F.4. Analytical Models and Simulation

Question 1

What are the four types of data analytics?

Answer 1

• Descriptive analytics
• Diagnostic analytics
• Predictive analytics
• Prescriptive analytics

Question 2

What question does descriptive analytics answer?

Answer 2

What happened?

Question 3

What is the purpose of diagnostic analytics?

Answer 3

To answer the question, ‘Why did it happen?’ by analyzing historical data.

Question 4

What is the focus of predictive analytics?

Answer 4

It focuses on the future using correlative analysis to answer the question, ‘What is likely to happen?”

Question 5

What question does prescriptive analytics answer?

Answer 5

What needs to happen?

Question 6

What is a model in data analytics?

Answer 6

A representation of a relationship between variables in data.

Question 7

What is statistical modeling?

Answer 7

The process of using statistical analysis on a dataset, usually a sample drawn from a population, to identify patterns and infer something about the population.

Question 8

What is linear regression analysis used for?

Answer 8

To develop a mathematical equation modeling the extent to which one variable (called the dependent or response variable) has historically been affected by one or more other variables (called the independent or predictor variables).

Question 9

What is a time series?

Answer 9

A sequence of measurements of the same variable taken at equally spaced, ordered points in time.

Question 10

What are the four patterns in time series analysis?

Answer 10

• Trend pattern
• Cyclical pattern
• Seasonal pattern
• Irregular pattern

Question 11

What is a trend pattern in time series analysis?

Answer 11

The historical data exhibits a gradual shifting to a higher or lower level over time, useful for making predictions.

Question 12

What is a cyclical pattern in time series analysis?

Answer 12

A cyclical pattern exhibits fluctuations that last longer than one year, often due to the cyclical nature of the economy.

Question 13

What is a seasonal pattern in time series analysis?

Answer 13

Variability in a time series within a period such as a year due to seasonal influences, identified by regularly spaced peaks and troughs.

Question 14

What is an irregular pattern in a time series?

Answer 14

Random variations not repeating in any regular pattern, caused by short-term, non-recurring factors.

Question 15

What is the equation of a simple linear regression line?

Answer 15

ŷ = a + bx

Question 16

What does the “a” represent in the linear regression equation
ŷ = a + bx?

Answer 16

The constant coefficient, or the y-intercept.

Question 17

What does the “b” represent in the linear regression equation
ŷ = a + bx?

Answer 17

The variable coefficient, or the slope of the line.

The slope of the line is the amount of change in the predicted value of the dependent variable for each unit of increase in the independent variable.

Question 18

What is the purpose of the regression line in time series analysis?

Answer 18

To make forecasts using historical data.

Question 19

What is the purpose of linear regression analysis?

Answer 19

To calculate the location of the regression line mathematically and predict the value of y for any given value of x if the independent variable serves well as the predictor variable.

Linear regression minimizes the sum or mean of the squares of the residuals using the least squares method.

Question 20

What must be determined before using linear regression analysis to develop a prediction?

Answer 20

Whether the dependent variable, y, has a linear relationship with the independent variable, x.

A scatterplot can be used to determine if a linear relationship exists between the variables.

Question 21

What is correlation analysis used for in simple linear regression analysis?

Answer 21

To understand the relationship or absence of a relationship between the independent variable and the dependent variable and to determine the strength of the linear relationship between the two variables.

Question 22

What does a positive correlation coefficient indicate about a regression?

Answer 22

Increasing measurements of the independent x-variable tend to be associated with increasing measurements of the dependent y-variable; and decreasing measurements of x tend to be associated with decreasing measurements of y.

Question 23

What does a negative correlation coefficient indicate about a regression?

Answer 23

Increasing measurements of the independent x-variable tend to be associated with decreasing measurements of the dependent y-variable and vice versa.

Question 24

What is the correlation coefficient (r) in simple linear regression and what does it measure?

Answer 24

A number between −1 and +1 that measures the strength and direction of the relationship between the independent and dependent variables.

A number close to either +1 or −1 means the two variables are correlated, and if there is a cause-and-effect relationship, a simple linear regression could be useful for forecasting.

A correlation coefficient of +1 indicates a perfectly positive linear relationship, while −1 indicates a perfectly negative linear relationship.

Question 25

What does the coefficient of determination (r²) of a regression analysis represent?

Answer 25

The percentage of the total variation in the dependent variable (y) that can be explained by variations in the independent variable (x).

Question 26

What does a high coefficient of determination (r²) indicate?

Answer 26

The coefficient of determination is a number between 1 and 0. The closer the coefficient is to 1, the greater is the percentage of variation in the dependent variable that is explained by variations in the independent variable. When the coefficient of determination is high (near 1), the data points lie close to the regression line, indicating better predictive ability of the regression.

Question 27

What is the standard error of the estimate (SEE) of a regression analysis?

Answer 27

A measure of the average distance of the actual observed data points from the regression line, indicating how well the regression model explains the relationship between the independent variable and the dependent variable and thus its predictive ability.

Question 28

What does the standard error of the estimate (SEE) measure for a linear regression of a time series, when the actual observed values of y constitute the whole population?

Answer 28

The standard error of the estimate (SEE) for a linear regression of a time series, when the actual observed values of y constitute the whole population, is a measure of the average distance of the actual observed data points from the regression line. It gives an indication of how well the regression model explains the relationship between the independent variable and the dependent variable and thus its predictive ability.

Question 29

What is the standard form of the simple linear regression equation when the correlation is positive?

Answer 29

ŷ = a + bx ## Footnote The constant coefficient "a" represents the y-intercept, and "b" represents the slope of the regression line.

Question 30

What is multiple regression analysis used for?

Answer 30

To forecast a dependent variable by using more than one independent variable, usually for causal forecasting. ## Footnote To use causal forecasting, there must be a reasonable basis to assume a cause-and-effect relationship between the independent variables and the dependent variable.

Question 31

What is the purpose of the coefficient of determination, R², in multiple regression analysis?

Answer 31

To evaluate the reliability of the whole regression, including all the independent variables used. ## Footnote The higher the R², the better the model explains the relationships between the variables.

Question 32

What does a confidence interval describe in regression analysis?

Answer 32

A confidence interval describes the amount of uncertainty in an estimate derived from sample data. It consists of a range of values, calculated from the sample, within which the true population parameter is expected to fall with a specified probability (the confidence level). ## Footnote A 95% confidence level means that if the same sampling procedure were repeated many times, approximately 95% of the confidence intervals constructed from those samples would contain the true population parameter.

Question 33

What is logistic regression used for?

Answer 33

To make a prediction when the need is to make a yes or no prediction, called a binary outcome. ## Footnote Logistic regression is used to predict the probability of a binary (yes or no) event occurring based on various identified factors. That probability can then be used to classify outcomes (for example, by deciding that probabilities above 50% are classified as “yes”).

Question 34

What is the term "goodness of fit" used to describe?

Answer 34

It indicates how well a model fits the sample data and explains the relationship between the variables. ## Footnote While a model with good fit to the sample data may be useful for prediction, goodness of fit alone does not guarantee the model will generalize well to predict future values.

Question 35

What is underfitting in the context of fitting an analytic model to data?

Answer 35

Underfitting occurs when the model is too simple to capture the true patterns in the data. The model does not represent the actual relationships, and it does not work well on either training data or test data.

Question 36

What is overfitting in the context of fitting an analytic model to data?

Answer 36

Overfitting means the model shows high goodness of fit on training data but low goodness of fit on test data. The model has learned not only the features of the historical data used for training the model, but it has also learned the random fluctuations, or “noise,” within the data. ## Footnote Overfitting can also occur if a model is too complex, such as a multiple regression that contains too many predictor variables.

Question 37

What are the benefits of regression analysis?

Answer 37

* Objective * Provides specific results from a given data set * A tool for drawing insights, making recommendations, and decision-making

Question 38

What are the limitations of regression analysis?

Answer 38

* Requires historical data * Historical data may not be valid for making predictions if conditions have changed * Results depend on the choice of predictor variables * Statistical relationships may be valid only for the range of data in the sample

Question 39

What is sensitivity analysis used for?

Answer 39

To determine how much the prediction of a model will change if one input to the model is changed. ## Footnote Sensitivity analysis is known as 'what-if' analysis and helps identify the most important input parameters for achieving accurate predictions.

Question 40

What is Monte Carlo simulation analysis?

Answer 40

A method used to find solutions to mathematical problems involving changes to multiple variables at the same time using repeated random sampling. It can develop probabilities of various scenarios coming to pass that can be used to compute a predicted result.

Question 41

How can data analytics improve data quality?

Answer 41

The process of cleaning the data preparatory to processing it can detect errors, duplicate information, and missing values. If the errors and duplicate information can be corrected and the missing values supplied, the data quality can be improved.

Question 42

What is a benefit of data analytics in terms of fraud prevention?

Answer 42

Data analytics can help reduce fraud losses by recognizing potentially fraudulent transactions and flagging them for investigation.

Question 43

# True or False: When two variables are correlated, one variable must have caused the other.

Answer 43

False ## Footnote Correlation does not prove causation, and both variables could be caused by a third, unidentified factor.

Question 44

What are two risks associated with using Big Data?

Answer 44

* Data breaches * Customer privacy issues

Question 45

What is a potential drawback of using easy-to-use data analytics tools?

Answer 45

Use by those without a background in data science can lead to data inconsistency and poor decisions.