Time Series and Linear Trend Analysis

Vocabulary and key formulas from the lecture on Time-Series Analysis, Linear Trend Analysis, and Least Squares Regression for cost estimation.

Time-series analysis

Involves looking at what has happened in the recent past to help predict what will happen in the near future.

Time-series

A sequence of results over a period of time.

Seasonal Variation (SV)

A regularly repeating pattern over a fixed number of months.

Trend (T)

A long-term movement in a consistent direction.

Three-period moving averages

A calculation involving averaging the sales for three months at a time and then moving down to the next three months to identify the trend.

Extrapolating Trend

Expecting the trend (T) to continue to move in a consistent direction into future periods.

Linear Trend Analysis Equation

$y = a + bx$, where $y$ is the dependent variable, $x$ is the independent variable, and $a$ and $b$ are two parameters.

Regression coefficients

The parameters $a$ and $b$ in the linear regression equation.

Intercept (a)

The parameter in the regression equation representing the value where the line crosses the y-axis; in cost estimation, it equals the approximate fixed cost.

Slope intercept (b)

The parameter in the regression equation representing the slope of the line; in cost estimation, it equals the average variable cost per unit of activity.

Least Squares Regression

A statistical technique that minimizes the squared deviations between the regression line (the expected relation) and actual data points.

Formula for Intercept ($a$)

$$a = \frac{(\sum Y)(\sum X^2) - (\sum X)(\sum XY)}{n(\sum X^2) - (\sum X)^2}$$

Formula for Slope ($b$)

$$b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2}$$

Cost Estimation

A statistical technique used to estimate a linear total cost function for a mixed cost based on past cost data.

Total Fixed Cost Formula ($a$)

$$a = \frac{\sum Y - b\sum X}{n}$$