Fitting a linear model
What this lesson covers
- The line is y = a + bx.
- The slope gives the change in y per unit of x.
- The line goes through the mean of x and the mean of y.
A small data set
- Five students from a made-up class.
| Hours studied, x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Test mark, y | 52 | 55 | 61 | 64 | 68 |
Finding the line
- Calculators do this, but the working shows where it comes from.
- mean x = 3, mean y = 60
- sum of (x − 3)(y − 60) = 41
- sum of (x − 3)² = 10
- b = 41 ÷ 10 = 4.1
- a = 60 − 4.1 × 3 = 47.7
- y = 47.7 + 4.1x
Reading the slope
- Write it in context.
- Each extra hour is linked to about 4.1 more marks
Common mistakes
- Swapping x and y.x is the explanatory variable.
- Saying each hour causes 4.1 marks.Say it is linked to, on average.
Your turn
- 1. For y = 12 + 3.5x, what does the 3.5 mean?
- 2. Predict y when x = 4.
Show answer
1. y rises by about 3.5 for each extra unit of x 2. 26
What to take away
- Slope in context, with units.
- The line passes through the means.
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