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

Question 1 of 8

Calculator allowed

Treat rainfall as the explanatory variable for stream inflow. Use technology to analyse the displayed bivariate data

stream inflow (ML)	rainfall (mm)
132	61
141	64
158	66
151	68
131	69
135	73
145	74
153	76
161	78
173	81

(a)1 mark

Which variable-role statement matches the prediction direction?

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

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

(b)1 mark

How should the association in the scatterplot be classified?

The scatterplot shows a weak positive linear association

The scatterplot shows a moderate positive linear association

The scatterplot shows a moderate negative linear association

The scatterplot shows a strong positive linear association

Calculate the fitted-line parameters with rainfall entered as x. Give both values to 1 decimal place

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

\(a\) \(b\)

(d)1 mark

How should the fitted slope and its EV = 0 intercept be interpreted? The observed rainfall values are 61–81 mm

For each 1-unit increase in rainfall (mm), predicted stream inflow increases by about 1.4 on the displayed ML scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in rainfall (mm), predicted stream inflow increases by about 1.4 on the displayed ML scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in rainfall (mm), the slope 1.4 proves the association between the two plotted variables is strong; the intercept at EV = 0 is outside the observed range

Across the displayed bivariate data, predicted stream inflow increases by about 1.4 on the displayed ML scale in total; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in stream inflow (ML), predicted rainfall increases by about 0.3 on the displayed mm scale; the intercept at EV = 0 is outside the observed range

(e)1 mark

What response does the fitted line predict for 66 mm of rainfall? Give the answer to 1 decimal place

\widehat{\text{stream inflow}}=\frac{18787}{374}+\frac{515}{374}\bigl(\text{rainfall}\bigr)

stream inflow (ML) Format: 1 d.p.

(f)1 mark

Which statement correctly judges the prediction against the data used to fit the model? The observed rainfall range is 61–81 mm, and the query uses 66 mm

This is interpolation: 66 mm is inside the observed 61–81 mm explanatory range, so the fitted data support the prediction

This is interpolation: the least-squares line returns a value at 66 mm, so the fitted data support the prediction at every explanatory value

This is extrapolation: 66 mm is inside the observed 61–81 mm explanatory range, so the fitted data do not support the prediction

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