(2 points) The least squares method requires that the variance σ2σϵ2 of the error variable ϵ is a constant no matter what the value of x is. When this requirement is violated, the condition is called: A. homoscedasticity B. non-independence of ϵ C. heteroscedasticity D. influential observation In regression analysis, the coefficient of determination R2R2 measures the amount of variation in y that is: A. caused by variation in x B. unexplained by variation in x C. explained by variation in x D. both A and B are correct answers Help Entering Answers

C. heteroscedasticity

Step-by-step explanation:

The  OLS regression assumption of error variance being constant irrespective of independent variables, is called Homoscedasticity.

Var (u | x) = σ^2 (u) ;

where u = error term, x = independent variable, σ^2 (u) = constant error variance

The violance of this assumption ie Var (u | x) is related to independent variable x, is called Heteroscedasticity.

a

step-by-step explanation:

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.