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.
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
1 answer