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.