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Skill map
General Mathematics
Time series
Chapter 5
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RESTS ON
Classify a variable as categorical or numerical
CH 1
Plot a table of values and draw the straight line through the points
FOUNDATIONS
Read coordinates off a graphed line respecting its axis scales
FOUNDATIONS
Order data and locate a value by position
CH 1
Percent as parts per hundred
FOUNDATIONS
Decimal place value
FOUNDATIONS
Percentage of a quantity
CH 9
Express one quantity as a percentage of another
FOUNDATIONS
Signed numbers
FOUNDATIONS
Compute r from a displayed bivariate data set with technology and report it at a stated precision
CH 2
Calculate the standard deviation
CH 1
Write a line's equation from its y-intercept and slope
CH 3
State in context words what a model's intercept and slope mean
CH 3
Use a linear model to predict a response or solve for an explanatory value
CH 3
Time series data and plots
Smoothing with moving means and medians
Smoothing and seasonal indices
Trend models and forecasts
Recognise a sequence of observations recorded in time order as time series data with time as the explanatory variable and the measured quantity as the response variable
Represent a time-indexed data table with time on the horizontal axis, plot each ordered pair and join consecutive observations in time order
Describe the long-term direction as increasing, decreasing or approximately level, allowing for short-term variation and for a change in trend across subintervals
Distinguish calendar-linked repetition within a year from a longer, not necessarily regular cycle, identifying the approximate period only when more than one repetition supports it
Identify a persistent abrupt change in the level, trend or seasonal pattern and locate its change interval
Identify an isolated observation that departs clearly from the surrounding pattern without treating a persistent level change as one outlier
Recognise remaining unsystematic short-term variation after trend, periodic structure, structural change and isolated outliers have been considered
Name the explanatory and response variables from the direction of the question asked
Plot a bivariate data table with the EV on the horizontal axis and the RV on the vertical
Read a scatterplot's case count, axis roles and a point's coordinates
Calculate an odd-term moving mean at its central period or a complete moving-mean series by averaging each consecutive window and placing the result at the window centre
Centre an even-term moving mean by averaging each adjacent pair of preliminary moving means and aligning the result with the intervening original period
Calculate an odd-term moving median by ordering the response values in each consecutive window, retaining the central time coordinate and joining the resulting median points
Calculate the mean
Calculate the median
Select a mean or median smoothing method and a suitable window length for the stated purpose and determine the number and locations of retained smoothed values
Interpret a seasonal index as a typical seasonal level of that index times the average season, including the correct above-average or below-average percentage
Use the facts that seasonal indices average exactly one and sum to the number of seasons to check a set or recover one missing index
Deseasonalise by dividing an actual value by its seasonal index and reseasonalise by multiplying a deseasonalised value by the applicable index
Determine the signed percentage change, or the direction and positive magnitude of change, required to convert an actual value to its deseasonalised value using the multiplier one over the index
Calculate seasonal indices from one or more complete seasonal cycles by finding each cycle mean, forming season-to-cycle-mean ratios and averaging corresponding ratios across cycles without rounding intermediate values
Rounding
Convert a decimal to a percentage
Calculate a percentage change
Substitute known values into a formula and evaluate it correctly
Multiply and divide fractions
Multiplication and division
Map named calendar periods to a consecutive numerical time index and map a future named period back to the correct index without an off-by-one error
For seasonal data, deseasonalise the observations, fit or use a linear trend model with time as the explanatory variable, forecast the required period, reseasonalise with the target period's index and judge the limitations of extending the model
Compute the least squares slope and intercept from summary statistics, and run the relation backwards
Read and interpret a regression equation's slope and intercept in context, flagging a non-sensible intercept
Predict from the model at a stated EV value, classify it as interpolation or extrapolation, and judge reliability