Examples
Now try the example questions below.
Question
The equation of the line of best fit is \(w = 1.5h - 170\)
Use this equation to obtain an estimate for the weight of Louise, who is 156 cm tall.
We substitute \(h = 156\) into the equation.
\(w = 1.5 \times 156 - 170\)
\(w = 234 - 170\)
\(w = 64\)
Therefore Louise weighs approximately 64 kg.
Question
Use the equation of the line of best fit to estimate Jill's score in her science test if she scored 14 in her Maths test.
The general equation for a straight line is \(y = mx + c\).
To determine the equation of a straight line we need to know the In a graph, the gradient is the steepness of the line. The greater the gradient, the greater the rate of change. and the The value of the y-coordinate when a graph crosses the y-axis..
Looking at the scattergraph above, we can see that that the y-intercept is 10.
In order to calculate the gradient, we need to choose 2 points on the line of best fit:
(0, 10) and (8, 14)
\(m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\)
\(= \frac{{14 - 10}}{{8 - 0}}\)
\(= \frac{4}{8} = \frac{1}{2}\)
Therefore the equation of the line of best fit is:
\(y = \frac{1}{2}x + 10\) or \(s = \frac{1}{2}m + 10\) where s = science test and m = maths test.
So when m = 14:
\(s = \frac{1}{2} \times 14 + 10\)
\(s = 7 + 10\)
\(s = 17\)
Therefore it is estimated that Jill scored 17 in her Science Test.