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

Question 1 of 8

Calculator allowed

Treat event attendance as the explanatory variable for waste collected. Use technology where required to analyse the fitted model, its residuals and its limitations

waste collected (kg)	event attendance (hundreds of people)
311	11
307	13
321	15
336	18
331	19
327	21
322	22
337	25
345	27
323	29

(a)1 mark

Select the statement that correctly gives direction, form and strength

The scatterplot shows a moderate negative linear association

The scatterplot shows a strong positive linear association

The scatterplot shows a moderate positive linear association

The scatterplot shows a weak positive linear association

(b)1 mark

Determine Pearson's r for the displayed data using technology. Give the answer to 2 decimal places

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

Use technology to determine a and b for the least-squares line. Give both values to 1 decimal place

Use the form: predicted waste collected = a + b × event attendance

\(a\) \(b\)

(d)1 mark

What percentage of the variation in waste collected is explained by event attendance through this fitted linear model? Give the answer to 1 decimal place

\(r^2\) (%) Format: 1 d.p.

(e)1 mark

Use the residual pattern to assess whether a linear model is appropriate

The response values should be on the horizontal axis instead of the explanatory values, so this residual plot cannot assess the linear model

The residuals include both positive and negative values, so they cancel and show that the fitted line predicts every response exactly

The residuals do not all lie exactly on the zero line, so the residual evidence always rules out the use of a linear model

The residuals are irregularly scattered on both sides of zero, so the residual evidence supports the use of a linear model

(f)1 mark

Select the regression summary that keeps the variable roles, model evidence and limitations consistent

The observed event attendance range is 11–29 hundreds of people, and the report considers an explanatory value of 18 on the hundreds of people scale

event attendance is used to predict waste collected; 44.7% of variation in waste collected is explained through the fitted linear model, the irregular residual scatter supports the linear model, and the queried value is an interpolation supported by the observed explanatory range. This observational analysis does not establish causation

event attendance is used to predict waste collected; 44.7% of variation in waste collected is explained through the fitted linear model, the irregular residual scatter supports the linear model, but the model is then used at every explanatory value without checking the observed range. This observational analysis does not establish causation

event attendance is used to predict waste collected; 44.7% explained variation is treated as enough by itself to prove the fitted linear model is appropriate even when residual evidence conflicts, and the queried value is treated as supported at every explanatory value. This observational analysis does not establish causation

event attendance is used to predict waste collected; 44.7% of variation in waste collected is explained through the fitted linear model, the irregular residual scatter supports the linear model, and the queried value is an interpolation supported by the observed explanatory range. Therefore changing event attendance causes waste collected to change

waste collected is used to predict event attendance; 44.7% of variation in event attendance is explained through the fitted linear model, the irregular residual scatter supports the linear model, and the queried value is an interpolation supported by the observed explanatory range. This observational analysis does not establish causation