A full bivariate investigation practice questions | General Mathematics (Year 11, VCE Units 1 & 2, Bivariate data, Scatterplots)

Question 1 of 8

Calculator allowed

Investigate whether rainfall can be used to predict stream inflow. Use technology where required

stream inflow (ML)	rainfall (mm)
290	58
299	61
309	63
318	66
320	68
303	71
319	73
314	76

(a)1 mark

Choose the direction–form–strength description supported by the points

The scatterplot shows a moderate positive linear association

The scatterplot shows a moderate negative linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a weak positive linear association

(b)1 mark

Report the correlation coefficient r produced by technology. Give the answer to 2 decimal places

\(r\) Format: 2 d.p.

Report the regression intercept a and slope b for the stated prediction direction. Give both values to 2 decimal places

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

\(a\) \(b\)

(d)1 mark

Choose the statement that gives a per-unit slope meaning and checks the intercept against the data range. The observed rainfall values are 58–76 mm

For each 1-unit increase in rainfall (mm), the slope 1.17 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 1.17 on the displayed ML scale; the intercept at EV = 0 is outside the observed range

Across the displayed bivariate data, predicted stream inflow increases by about 1.17 on the displayed ML scale in total; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in rainfall (mm), predicted stream inflow increases by about 1.17 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 0.38 on the displayed mm scale; the intercept at EV = 0 is outside the observed range

(e)1 mark

Substitute 83 mm into the exact least-squares model. Give the answer to 2 decimal places

\widehat{\text{stream inflow}}=\frac{461}{2}+\frac{157}{134}\bigl(\text{rainfall}\bigr)

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

(f)1 mark

Compare the queried explanatory value with its observed range and choose the supported verdict. The observed rainfall range is 58–76 mm, and the query uses 83 mm

This is interpolation: 83 mm is outside the observed 58–76 mm explanatory range, so the fitted data support the prediction

This is extrapolation: the least-squares line returns a value at 83 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: 83 mm is outside the observed 58–76 mm explanatory range, so the fitted data do not support the prediction