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
−0.202
negative 0.202
−4.430
negative 4.430
0.202
0.202
4.430
To find the slope of the line of best fit using the least squares method, we need to calculate the mean of x (x̄), the mean of y (ȳ), the sum of xy, the sum of x^2, and then use the formula for the slope of the line of best fit:
x̄ = (67+28+26+47+86+32+15+70) / 8 = 48.375
ȳ = (46+34+33+38+46+37+35+44) / 8 = 38.125
Sum of xy = 67*46 + 28*34 + 26*33 + 47*38 + 86*46 + 32*37 + 15*35 + 70*44 = 10817
Sum of x^2 = 67^2 + 28^2 + 26^2 + 47^2 + 86^2 + 32^2 + 15^2 + 70^2 = 18040
Now we can calculate the slope using the formula:
m = (Sum of xy - 8*x̄*ȳ) / (Sum of x^2 - 8*x̄^2)
m = (10817 - 8*48.375*38.125) / (18040 - 8*48.375^2)
m = (10817 - 14896.875) / (18040 - 18634.2656)
m = (-4079.875) / (-5934.2656)
m ≈ 0.687
Therefore, the slope of the line of best fit for the given data set is approximately 0.687. Rounded to three decimal places, the slope is 0.687.