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 waste collected from event attendance. Use technology to complete the investigation

event attendance (hundreds of people)	waste collected (kg)
15	193
17	185
19	225
21	185
23	241
25	201
27	241
29	233

(a)1 mark

Which assignment of explanatory and response variables matches the investigation?

event attendance is the explanatory variable and waste collected is the response variable

waste collected is the explanatory variable and event attendance is the response variable

(b)1 mark

Which complete description matches the plotted association?

The scatterplot shows a weak positive linear association

The scatterplot shows a moderate negative linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a moderate positive linear association

Use technology to calculate Pearson's correlation coefficient r. Give the answer to 2 decimal places

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

(d)1 mark

Which statement correctly interprets the slope 3.24 and the intercept? The observed event attendance values are 15–29 hundreds of people

For each 1-unit increase in event attendance (hundreds of people), predicted waste collected increases by about 3.24 on the displayed kg scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in event attendance (hundreds of people), the slope 3.24 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 event attendance (hundreds of people), predicted waste collected increases by about 3.24 on the displayed kg scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in waste collected (kg), predicted event attendance increases by about 0.13 on the displayed hundreds of people scale; the intercept at EV = 0 is outside the observed range

Across the displayed bivariate data, predicted waste collected increases by about 3.24 on the displayed kg scale in total; the intercept at EV = 0 is outside the observed range

(e)1 mark

Use the exact fitted equation to predict waste collected when event attendance is 24 hundreds of people. Give the answer to 2 decimal places

\widehat{\text{waste collected}}=\frac{2977}{21}+\frac{68}{21}\bigl(\text{event attendance}\bigr)

waste collected (kg) Format: 2 d.p.

(f)1 mark

Is the prediction an interpolation or an extrapolation, and can it be trusted on the basis of the fitted data? The observed event attendance range is 15–29 hundreds of people, and the query uses 24 hundreds of people

This is interpolation: 24 hundreds of people is inside the observed 15–29 hundreds of people explanatory range, so the fitted data support the prediction

This is extrapolation: 24 hundreds of people is inside the observed 15–29 hundreds of people explanatory range, so the fitted data do not support the prediction

This is interpolation: the least-squares line returns a value at 24 hundreds of people, so the fitted data support the prediction at every explanatory value

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