STAT 2, SPRING 2006
A. Adhikari
REGRESSION REVIEW
PROBLEMS FOR QUIZ
2 (Chs 10, 11). Answers
here!
1. The scatter diagram of MSAT and VSAT scores of a large group of students is football shaped. The correlation between the two variables is 0.7.
a) A student on
the 90th
percentile of VSAT scores
is estimated to be on the ____________________ percentile of MSAT
scores.
b) A student on the 20th percentile of
VSAT scores
is estimated to be on the ____________________ percentile of MSAT
scores.
2. The scatter diagram of
MSAT and VSAT scores of a large group of students is football
shaped. The correlation is positive, but of course it is not
equal to 1.
a) A student is on the 70th percentile of
VSAT
scores and on the 70th percentile of MSAT scores. This student's
MSAT score (pick one)
(i) is
greater than
(ii) is equal to
(iii) is less than
(iv) cannot be compared to
the
average MSAT
score
of all students on the 70th percentile of the VSAT scores.
b) A student is on the 70th percentile
of
VSAT
scores and on the 60th percentile of MSAT scores. This student's
MSAT score (pick one)
(i) is greater than
(ii) is equal to
(iii) is less than
(iv) cannot be compared to
the average MSAT
score
of all students on the 70th percentile of the VSAT scores.
c)
A student is on the 25th percentile of
VSAT
scores. This student's MSAT score is estimated to be (pick one)
(i)
above
(ii)
on
(iii) below
the 25th percentile of all the MSAT scores.
3. The average height of
a large
group of children
is 43 inches and the SD is 1.2 inches. The average weight of
these
children
is 40 pounds and the SD is 2 pounds. A scatter diagram is drawn,
with height on the horizontal axis and weight on the vertical
axis.
The scatter diagram is football shaped. The correlation between
the
two variables is 0.65. The regression line for estimating
weight
based on height is drawn through the scatter.
a) One of
the children
weighs 37 pounds and
is 42 inches tall. The point corresponding to this student on the
scatter diagram (pick one)
(i) is above
(ii) is on
(iii) is below
(iv) cannot be placed relative to
the
regression
line for estimating weight based on height.
b) A
child who is 43 inches
tall is
estimated to weigh _____________ pounds, give or take
____________
pounds.
c) A
child who is 41.5 inches
tall
is estimated to weigh ______________ pounds, give or take _____________
pounds.
d) Of the
children who are 41.5
inches tall,
about what percent weigh more than 40 pounds?
e) Among all
the
children
in the group, about what percent weigh more than 40 pounds?
f) For
about 80% of the
children, the
regression estimate of weight based on height is correct to within
____________
pounds.
g) For about 20% of the
children,
the regression
estimate of weight based on height is off by more than _____________
pounds.
h) The
weights of about
____________% of
the children are within 2.5 pounds of the average.
i) For
about __________% of
the children,
the regression estimate of weight based on height is correct to within
2.5 pounds.
j) For about
__________% of
the children,
the regression estimate of weight based on height is off by more than
2.5 pounds.