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Unformatted text preview: 3 L â StatsZZl-Mortlock
LtÂ» July 29, 2002
Lab #5 Lab #5 â 9-9,10-12, 10-13, 10-16, 11-15 9-9
(a) As the average SAT score increased, the percentage of high school seniors
who took the SATsâ decreased. So when almost all the students took the SATsâ, the scores were generally lower. There clearly is a negative relationship between the two.
The correlation is 40.79 = 0.88. R= -0.88. So, -0.88 of the seniors takes the SATs. It is a strong correlation because it is close to â1. o 10 20 30 40 so so 70 so 90
SATAvg = -2.18R:tTalhg + 1147; v2 = 0.79 'I would conclude that there is a cause-and-eï¬âect relationship between these two 'ables. The higher the average SAT scores, the smaller the percent taken is. (a) The proportion of the variability in turnpike tolls is explained by the
regression line with mileage as 0.999.
.123 + 0.0402(150) = âThe toll for a person who needs to drive 150
miles 0 he pike is 1.407.
(c) The regression equation predicts that the toll will rise 0.0402 for each
additional mile that you drive on the turnpike. (d) 1/0.0402 = 24.88. You would have to drive 24.88 miles in order for the toll to
increase by one dollar.
10-13 (a) The least squares line for predicting receipts from attendance is: receipts =
65.4 (attendance) â 85000 r"2 = 0.93. 2000 m 10000
been: = mAAttandame - m r"2 = 0.93 (b) 65.4 (7 500).â 85000 = 405,500. So, the least squares line predicts for the
receipts of a show with a weekly attendance of 7,500 is 405,500.
(c) 65. (6531) â 85000 = 342,127.4. So, the ï¬tted value is 342,127.4. The
' residual alu for Death ofa Salesman is 351,082 â 342,127.4 = 8,954.6. â
(d) abaret = 65.4 (6647) â 85000 = 3497138
F0 e = 65.4 (8195.67) -â 85000 = 450996.818
show with the largest ï¬tted value is Fosse with 450,996.818. 10-16
(a) The regression line for predicting a playerâs weight from his jersey number is:
weight = 0.85 (number) + 180 where r"2=0.36. 0 102030405060708090100
\Abiglt=0.850Nnber+1&Ir"2=0.1Â£ (b) 0.85 (50) +180 = 222.5. So, the weight of a player wearing number 50 is
222.5. (c) The slope coeï¬icient in context is 0.85, where 0.85 is used for determining
from the sample data when minimizing the sum of the squared residuals. We use this
coefï¬cient expression for calculating the means and standard deviations of the two
variables. (d) If Dan Loney, a 300-pound center wearing number 66 were to exchange his
jersey in practice one day for number 16, previously worn by l85-pound quarterback,
Kevin Cooper, I would expect Loney to neither gain nor lose weight. This is due to the
fact that that it would only be for one day. Furthermore, for that one day, no ones weight
is going to change just because their jersey number does. For this one-day, the weights
and jersey numbers are not calculated into this regression line. (e) Knowing a playerâs jersey number is of no real use in predicting his weight. I
say this because they are not given their jersey numbers by how much they weigh, they
are given their numbers at random, so there really should be no correlation between the
two. If there were to be, then the higher the number, the more a player would weigh, or
the lower the number the higher they would weigh; however, the randomness makes this
hard to ï¬nd the relationship. 1 1-1 5 (a) The residuals seem to be randomly scattered. When a straight line is a
reasonable model, the residual plot should reveal a seemingly random scattering of
points. (b) Despite the very high correlation of .999 the residual plot does give you
reason to suspect that the relationship between toll and mileage is not linear. This is
because the residual plot reveals a pattern of some kind. It appears to start above zero, then a little below, and then a little more above, a little farther below, then even farther above zero. ...
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