A graph has the points (0, 4) (2, 0) (-2, 0) (-3, -6) (3, -6) what is the line of best fit?
To find the line of best fit for these points, we will use linear regression. Linear regression finds the equation of a line that minimizes the sum of the squared differences between the predicted y-values and the actual y-values.
We'll start by finding the slope of the line:
slope (m) = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)
First, let's calculate the sums needed for the formula:
Σ(x) = 0 + 2 + (-2) + (-3) + 3 = 0
Σ(y) = 4 + 0 + 0 + (-6) + (-6) = -8
Σ(x^2) = 0^2 + 2^2 + (-2)^2 + (-3)^2 + 3^2 = 0 + 4 + 4 + 9 + 9 = 26
Σ(xy) = (0 * 4) + (2 * 0) + (-2 * 0) + (-3 * -6) + (3 * -6) = 0 + 0 + 0 + 18 + (-18) = 0
Now, we can substitute these values into the slope formula:
slope (m) = (0 - (0)(-8)/5) / (26 - (0)^2/5)
slope (m) = (0-0)/26
slope (m) = 0/26
slope (m) = 0
Since the slope is 0, the line that fits the data is a horizontal line.
To find the y-intercept, we can use the formula:
y-intercept (b) = Σ(y)/n - (slope * Σ(x))/n
Plugging in the values:
y-intercept (b) = (-8)/5
Therefore, the equation of the line of best fit is: y = -8/5