Data Transformation Flashcards

Vocabulary flashcards based on lecture notes on data transformation, focusing on univariate data transformation, natural logs, exponential functions, and their applications in business and economics.

Univariate Data Transformation

Data transformation involving a single variable.

Natural Logarithm (ln)

Logarithm to the base e, where e is approximately 2.7182. Used to transform data for easier analysis and quick answers.

Exponential Function

A function of the form e^x, related to the natural logarithm. If y = e^x, then x = ln(y).

Approximation of Natural Log

For small x, ln(1 + x) ≈ x. Used to simplify formulas and obtain quick estimations.

Approximation of Exponential

For small x, e^x ≈ 1 + x. Approximation applicable only for small x values.

Exponential Growth (r > 0)

Growth that increases exponentially over time when the growth rate (r) is positive.

Exponential Decay (r < 0)

Decrease that reduces exponentially over time when the growth rate (r) is negative.

Linearization of Exponential Growth

Applying a log transformation to exponential data to create a linear relationship, making it easier to work with in regressions.

Proportionate Change

Change in a variable divided by its original value, calculated as (x1 - x0) / x0.

Rule of 72

A simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. Approximation = 72 / interest rate (in percent).

Skewness

A measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Logs are used to reduce right skewness in economic data.

Compounding Period

The frequency with which interest is added to an account during the investment period.

Effective Interest Rate (APY)

The actual rate of return on an investment when compounding is taken into account. Calculated as (1 + r/n)^n - 1.

Nominal Interest Rate (APR)

The stated interest rate without considering the effects of compounding.

Standardized Scores (Z-scores)

A measure of how many standard deviations an element is from the mean. Calculated as (observation - sample mean) / sample standard deviation.

Moving Average

The average of data points over a specified period, used to smooth out fluctuations.

Simple Moving Average (SMA)

Average of the current and immediate past observations.

Centered Moving Average

Averages data points where the current observation is in the middle of the range being averaged.

Seasonal Adjustment

A statistical technique to remove the seasonal component of a time series.

Per Capita Data

Data expressed per person, usually calculated by dividing a total by the population size.

Growth Rate

The rate at which a quantity increases or decreases. Commonly converted to annualized rates for comparison.

Percentage Point

The arithmetic difference between two percentages.

Basis Point

One hundredth of one percentage point (0.01%).