Descriptive and Inferential Statistics

Study Notes

Measures of Central Tendency:
- Mean: average value of a dataset
- Median: middle value of a dataset when arranged in order
- Mode: most frequently occurring value in a dataset
Measures of Variability:
- Range: difference between the largest and smallest values
- Variance: average of the squared differences from the mean
- Standard Deviation: square root of the variance

Hypothesis Testing:
- Null Hypothesis (H0): a statement of no difference or effect
- Alternative Hypothesis (H1): a statement of difference or effect
- Test Statistic: a value calculated from the sample data to determine the probability of the null hypothesis
- P-Value: the probability of obtaining the test statistic (or a more extreme value) assuming the null hypothesis is true
Confidence Intervals:
- A range of values within which the true population parameter is likely to lie
- Confidence Level: the probability that the interval contains the true parameter (e.g. 95%)

Types of Plots:
- Histogram: a graph of frequency vs. value for a single variable
- Box Plot: a graph of the five-number summary (min, Q1, median, Q3, max) for a single variable
- Scatter Plot: a graph of two variables to show relationships
Types of Charts:
- Bar Chart: a graph of categorical data with bars representing frequencies or proportions
- Pie Chart: a circular graph showing proportions of a whole

Basic Concepts:
- Experiment: an action or situation that can produce a set of outcomes
- Outcome: a specific result of an experiment
- Event: a set of one or more outcomes of an experiment
Probability Rules:
- The probability of an event is a number between 0 and 1
- The probability of the sample space (all outcomes) is 1
- The probability of the empty set (no outcomes) is 0
- The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection

Simple Linear Regression:
- A model that predicts a continuous outcome variable (y) based on a single predictor variable (x)
- Equation: y = β0 + β1x + ε
- Coefficients: β0 (intercept) and β1 (slope)
Multiple Linear Regression:
- A model that predicts a continuous outcome variable (y) based on multiple predictor variables (x1, x2, ...)
- Equation: y = β0 + β1x1 + β2x2 + … + ε

Null Hypothesis (H0) is a statement of no difference or effect.
Alternative Hypothesis (H1) is a statement of difference or effect.
Test Statistic is a value calculated from the sample data to determine the probability of the null hypothesis.
P-Value is the probability of obtaining the test statistic (or a more extreme value) assuming the null hypothesis is true.
A Confidence Interval is a range of values within which the true population parameter is likely to lie.
Confidence Level is the probability that the interval contains the true parameter (e.g. 95%).

Histogram is a graph of frequency vs. value for a single variable.
Box Plot is a graph of the five-number summary (min, Q1, median, Q3, max) for a single variable.
Scatter Plot is a graph of two variables to show relationships.
Bar Chart is a graph of categorical data with bars representing frequencies or proportions.
Pie Chart is a circular graph showing proportions of a whole.

Experiment is an action or situation that can produce a set of outcomes.
Outcome is a specific result of an experiment.
Event is a set of one or more outcomes of an experiment.
The probability of an event is a number between 0 and 1.
The probability of the sample space (all outcomes) is 1.
The probability of the empty set (no outcomes) is 0.
The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.

Simple Linear Regression is a model that predicts a continuous outcome variable (y) based on a single predictor variable (x).
The equation for Simple Linear Regression is y = β0 + β1x + ε.
β0 is the intercept and β1 is the slope in Simple Linear Regression.
Multiple Linear Regression is a model that predicts a continuous outcome variable (y) based on multiple predictor variables (x1, x2,...).
The equation for Multiple Linear Regression is y = β0 + β1x1 + β2x2 + … + ε.