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STTN Test 3
unit 6-8
| Term | Definition |
|---|---|
| Multivariate dataset | Observations on 2+ variables |
| Bivariate dataset | Paired observations (x, y) |
| Correlation | Linear relationship between 2 variables |
| Correlation coefficient (Pearson's) | r: measures degree of linear relationship between two variables |
| Regression | Determine relationship & forecast values Theoretical: y=alpha+betha(x)+error term Estimated: y-hat= a+b(x) |
| Method of least squares | Line so that vertical distances between points & the line is as small as possible Minimises sum of sqaures of residuals |
| Residual | Difference between y-hat(estimated balue) and y(observed value) |
| Interpolation | INSIDE interval of observed values |
| Extrapolation | OUTSIDE interval of observed values |
| Coefficient of determination | R^2: indicates how well least-squares curve fits Linear: r^2 = R^2 |
| Time series | Observations taken at different points in time with equal durations between points |
| Graphical representation of a time series | Determines presence & scope of changes, general direction of changes & is used to compare |
| General goal of a time series | Determine the influence of factors on a specific magnitude, to better manage influence of other factors. Can also estimate future values |
| Movement components | LICS Long-term trend Irregular variation Cyclic movement Seasonal movement Time series aims to separate & isolate movement components |
| Long-term trend | General tendency or trend caused by factors over a long duration Ex: Population growth, Tech improvements or economic development |
| Irregular variation | Unpredictable & Randomly occurs Ex: Natural disasters or man-made disasters |
| Cyclic movement | Movement on long term around long term trends Ex: Business cycle |
| Seasonal movements | Leads to identical monthly or quarterly patterns of variation Ex: weather, holidays |
| Time series models | Additive(L+I+C+S) & Multiplicative(L*I*C*S) |
| Reasons to study long term trends | Historical patterns can be useful Project future trends Elimination of components out of time series |
| Methods to describe long-term trends | Method of least squares & Method of moving averages |
| Method of least squares | Clear linear relationship Use zero-sum method |
| Zero-sum method | X's sum to 0, so middle year is origin=0, everything above negative, everything below positive |
| Method of moving averages | Artificial time-series where each obs is substituted by average of itself & previous & subsequent obs Pro's: Easier to find suitable curve Con's: Period of time is lost, No explicit math expression |
| Probability | Measure of certainty that a future event will occur Used when obs cannot be predicted with certainty Based on long term relative frequencies P = # times an event occurs/ total tries P(a) = n(a) / n(omega) |
| Sample space | Omega - set of possible outcomes |
| Experiment | Making an obs or taking measurement that leads to collection of outcomes |
| Event | Subset of the sample space |
| Random variable X | Numerical value with each individual outcome of an experiment Continuous: is measured on continuous scale like mass or age |
| Continuous random variable X curve: | Mean: mu Variance: sigma^2 Standard deviation: sigma |
| Normal distribution | Symmetric curve Small standard deviation = high curve Big standard deviation = flat curve Notation: N(mu; sigma^2) Area under curve is 1 |
| Z and X standardisation | Z = (X-mu)/sigma |
| Sample distribution | Probability distribution of a statistic since a stat is a random variable in itself |
| Mean & standard deviation of x-bar | E(x-bar) = mu Variance(x-bar) = sigma^2 / n Standard dev(x-bar) = sigma/sqr root(n) |
| Central Limit Theorem | Distribution of x-bar is normal where n is large Z = (x-bar - mu)/ (sigma/sqr root(n)) |
Created by:
CARA.FAURIE
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