A full bivariate investigation practice questions | General Mathematics (Year 12, VCE Units 3 & 4, Linear regression, Regression analysis)

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)
15	439
18	432
20	441
22	439
23	442
27	446
28	445
30	451
32	446
35	459

(a)1 mark

Which assignment of explanatory and response variables matches the investigation?

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

Which complete description matches the plotted association?

The scatterplot shows a strong positive linear association

The scatterplot shows a weak positive linear association

The scatterplot shows a strong negative 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 1.0 and the intercept? The observed weekly training distance values are 15–35 km

Across the displayed bivariate data, predicted fitness test total increases by about 1.0 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 1.0 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 weekly training distance (km), predicted fitness test total increases by about 1.0 on the displayed points scale; the intercept at EV = 0 is a reliable prediction

For each 1-unit increase in weekly training distance (km), predicted fitness test total increases by about 1.0 on the displayed points scale; 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 0.8 on the displayed km scale; the intercept at EV = 0 is outside the observed range

(e)1 mark

Use the exact fitted equation to predict fitness test total when weekly training distance is 28 km. Give the answer to 1 decimal place

\widehat{\text{fitness test total}}=419+1\bigl(\text{weekly training distance}\bigr)

fitness test total (points) Format: 1 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 weekly training distance range is 15–35 km, and the query uses 28 km

This is interpolation: the least-squares line returns a value at 28 km, so the fitted data support the prediction at every explanatory value

This is interpolation: 28 km is inside the observed 15–35 km explanatory range, so the fitted data support the prediction

This is extrapolation: 28 km is inside the observed 15–35 km 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