

Question 13

p-value

Answer 13

probability of observing a sample statistic at least as extreme as the statistic actually observed,
if we assume that H0= is true.

Question 14

1-sample t-test

Answer 14

H0: μ = μ0
Can be used for a numerical variable

the test statistics is t from t distribution

Question 15

Test for Proportion

Answer 15

H0: π = π0
Can be used for a categorical variable

the test statistics is Z from standard normal distribution

Question 16

Two-sample t-test

Answer 16

H0: μ1 = μ2
Can be used for a numerical and a binary variable

the test statistics is t from t distribution

Question 17

Two-sample Z-test

Answer 17

H0: π1 = π2
Can be used for two binary variables

the test statistics is Z from standard normal distribution

Question 18

Chi-square test

Answer 18

H0: π1 = π2 = π3
or
H0: π1=ρ1; π2=ρ2; π3=ρ3
Can be used for two Categorical variables (with > 2 categories)

test statistic is χ^2 from chi-square distribution

Question 19

Analysis of Variance (ANOVA)

Answer 19

H0: μ1 = μ2 = μ3
Can be used for a numerical and a categorical ( with > 2 categories) variables.

test statistic is F=MSTR/MSE from F distribution

Question 20

Correlation Test

Answer 20

H0: ρ = 0
Can be used for two numerical variables

the test statistics is t

Question 21

k-Nearest Neighbor Algorithm

Answer 21

The k-Nearest Neighbor algorithm is an instance-based learning where training
set records are first stored. Next, the classification of a new unclassified record
is performed by comparing it to the most similar records in the training set.

Question 22

Consequences of smaller k

Answer 22

• Choosing a small value for k may lead the algorithm to overfit the data.
• Noise or outliers may unduly affect classification.

Question 23

Consequences of larger k

Answer 23

• Larger values will tend to smooth out idiosyncratic or obscure data values in the
training set.
• If k becomes too large, locally interesting values will be overlooked

Question 24

Overfitting

Answer 24

Overfitting occurs when the model tries to fit every possible trend/structure in the
training set.

Question 25

ROC curve

Answer 25

An ROC curve (receiver operating characteristic curve) is a graph showing the performance of a binary classification model at all classification thresholds. The y-axis shows the True Positive Rate, which is the same thing as Sensitivity. The x-axis shows the False Positive Rate, which is the same thing as 1 - Specificity.

Question 26

AUC

Answer 26

The Area Under the Curve (AUC) is often a measure of the quality of the classification models.

Question 27

MSE

Answer 27

Mean Squared Error (MSE) is a measurement of predictive accuracy. Lower MSE means more accurate classification. (POSITIVE VALUES)

Question 28

Decision Tree

Answer 28

Decision Tree - tree shaped algorithm used to determine course of action (each branch represents possible decision)

Question 29

Nodes, root nodes, leaf nodes, decision rule

Answer 29

``` Nodes - test which splits into different categories Root node - node at the top of decision tree Leaf node - each external node in decision tree (a.k.a. category) Decision rule (association rule) - all possible paths in decision tree (IF ... and ... THEN ...) ```

Question 30

Entropy

Answer 30

measure of messiness of data collection.

Question 31

Information gain

Answer 31

decrease obtained in entropy by splitting data set based on some condition.

Question 32

Dangers of extrapolation

Answer 32

``` Extrapolation - estimating or concluding something by assuming that existing trends will continue. 1. Analysts should restrict estimates and predictions to the values within the range of the values of x in dataset. ```

Question 33

Residual standard error

Answer 33

The value of the Residual standard error indicates the size of the “typical” prediction error. It has POSITIVE VALUES in which the lower values could be a sign of better predictions.

Question 34

Confusion Matrix

Answer 34

``` Table that shows number of correct and incorrect predictions made by classification model compared to actual outcomes (target value) in data. True Positive (TP) --- False Positive (FP) False Negative (FN) --- True Negative (TN) ```

Question 35

R-squared statistic r^2

Answer 35

Measures how closely the linear regression fits the data (ranges from 0 to 1) - The model has the R-squared value of 0.7455 which means 75% of the variability of the target variable revenue is explained by our regression model.

Question 36

Four assumptions of linear regression

Answer 36

``` Before implementing a model, the requisite model assumptions must be verified. The assumptions are: Linearity of residuals Independence of residuals Normal distribution of residuals Constant variance of residuals ```

Question 37

Types of tests to validate partition for these types of target variables? 1. Continuous 2. Flag/Binary 3. Multinomial

Answer 37

1. Two-sample t-test for difference in means 2. Two-sample Z-test for difference in proportions 3. Test for homogeneity of proportions