(2 points) the director of an alumni association for a university wants to look at the relationship between the number of years since graduation and the amount of monetary contribution an alumnus makes to the university. he collects data on 50 alumni who have made contributions this year and fits a least squares regression line to the data, with the monetary contribution as the response variable. james, one of the 50 alumni, has made a contribution which gives a negative residual. which of the following statements must be true about james' actual contribution?

(a) it is less than the contribution predicted by the regression line.
(b) it is less than the average contribution made by the 50 alumni.
(c) both (a) and (b)
(d) neither (a) nor (b).

(A) It is less than the contribution predicted by the regression line.

Step-by-step explanation:

The residual is the subtraction of the observed value by the predicted value.

So, if James has a negative residual, it means that his contribution is less than what was expected by the regression line.

The correct answer is:

(A) It is less than the contribution predicted by the regression line.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.