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

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)
224	70
225	72
231	74
237	77
239	78
241	80
241	81
241	84
239	86
242	88

(a)1 mark

Which assignment of explanatory and response variables matches the investigation?

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

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)2 marks

Find the least-squares intercept a and slope b for predicting fitness test total. Give both values to 1 decimal place

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

\(a\) \(b\)

(e)1 mark

Use the exact fitted equation to predict fitness test total when weekly training distance is 44 km. Give the answer to 1 decimal place

\widehat{\text{fitness test total}}=157+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 70–88 km, and the query uses 44 km

This is extrapolation: the least-squares line returns a value at 44 km, so the fitted data support the prediction at every explanatory value

This is interpolation: 44 km is outside the observed 70–88 km explanatory range, so the fitted data support the prediction

This is extrapolation: 44 km is outside the observed 70–88 km explanatory range, so the fitted data do not 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