A full bivariate investigation practice questions | General Mathematics (Year 11, VCE Units 1 & 2, Bivariate data, Pearson's correlation coefficient)

Question 1 of 8

Calculator allowed

The data below are used to explain stream inflow from rainfall. Use technology to complete the investigation

stream inflow (ML)	rainfall (mm)
401	30
439	32
399	34
437	36
463	38
441	40
461	42
439	44

(a)1 mark

Identify the explanatory variable and the response variable

stream inflow is the explanatory variable and rainfall is the response variable

rainfall is the explanatory variable and stream inflow is the response variable

(b)1 mark

Select the statement that correctly gives direction, form and strength

The scatterplot shows a moderate negative linear association

The scatterplot shows a weak positive linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a moderate positive linear association

Use technology to determine a and b for the least-squares line. Give both values to 2 decimal places

Use the form: predicted stream inflow = a + b × rainfall

\(a\) \(b\)

(d)1 mark

Select the contextual meaning of b = 3.14, including whether the intercept is sensible. The observed rainfall values are 30–44 mm

For each 1-unit increase in rainfall (mm), the slope 3.14 proves the association between the two plotted variables is strong; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in rainfall (mm), predicted stream inflow increases by about 3.14 on the displayed ML scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in rainfall (mm), predicted stream inflow increases by about 3.14 on the displayed ML scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in stream inflow (ML), predicted rainfall increases by about 0.13 on the displayed mm scale; the intercept at EV = 0 is outside the observed range

Across the displayed bivariate data, predicted stream inflow increases by about 3.14 on the displayed ML scale in total; the intercept at EV = 0 is outside the observed range

(e)1 mark

Calculate the model prediction at rainfall = 81 mm. Give the answer to 2 decimal places

\widehat{\text{stream inflow}}=\frac{2231}{7}+\frac{22}{7}\bigl(\text{rainfall}\bigr)

stream inflow (ML) Format: 2 d.p.

(f)1 mark

Classify the prediction and select the reason supported by the observed explanatory range. The observed rainfall range is 30–44 mm, and the query uses 81 mm

This is extrapolation: the least-squares line returns a value at 81 mm, so the fitted data support the prediction at every explanatory value

This is extrapolation: the predicted response is outside its plotted range, so the response range decides whether the fitted data support it

This is extrapolation: 81 mm is outside the observed 30–44 mm explanatory range, so the fitted data do not support the prediction

This is interpolation: 81 mm is outside the observed 30–44 mm explanatory range, so the fitted data support the prediction