Stats for Data Science

Question 1

Descriptive Analytics

Answer 1

Leveraging historical data to determine “What” happened.

Question 2

Predictive Analytics

Answer 2

Leveraging historical data to determine “What will” happen.

Question 3

Prescriptive Analytics

Answer 3

Based on information gained from predictive analytics, the information is used to determine “What will we do”.

Question 4

Probability

Answer 4

The measure of the likelihood that an event will occur based on a random experiment.

Question 5

Complement

Answer 5

P(A) + P(A’) = 1

Question 6

Intersection

Answer 6

P(A∩B)=P(A)P(B) Set off all elements that are members of both A and B.

Question 7

Union

Answer 7

P(A∪B)=P(A)+P(B)−P(A∩B) Set of all elements in the collection.

Question 8

Conditional Probability

Answer 8

P(A|B) is a measure of the probability of one event occurring with some relationship to one or more other events.

Question 9

Independent Events

Answer 9

Two events are independent if the occurrence of one does not affect the probability of occurrence of the other.

Question 10

Mutually Exclusive Events

Answer 10

Two events are mutually exclusive if they cannot both occur at the same time.

Question 11

Bates’ Theorem

Answer 11

Bayes’ Theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event.

Question 12

Mean

Answer 12

The average of the dataset.

Question 13

Median

Answer 13

The middle value of an ordered dataset.

Question 14

Mode

Answer 14

The most frequent value in the dataset.

Question 15

Skewness

Answer 15

A measure of symmetry.

Question 16

Kurtosis

Answer 16

A measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution

Question 17

Range

Answer 17

The difference between the highest and lowest value in the dataset.

Question 18

Interquartile Range

Answer 18

IQR = Q3−Q1

Question 19

Variance

Answer 19

The average squared difference of the values from the mean to measure how spread out a set of data is relative to mean.

Question 20

Standard Deviation

Answer 20

The standard difference between each data point and the mean and the square root of variance.

Question 21

Standard Error

Answer 21

An estimate of the standard deviation of the sampling distribution.

Question 22

Causality

Answer 22

Relationship between two events where one event is affected by the other.

Question 23

Covariance

Answer 23

A quantitative measure of the joint variability between two or more variables.

Question 24

Correlation

Answer 24

Measure the relationship between two variables and ranges from -1 to 1, the normalized version of covariance.

Question 25

Probability Mass Function

Answer 25

A function that gives the probability that a discrete random variable is exactly equal to some value.

Question 26

Probability Density Function

Answer 26

A function for continuous data where the value at any given sample can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

Question 27

Cumulative Density Function

Answer 27

A function that gives the probability that a random variable is less than or equal to a certain value.

Question 28

Uniform Distribution

Answer 28

Also called a rectangular distribution, is a probability distribution where all outcomes are equally likely.

Question 29

Normal/Gaussian Distribution

Answer 29

The curve of the distribution is bell-shaped and symmetrical and is related to the Central Limit Theorem that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger.

Question 30

Central Limit Theorem

Answer 30

the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger.

Question 31

Exponential Distribution

Answer 31

A probability distribution of the time between the events in a Poisson point process.

Question 32

Chi-Squared Distribution

Answer 32

The distribution of the sum of squared standard normal deviates.

Question 33

Bernoulli Distribution

Answer 33

The distribution of a random variable which takes a single trial and only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1-p).

Question 34

Binomial Distribution

Answer 34

The distribution of the number of successes in a sequence of n independent experiments, and each with only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1-p).

Question 35

Poisson Distribution

Answer 35

The distribution that expresses the probability of a given number of events k occurring in a fixed interval of time if these events occur with a known constant average rate λ and independently of the time.

Question 36

Null Hypothesis

Answer 36

A general statement that there is no relationship between two measured phenomena or no association among groups.

Question 37

Alternative Hypothesis

Answer 37

Contrary to the null hypothesis.

Question 38

Type 1 Error

Answer 38

rejection of a true null hypothesis.

Question 39

Type 2 Error

Answer 39

the non-rejection of a false null hypothesis.

Question 40

P-Value

Answer 40

When p-value > α, we fail to reject the null hypothesis, while p-value ≤ α, we reject the null hypothesis and we can conclude that we have the significant result.

Question 41

Critical Value

Answer 41

A point on the scale of the test statistic beyond which we reject the null hypothesis, and, is derived from the level of significance α of the test.

Question 42

Significance Level & Rejection Region

Answer 42

The rejection region is actually depended on the significance level. The significance level is denoted by α and is the probability of rejecting the null hypothesis if it is true.

Question 43

Z-Score

Answer 43

finds the distance from the sample’s mean to an individual data point expressed in units of standard deviation. (Large sample size)

Question 44

T - Score

Answer 44

A T-test is the statistical test if the population variance is unknown and the sample size is not large (n < 30).

Question 45

Paired Sample

Answer 45

means that we collect data twice from the same group, person, item or thing.

Question 46

Independent Sample

Answer 46

implies that the two samples must have come from two completely different populations.

Question 47

1 -Way ANOVA

Answer 47

compare two means from tow independent group using only one independent variable.

Question 48

2 -Way ANOVA

Answer 48

is the extension of one-way ANOVA using two independent variables to calculate main effect and interaction effect.

Question 49

Chi -Square Goodness of Fit Test

Answer 49

determine if a sample matches the population fit one categorical variable to a distribution.

Question 50

Chi -Square Test for Independence

Answer 50

compare two sets of data to see if there is a relationship.

Question 51

Linear Regression

Answer 51

is a linear approach to modeling the relationship between a dependent variable and one independent variable.

Question 52

Independent Variable

Answer 52

is the variable that is controlled in a scientific experiment to test the effects on the dependent variable.

Question 53

Dependent Variable

Answer 53

is the variable being measured in a scientific experiment.

Question 54

Multiple Linear Regression

Answer 54

is a linear approach to modeling the relationship between a dependent variable and two or more independent variables.

Question 55

Linear Regression: Step#1

Answer 55

Understand the model description, causality and directionality

Question 56

Linear Regression: Step#2

Answer 56

Check the data, categorical data, missing data and outliers

Question 57

Linear Regression: Step#3

Answer 57

Simple Analysis — Check the effect comparing between dependent variable to independent variable and independent variable to independent variable

Question 58

Linear Regression: Step#4

Answer 58

Multiple Linear Regression — Check the model and the correct variables

Question 59

Linear Regression: Step#5

Answer 59

Residual Analysis: Check normal distribution and normality for the residuals.

Question 60

Linear Regression: Step#5

Answer 60

Interpretation of Regression Output: R-Squared is a statistical measure of fit that indicates how much variation of a dependent variable is explained by the independent variables. Higher R-Squared value represents smaller differences between the observed data and fitted values.

• P - Value
• Regression Equation