a graph has the points (14, 71) (9, 57) (13, 67) what is the equation for the line of best fit
To find the equation of the line of best fit, we first need to calculate the slope of the line. We can do this using the formula for the slope of a line:
m = (Σ(xy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2)
Where:
Σ represents the sum of a set of values
n is the number of data points
Given points (14, 71), (9, 57), and (13, 67), we can calculate the following sums:
Σx = 14 + 9 + 13 = 36
Σy = 71 + 57 + 67 = 195
Σxy = (14*71) + (9*57) + (13*67) = 994
Σx^2 = 14^2 + 9^2 + 13^2 = 436
Plugging these values into the formula for the slope:
m = (994 - (36*195) / 3*(436) - 36^2
m = (994 - 7020) / 1308 - 1296
m = -6026 / 12
m = -502.17
Now that we have the slope, we can use one of the points to find the y-intercept of the line. Let's use the point (14, 71):
y = mx + c
71 = (-502.17)(14) + c
71 = -7030.38 + c
c = 7101.38
Therefore, the equation for the line of best fit is:
y = -502.17x + 7101.38
thats incorrect try again
My apologies for the mistake. Let's try again.
To find the equation of the line of best fit, we can use linear regression. We can use the formula:
y = mx + b
Where:
m is the slope
b is the y-intercept
To calculate the slope (m) and y-intercept (b), we can use the following formulas:
m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
b = (Σy - mΣx) / n
Given points (14, 71), (9, 57), and (13, 67), we can calculate the following sums:
Σx = 14 + 9 + 13 = 36
Σy = 71 + 57 + 67 = 195
Σxy = (14*71) + (9*57) + (13*67) = 994
Σx^2 = 14^2 + 9^2 + 13^2 = 436
n = 3
Now we can plug these values into the formulas to find the slope (m) and y-intercept (b):
m = (3*994 - 36*195) / (3*436 - 36^2)
m = (2982 - 7020) / (1308 - 1296)
m = -4038 / 12
m = -336.5
b = (195 - (-336.5)*36) / 3
b = (195 + 12114) / 3
b = 12309 / 3
b = 4103
Therefore, the equation for the line of best fit is:
y = -336.5x + 4103