Worked solution
Identify explanatory and response variables
Identify the independent and dependent variables in each source situation:
- Investigate whether increased calcium intake would help prevent osteoporosis.
- Investigate how the concentration of an injected drug in the bloodstream varies with time.
- Investigate the time taken to complete a chemical reaction when different amounts of catalyst are used.
- Record air temperature and altitude at noon on a particular day at eight mountainous locations.
- Tabulate the distances of seven cities from the capital and the corresponding railway fares.
CJC · Lecture · Variable-identification examples
Calcium intake and osteoporosis
Answer
Explanatory: calcium intake. Response: occurrence of osteoporosis.
These two labels are already filled in the printed Student table. The investigation asks whether intake is associated with the occurrence; the variable labels alone do not answer the causal question.
Drug concentration over time
Answer
Explanatory: elapsed time. Response: drug concentration in the bloodstream.
The stated relationship is how concentration varies with time. Use time horizontally and concentration vertically. This completion is authored for the blank source cells.
Catalyst and reaction time
Answer
Explanatory: amount of catalyst. Response: time to complete the reaction.
The catalyst amount is varied and reaction time observed. The source asks for variables, not a numerical rate law; none is invented.
Altitude and temperature
Answer
For modelling temperature against altitude: explanatory altitude, response air temperature.
Both values are observed at the same noon across eight locations. This is an explanatory choice for that modelling question, not a controlled change in altitude or proof that other factors are fixed. The blank source cells have no supplied Teacher answer.
Distance and railway fare
Answer
For estimating fare from distance: explanatory distance from the capital, response railway fare.
Keep each city’s distance paired with its corresponding fare. This conventional modelling direction is an authored completion of the source table; another prediction task could require a different direction.
Common mistakes
An explanatory variable need not be experimentally controlled, and its name does not establish statistical independence.
Solution notes
The first table row is visibly completed in the supplied Student PDF; the other four rows are blank. Their proposed completions and modelling qualifications are authored here. No Teacher lecture copy is in the supplied collection.