Coaching Centre
Lines of best fit
Drawing a line of best fit by eye, finding its equation, using it to make predictions, interpolation and extrapolation, and linear regression with technology.
Line of best fit
Draw a line that follows the trend with about as many points above as below. Technology finds the least-squares regression line exactly.
Adjust m and c until the line passes through the middle of the points.
A line of best fit is $y = 2.5x + 10$, where $x$ is hours of practice and $y$ is score. Predict the score for $8$ hours.
$y = 2.5x + 10$. Predict $y$ when $x = 8$.
$20 + 10$.
The data covers $x = 1$ to $8$. Predicting at $x = 20$ is:
Outside the range.
For $y = 2.5x + 10$, how much does $y$ increase per extra hour?
The gradient.
For $y = 2.5x + 10$, what $x$ gives $y = 20$?
$2.5x = 10$.
A line of best fit passes through $(2, 7)$ and $(6, 15)$. Gradient?
$8 \div 4$.
Same line: $y$-intercept?
$7 = 2(2) + c$.
Which prediction is most reliable?
Inside the range, with points close to the line.
Using $y = -5x + 120$ ($x$ = age of car in years, $y$ = value in thousands), predict the value of a $10$-year-old car in thousands.
$-50 + 120$.
New numbers every time. Keep going until you get five in a row.