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.
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
1 answer
1 answer