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

Question 1 of 8

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Treat weekly training distance as the explanatory variable for fitness test total. Use technology to analyse the displayed bivariate data

weekly training distance (km)	fitness test total (points)
22	232
25	232
28	240
29	244
31	246
32	244
35	242
38	248

(a)1 mark

Which variable-role statement matches the prediction direction?

fitness test total is the explanatory variable and weekly training distance is the response variable

weekly training distance is the explanatory variable and fitness test total is the response variable

(b)1 mark

How should the association in the scatterplot be classified?

The scatterplot shows a moderate positive linear association

The scatterplot shows a weak positive linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a strong negative linear association

Use a technology regression calculation to find r. Give the answer to 2 decimal places

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

(d)1 mark

How should the fitted slope and its EV = 0 intercept be interpreted? The observed weekly training distance values are 22–38 km

Across the displayed bivariate data, predicted fitness test total increases by about 1.00 on the displayed points scale in total; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in weekly training distance (km), the slope 1.00 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 fitness test total (points), predicted weekly training distance increases by about 0.73 on the displayed km scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in weekly training distance (km), predicted fitness test total increases by about 1.00 on the displayed points scale; the intercept at EV = 0 is outside the observed range

For each 1-unit increase in weekly training distance (km), predicted fitness test total increases by about 1.00 on the displayed points scale; the intercept at EV = 0 is a reliable prediction

(e)1 mark

What response does the fitted line predict for 19 km of weekly training distance? Give the answer to 2 decimal places

\widehat{\text{fitness test total}}=211+1\bigl(\text{weekly training distance}\bigr)

fitness test total (points) Format: 2 d.p.

(f)1 mark

Which statement correctly judges the prediction against the data used to fit the model? The observed weekly training distance range is 22–38 km, and the query uses 19 km

This is extrapolation: the least-squares line returns a value at 19 km, so the fitted data support the prediction at every explanatory value

This is interpolation: 19 km is outside the observed 22–38 km explanatory range, so the fitted data 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: 19 km is outside the observed 22–38 km explanatory range, so the fitted data do not support the prediction