To find the equation of the least squares regression line, we use the formula:
y = a + bx
where:
- b is the slope of the regression line
- a is the y-intercept
The slope b is calculated using the formula:
b = r * (sᵧ / sₓ)
Let’s substitute the values:
- r = 0.2
- sᵧ = 4
- sₓ = 2
Thus,
b = 0.2 * (4 / 2) = 0.2 * 2 = 0.4
Next, we calculate the y-intercept a using the formula:
a = ȳ – b * x̄
Substituting the values:
- ȳ = 10
- x̄ = 20
So,
a = 10 – (0.4 * 20) = 10 – 8 = 2
Now we can write the least squares regression line equation:
y = 2 + 0.4x
This equation shows that for each unit increase in x, the predicted value of y increases by 0.4, starting from a base value of 2 when x is 0.