Descriptive and Inferential Statistics in Economics

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 Dispersion:
- 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): statement of no difference or no effect
- Alternative Hypothesis (H1): statement of difference or effect
- Test Statistic: value used to determine whether to reject H0
- P-Value: probability of observing the test statistic assuming H0 is true
Confidence Intervals:
- Estimate of a population parameter using a sample statistic
- Margin of Error: maximum amount by which the sample statistic may differ from the population parameter

Simple Linear Regression:
- Equation: Y = β0 + β1X + ε
- Coefficient of Determination (R²): measures the proportion of variation in Y explained by X
- Slope (β1): change in Y for a one-unit change in X
Multiple Linear Regression:
- Equation: Y = β0 + β1X1 + β2X2 + … + ε
- Coefficient of Determination (R²): measures the proportion of variation in Y explained by multiple independent variables

Components of a Time Series:
- Trend: long-term pattern or direction
- Seasonality: regular fluctuations that occur at fixed intervals
- Irregularity: random, unpredictable fluctuations
Autocorrelation: correlation between a time series and lagged versions of itself
Stationarity: a time series with constant mean and variance over time

Measures of Central Tendency:
- Mean is sensitive to extreme values
- Median is resistant to extreme values
- Mode can be used for categorical data
Measures of Dispersion:
- Range is sensitive to extreme values
- Variance is affected by the unit of measurement
- Standard Deviation is expressed in the same units as the data

Hypothesis Testing:
- Null Hypothesis is a statement of no effect or difference
- Alternative Hypothesis is a statement of effect or difference
- P-Value determines the probability of rejecting the Null Hypothesis
- Type I Error: rejecting the Null Hypothesis when it is true
- Type II Error: failing to reject the Null Hypothesis when it is false
Confidence Intervals:
- Width of the interval depends on the sample size and confidence level
- Margin of Error is proportional to the standard deviation

Simple Linear Regression:
- Slope (β1) measures the change in Y for a one-unit change in X
- Coefficient of Determination (R²) measures the goodness of fit
- Residuals (ε) represent the unexplained variation in Y
Multiple Linear Regression:
- Coefficient of Determination (R²) measures the goodness of fit
- Multiple independent variables can improve the predictive power
- Coefficients of multiple independent variables can be compared

Components of a Time Series:
- Trend can be upwards, downwards, or stationary
- Seasonality can be additive or multiplicative
- Irregularity is unpredictable and random
Autocorrelation:
- Measured by the correlation coefficient (ρ)
- Positive autocorrelation indicates persistence
- Negative autocorrelation indicates reversals
Stationarity:
- Necessary for many time series models and techniques
- Can be achieved through differencing or transformation