Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.



A. Interpret b1, b2, b3, and b4 in this estimated regression equation. Assume that for each coefficient statement, the remaining three variables are heldconstant.

b1 = estimated change in y per 1 unit change in x1
b2 = estimated change in y per 1 unit change in x2
b3 = estimated change in y per 1 unit change in x3
b4 = estimated change in y per 1 unit change in x4

B. Estimate y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2 (to 1 decimal).

Answer 1

:
A.
b3 = estimated change in y per 1 unit change in x3
B.
help from this
Let X represent the leftmost point. Its position is uniformly distributed between 0 and
L
2
.
Let Y represent the rightmost point. Its position is uniformly distributed between
L
2
and
L. We want to nd the probability that P

Y X >
L
3

. Note that P

jX Y j >
L
3

is the
same thing, but since we assigned Y to be the leftmost point, the rst representation is also
appropriate.
Z Z
Y X> L
3

1
L
2 0
!
1
L
L
2
!
dydx =
Z Z
Y X> L
3
4
L2
dydx
We have to be careful here. There are two possible scenarios. First, we can x X in its
domain 0 < x <
L
2
and let Y vary within its domain restricted to the condition that
the distance between the points is greater than
L
3
, so the restricted domain would be
0 < x <
L
6
.
P

Y X >
L
3

=
4
L2
Z Z
Y X> L
3
dxdy
=
4
L2
"
Z L
6
0
Z
L
L
2
dydx +
Z L
2
L
6
Z
L
x+ L
3
dydx
#
=
4
L2

L
2
12
+
5
24
L
2

7
72
L
2

=
7
9
19. Show that f(x; y) =
1
x
; 0 < y < x < 1 is a joint density function. Assuming that f is the joint