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ACMGM058

use a residual plot to assess the appropriateness of fitting a linear model to the data

ACMGM059

interpret the intercept and slope of the fitted line

ACMGM060

use the coefficient of determination to assess the strength of a linear association in terms of the explained variation

ACMGM061

use the equation of a fitted line to make predictions

ACMGM062

distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation

ACMGM063

write up the results of the above analysis in a systematic and concise manner.

ACMGM064

recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them

identify possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner.

ACMGM066

implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables; for example, is there an association between attitude …

ACMGM067

use recursion to generate an arithmetic sequence

ACMGM068

display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations

ACMGM069

deduce a rule for the nth term of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions

ACMGM070

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating …

ACMGM071

use recursion to generate a geometric sequence

ACMGM072

display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations

ACMGM073

deduce a rule for the nth term of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions

ACMGM074

use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment, the growth of a bacterial population that doubles in …

ACMGM075

use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form

ACMGM076

recognise that a sequence generated by a first-order linear recurrence relation can have a long term increasing, decreasing or steady-state solution

ACMGM077

use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems; for example, investigating the growth of a trout population in a lake recorded at the end of each year and where limited recreational …

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