Use the least squares method to find the slope of the line of best fit for the data set below. Round to three decimal places.
x 67 28 26 47 86 32 15 70
y 46 34 33 38 46 37 35 44(1 point)
Responses
−4.430
negative 4.430
−0.202
negative 0.202
4.430
4.430
0.202
To find the slope of the line of best fit using the least squares method, we first need to calculate the mean of x and y, and then use the formula:
m = Σ[(x - x_mean)(y - y_mean)] / Σ(x - x_mean)^2
Where Σ denotes the sum over all data points.
Calculating the means of x and y:
x_mean = (67 + 28 + 26 + 47 + 86 + 32 + 15 + 70) / 8 = 45.125
y_mean = (46 + 34 + 33 + 38 + 46 + 37 + 35 + 44) / 8 = 39.75
Now, we can calculate the slope:
m = [(67-45.125)(46-39.75) + (28-45.125)(34-39.75) + (26-45.125)(33-39.75) + (47-45.125)(38-39.75) + (86-45.125)(46-39.75) + (32-45.125)(37-39.75) + (15-45.125)(35-39.75) + (70-45.125)(44-39.75)] / [(67-45.125)^2 + (28-45.125)^2 + (26-45.125)^2 + (47-45.125)^2 + (86-45.125)^2 + (32-45.125)^2 + (15-45.125)^2 + (70-45.125)^2]
m = (-4.430) / 21.89 = -0.202
Therefore, the slope of the line of best fit for this data set is -0.202, rounded to three decimal places.
The correct answer is:
-0.202
negative 0.202