2. Which of the following linear models best represents the line of best fit for the following set of data?
X: 2, 4, 5, 6, 8, 10, 11
Y: 26, 38, 45, 49, 64, 77, 82
A) y=-6.3x + 12.8
B) y=6.3x + 20.8
C) y=0.6x + 20.2
D) y=-0.6x + 20.2
To determine the best linear model that represents the line of best fit, we will first calculate the slope and y-intercept using the formula for slope:
m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
where:
n = number of data points
Σ = sum of
x = independent variable
y = dependent variable
Calculating the values:
n = 7
Σx = 46
Σy = 341
Σ(xy) = 1589
Σ(x^2) = 246
Now we can substitute these values into the formula to find the slope:
m = (7(1589) - 46*341) / (7*246 - 46^2)
m = (11123 - 15686) / (1722 - 2116)
m = (-4563) / (-394)
m = 11.58
Now that we have the slope, we can calculate the y-intercept using the formula:
b = (Σy - mΣx) / n
b = (341 - 11.58*46) / 7
b = (341 - 532.68) / 7
b = -191.68 / 7
b = -27.38
Now, we have the slope (m = 11.58) and the y-intercept (b = -27.38) for the line of best fit. Therefore, the correct linear model is:
y = 11.58x - 27.38
From the given options:
B) y=6.3x + 20.8
C) y=0.6x + 20.2
D) y=-0.6x + 20.2
None of the given options match the calculated line of best fit, so the correct answer is not provided in the choices.