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

Question 1 of 8

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Investigate whether parcel count can be used to predict processing time. Use technology where required

processing time (min)	parcel count (parcels)
80	33
74	36
46	38
76	41
84	43
114	46
140	48
98	51

(a)1 mark

Which variable-role statement matches the prediction direction?

processing time is the explanatory variable and parcel count is the response variable

parcel count is the explanatory variable and processing time is the response variable

(b)1 mark

How should the association in the scatterplot be classified?

The scatterplot shows a moderate negative linear association

The scatterplot shows a moderate positive linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a weak positive linear association

Calculate the fitted-line parameters with parcel count entered as x. Give both values to 2 decimal places

Use the form: predicted processing time = a + b × parcel count

\(a\) \(b\)

(d)1 mark

How should the fitted slope and its EV = 0 intercept be interpreted? The observed parcel count values are 33–51 parcels

For each 1-unit increase in parcel count (parcels), predicted processing time increases by about 3.13 on the displayed min scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in processing time (min), predicted parcel count increases by about 0.15 on the displayed parcels scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in parcel count (parcels), predicted processing time increases by about 3.13 on the displayed min scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in parcel count (parcels), the slope 3.13 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 processing time increases by about 3.13 on the displayed min scale in total; the intercept at EV = 0 is outside the observed range

(e)1 mark

What response does the fitted line predict for 42 parcels of parcel count? Give the answer to 2 decimal places

\widehat{\text{processing time}}=-\frac{2836}{67}+\frac{419}{134}\bigl(\text{parcel count}\bigr)

processing time (min) Format: 2 d.p.

(f)1 mark

Which statement correctly judges the prediction against the data used to fit the model? The observed parcel count range is 33–51 parcels, and the query uses 42 parcels

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

This is interpolation: the least-squares line returns a value at 42 parcels, so the fitted data support the prediction at every explanatory value

This is interpolation: 42 parcels is inside the observed 33–51 parcels explanatory range, so the fitted data support the prediction

This is extrapolation: 42 parcels is inside the observed 33–51 parcels explanatory range, so the fitted data do not support the prediction