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AustraliaVIC
VCE 12 General 2023

3.02 Interpret and make predictions

Interactive practice questions

Consider the following set of data.

The equation of the least squares line fitted to this data is approximately $y=3.15-0.18x$y=3.150.18x.

$x$x $0.8$0.8 $1.77$1.77 $2.7$2.7 $3.62$3.62 $4.9$4.9 $5.7$5.7 $7$7 $8.6$8.6 $10.1$10.1
$y$y $3.4$3.4 $2.9$2.9 $2.5$2.5 $2.4$2.4 $1.9$1.9 $1.9$1.9 $1.8$1.8 $1.7$1.7 $1.54$1.54
a

Predict the value of $y$y when $x=3$x=3 using the least square line.

b

Is this an interpolation or extrapolation?

Interpolation

A

Extrapolation

B
Easy
1min

Consider the following set of data.

The equation of the least squares line fitted to this data is approximately $y=3.15-0.18x$y=3.150.18x.

Easy
< 1min

Consider the following set of data.

The equation of the least squares line fitted to this data is approximately given by $\text{Average test score}=70.34-1.92\times\text{Number of tests}$Average test score=70.341.92×Number of tests.

Easy
1min

A least squares regression line is given by $y=3.59x+6.72$y=3.59x+6.72.

Easy
1min
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Outcomes

U3.AoS1.26

calculate the coefficient of determination, 𝑟^2, and interpret in the context of the association being modelled and use the model to make predictions, being aware of the problem of extrapolation

U3.AoS1.24

determine the equation of the least squares line giving the coefficients correct to a required number of decimal places or significant figures as specified, and distinguish between correlation and causation

U3.AoS1.25

use the least squares line of best fit to model and analyse the linear association between two numerical variables and interpret the model in the context of the association being modelled

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