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

Question 1 of 8

Calculator allowed

The data below are used to explain fitness test total from weekly training distance. Use technology to complete the investigation

fitness test total (points)	weekly training distance (km)
274	68
298	71
278	74
294	75
302	77
294	78
338	81
338	84

(a)1 mark

Select the correct EV and RV assignment for these data

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

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

(b)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 strong negative linear association

Report the correlation coefficient r produced by technology. Give the answer to 2 decimal places

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

(d)2 marks

Report the regression intercept a and slope b for the stated prediction direction. Give both values to 2 decimal places

Use the form: predicted fitness test total = a + b × weekly training distance

\(a\) \(b\)

(e)1 mark

Substitute 79 km into the exact least-squares model. Give the answer to 2 decimal places

\widehat{\text{fitness test total}}=-2+4\bigl(\text{weekly training distance}\bigr)

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

(f)1 mark

Compare the queried explanatory value with its observed range and choose the supported verdict. The observed weekly training distance range is 68–84 km, and the query uses 79 km

This is extrapolation: 79 km is inside the observed 68–84 km explanatory range, so the fitted data do not support the prediction

This is interpolation: the least-squares line returns a value at 79 km, so the fitted data support the prediction at every explanatory value

This is interpolation: 79 km is inside the observed 68–84 km explanatory range, so the fitted data 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