Quantitative data analysis

Question 1

What is statistics and what are two types?

Answer 1

The science of collecting and analyzing data for drawing conclusions and making decisions
1. Descriptive statistics
2. Inferential statistics

Question 2

What is descriptive statistics?

Answer 2

It is a method of organizing, summarizing and presenting data in a convenient and informative way
- For example through graphs or numbers

Question 3

What is inferential statistics?

Answer 3

• A branch of statistics that allows us to make predictions, estimates or generalizations about a popluation about a sample
• Statistical inference is the process where we can acquire information about populations

Question 4

What is the difference between probability and statistics?

Answer 4

Probability is deductive, meaning given the information in a box, you can figure out what is in your hand

Statistics is inductive, meaning given the information in your hand, you can figure out what is in a box

Question 5

Qualitative (categorical) data representation vs quantitative data representation

Answer 5

Qualitative data representation means data is grouped into non-numerical and descriptive categories, and is then used to compare categories or proportions. Ex: Car colors

Quantitative data representation involves data that includes numbers and measurable quantities, and is used to analyze distributions, patterns or correlations. Ex: Car speeds

Question 6

Common tools for qualitative data representation

Answer 6

• Summary table
• Bar chart
• Pie chart
• Pareto diagram (innehåller både staplar och linjer)

Question 7

Common tools for quantitative data representation

Answer 7

• Scatter plot
• Histogram

Question 8

What are three good practices when presenting data?

Answer 8

1. Clearly labeled with title, labeled variables and specified units
2. Source of data is identified
3. Data have a date

Question 9

What are 10 good practices when visualizing data?

Answer 9

1. Identify target audience
2. Make sure the data is clean
3. Select the right chart
4. Label the chart effectively
5. Emphasize the important points
6. Choose the best dashboard
7. Format your chart for accessability
8. Make use of color
9. Ensure data is readable in all formats
10. Accept feedback

Question 10

What are two key concepts in numerical representation of data?

Answer 10

1. Measure of location: Describe where the data is centered or positioned, key measures to do this are mean, median, mode and quartiles
2. Measure of variability and dispersion: Describe how spread out or dispersed the data is around the center, key measures to do this are range, variance, standard deviation, coefficient of variation and box plots

Question 11

What are box plots and why are they useful?

Answer 11

Shows the median, quartiles and outliers (important!)
- A graphical representation of dispersion, skewness, outliers and other prominent features in data using quartiles

They are useful because if the median is closer to the bottom or top of the box, it suggests skewness

Question 12

How do you compare boxplots?

Answer 12

1. Median: Compare the position of the median lines, higher median = higher central tendency (determine how typical values (medians) differ between datasets)
2. IQR (box length): Compare the size of the boxet, longer box = greater variability in the middle 50% of data (more numbers to include –> bigger box)
3. Whiskers: Compare length of whiskers, longer whiskers = greater spread in tails (more numbers in data –> longer whiskers)
4. Outliers: Compare number and position of outliers, more outliers = presence of extreme values

Question 13

How to construct boxplots

Answer 13

1. Organize the n observations in the data set from smallest to largest
2. Separate the smallest half and the largest half
3. Find the lower fourth (median of smaller data-half )
4. Find the highest fourth (median of larger data-helg)
5. Find the fourth spread fs = upper fourth - lower fourth, outliers are >=1.5fs, extreme outliers are >=3fs

Question 14

What are main concepts in inferential statistics?

Answer 14

• Sampling: Taking a subset (sample) of a population to estimate the characteristics of the whole population
• Estimation: Using sample data to estimate population parameters like mean, proportion, etc
• Hypothesis testing: Testing assumptions (hypotheses) about a population using sample data
• Confidence intervals: A range of values used to estimate the true value of a population parameter with a given level of confidence (e.g. 95%)

Question 15

What is a sample?

Answer 15

An observed subset of a population

Question 16

What does statistical inference include?

Answer 16

• Estimation: Determine the value of a population based on sample statistics
• Hypothesis testing: To determine whether there is enough statistical evidence in favor of a certain belief about a parameter

Question 17

What does 95% confidence level mean?

Answer 17

If we repeat the sampling process many times, 95% of the intervals would contain the true mean

Question 18

What is the purpose of hypothesis testing and how do you formulate a hypothesis?

Answer 18

The purpose is to determine whether there is enough statistical evidence in favor of a certain belief about a parameter.

Method
- A null hypothesis, H0, is formulated and is assumed to be true
- The alternative hypothesis, Ha, is a claim contrary to H0
- The possible conclusions from hypothesis-testing analysis is then to REJECT H0 (if there is enough statistical evidence that it is not true) or FAIL TO REJECT H0 (if there is not enough statistical evidence to draw the conclusion that H0 is not true)

Question 19

What are two concepts of modeling analysis?

Answer 19

1. Linear regression/regression analysis
2. Machine learning

Question 20

Describe the steps in model development and two types of models

Answer 20

1. Specification
2. Estimation
3. Validation
4. Application

Two types
1. Linear (positive or negative linear relationship)
2. Non-linear

Question 21

Regression analysis

Answer 21

A simple method of supervised learning that models causality and provides prediction
- Explains the effect of the independent variable X on the dependent variable Y

Linear regression is a type of regression analysis and has a deterministic and probabilistic component.
- Assumes that the dependence of Y on X is linear

Question 22

What three aspects are estimating the coefficients in linear regression determined by?

Answer 22

1. Drawing a sample from population of interest
2. Calculating sample statistics
3. Producing a line that cuts into the data

Question 23

Error term assumptions in regression models

Answer 23

For a valid model, some assumptions on error terms must be fulfilled
- Independent Identically Distributed (IID): Errors are independent from each other and have the same distribution across all observations
- Normally distributed (N): Errors follow a normal distribution with mean 0 and constant variance

Question 24

What are key considerations for variable selection in regression models?

Answer 24

Explanatory power: Variables should significantly explain the variation in the dependent variable
- Can be assessed using measures like R2 (coefficient of determination, more explanatory power if R2 is higher) or hypothesis test on coefficients

Explanatory power includes
- Causality: Causal relationship between independent and dependent variable
- Model performance: Evaluate models fit and accuracy using adjusted R2, residual analysis or other performance metrics

Question 25

Describe independence/no multicollineraity

Answer 25

It means that independent variables should not be highly correlated with each other

Question 26

What is important to remember with sample data and outliers?

Answer 26

Data need to be sufficient in size, be representative and free of bias

Larger samples are likely to lead to better estimates, but data collection is expensive. This means you should collect as much data as needed to provide the required level of statistical confidence.

It is also important to identify and handle outliers in sample data, for example using diagnostics like residual plots or boxplots

Question 27

What is the regression model building procedure?

Answer 27

1. Theoretical analysis -> Hypothesized model specification: Form a theory or hypothesis about variable relationship to understand them better
2. Initial examination prior to model building: Explore and prepare data before building regression model, select a sample and check for outliers, linearity and multicollinearity
3. Model building with regression equation: Specify regression model, estimate coefficients, look at t-value, assess model fit ex with R2, test IID assumptions on error terms
4. Make predictions: Within range of data it was trained on

Question 28

What are the four types of machine learning?

Answer 28

• Supervised learning, learns from labeled data
• Semi-supervised learning, learns from labeled and unlabeled data
• Unsupervised learning
• Reinforcement learning, learns through interactions with environment

Question 29

What are three types of machine learning models?

Answer 29

1. Conventional machine learning (ex linear regression)
2. Neural networks
3. Deep neural networks
   3.1 Neutral network structure with feature extraction layer or classification/regression layer
   3.2 Applications for text, image and video