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

Question 1 of 8

Calculator allowed

Treat event attendance as the explanatory variable for waste collected. Use technology to analyse the displayed bivariate data

event attendance (hundreds of people)	waste collected (kg)
24	444
27	438
29	422
31	412
32	446
36	450
37	478
39	474
41	512
44	464

(a)1 mark

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

The scatterplot shows a strong positive linear association

The scatterplot shows a moderate positive linear association

The scatterplot shows a weak positive linear association

The scatterplot shows a moderate negative 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 1 decimal place

Use the form: predicted waste collected = a + b × event attendance

\(a\) \(b\)

(d)1 mark

Choose the statement that gives a per-unit slope meaning and checks the intercept against the data range. The observed event attendance values are 24–44 hundreds of people

For each 1-unit increase in event attendance (hundreds of people), predicted waste collected increases by about 3.2 on the displayed kg scale; the intercept at EV = 0 is outside the observed range

Across the displayed bivariate data, predicted waste collected increases by about 3.2 on the displayed kg scale in total; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in event attendance (hundreds of people), predicted waste collected increases by about 3.2 on the displayed kg scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in waste collected (kg), predicted event attendance increases by about 0.2 on the displayed hundreds of people scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in event attendance (hundreds of people), the slope 3.2 proves the association between the two plotted variables is strong; the intercept at EV = 0 is outside the observed range

(e)1 mark

Substitute 10 hundreds of people into the exact least-squares model. Give the answer to 1 decimal place

\widehat{\text{waste collected}}=\frac{3810}{11}+\frac{592}{187}\bigl(\text{event attendance}\bigr)

waste collected (kg) Format: 1 d.p.

(f)1 mark

Compare the queried explanatory value with its observed range and choose the supported verdict. The observed event attendance range is 24–44 hundreds of people, and the query uses 10 hundreds of people

This is interpolation: 10 hundreds of people is outside the observed 24–44 hundreds of people explanatory range, so the fitted data support the prediction

This is extrapolation: 10 hundreds of people is outside the observed 24–44 hundreds of people explanatory range, so the fitted data do not support the prediction

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: the least-squares line returns a value at 10 hundreds of people, so the fitted data support the prediction at every explanatory value