Suppose the line of best fit for some data points has a slope of 1.885. if the mean of the x-coordinates of the data points is 3.448, and the mean of the y-coordinates is 12.318, what is the y-intercept of the line to three decimal places?

Step-by-step

One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).

Assuming the given "line of best fit" is a least-squares line, then we are given

a slope m=1.885 passing through (x0,y0)=(3.448,12.318).

Applying the standard point-slope formula:

(y-y0) = m (x-x0)

we get

y-12.318 = 1.885(x-3.448)

Expand and simplify,

y=1.885x -1.885*3.448 + 12.318, or

y=1.885(x) + 5.81852

(numbers to be rounded as precision dictates).

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west