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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:48.0pt'>Is the height just right to sink a shot <span
class=3DGramE>from</span> the stripe?<o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:48.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:22.0pt'>A study of player height versus the ability to s=
hoot a
free throw<o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Adam Charro=
n <span
class=3DGramE>brian</span> Williams Mikhail jenkins</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><span class=3DGramE><b style=3D'mso-bidi-font-weight:n=
ormal'>disclaimer</b></span><b
style=3D'mso-bidi-font-weight:normal'><o:p></o:p></b></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'>This study was done in an <=
span
class=3DGramE>ap</span> statistics course with relatively small sample
sizes.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The validity of such s=
tudies
must always be questioned.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Pl=
ease
keep this in mind if you use or report the results of this study.<span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'><b style=3D'mso-bidi-font-w=
eight:
normal'><o:p>&nbsp;</o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>Abstract<o:p>=
</o:p></b></p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>A
common thought, idea, or concept among basketball gurus is that bigger play=
ers,
typically centers, are not as proficient at shooting free throws as are the
smaller players.<span style=3D'mso-spacerun:yes'>&nbsp; </span>A free throw=
, a
shot taken without defense from 14 feet away from the basket is considered =
the
easiest shot in the game.<span style=3D'mso-spacerun:yes'>&nbsp; </span>This
concept appears to be verified by the low free throw percentages of big men
shaquille o&#8217;neal (7&#8217;1&#8221;, .469) and ben Wallace
(6&#8217;9&#8221;, .416).<span style=3D'mso-spacerun:yes'>&nbsp; </span>It =
also
appears to be verified by the higher percentages of guards Dwayne wade (6&#=
8217;4&#8221;,
.783) and Chauncey billups (6&#8217;3&#8221;, .894).</p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>The
problem is<span class=3DGramE>,</span> no one ever really looks at the
lesser-known players.<span style=3D'mso-spacerun:yes'>&nbsp; </span>What ab=
out
players such as DIRK NoWITzki (7&#8217;0&#8221;, .901) or reece <span
class=3DGramE>gaines</span> (6&#8217;6&#8221;, .250)?</p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>In
facilitating this observational study, the goal was to prove statistically,
rather than theoretically, that the height of a professional basketball pla=
yer
influences them negatively regarding free throw percentage.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This goal was obtained because any=
one
who watches basketball frequently will notice that the bigger players tend =
to
miss more free throws.<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>The
population is strictly that of the NBA.<span style=3D'mso-spacerun:yes'>&nb=
sp;
</span>More likely than not, the inferences drawn from this study can be
applied to college basketball or other forms of pro ball, but for this
study&#8217;s purpose, it is solely the NBA.<span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Once
the data was obtained, a least regression test was performed to check the
validity and strength of the correlation.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>Methodology<o=
:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp; </span></b>Essentially,
the question to be address is one of correlation.<span
style=3D'mso-spacerun:yes'>&nbsp; </span><span class=3DGramE>Is<span
style=3D'mso-spacerun:yes'>&nbsp; </span>the</span> height of a pro basketb=
all
player a predictor of how well he will shoot from the free throw line?<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The procedure for assessing this a=
nswer
is as follows:</p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.25in;mso-list:=
l1 level1 lfo1;
tab-stops:list .5in'><![if !supportLists]><span style=3D'font-family:Arial;
mso-fareast-font-family:Arial'><span style=3D'mso-list:Ignore'>&#8226;<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>All data was found on <a
href=3D"http://www.nba.com/" target=3D"_parent">www.nba.com</a> and was not
generated by the conductors of the experiment. </p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.25in;mso-list:=
l1 level1 lfo1;
tab-stops:list .5in'><![if !supportLists]><span style=3D'font-family:Arial;
mso-fareast-font-family:Arial'><span style=3D'mso-list:Ignore'>&#8226;<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>First step: CHOOSE SAMPLE SIZE</p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Since
there are 406 players currently in the NBA (our population), it is appropri=
ate
to use a sample size of 33, or 8% of the total population.<span
style=3D'mso-spacerun:yes'>&nbsp; </span><span class=3DGramE>Big enough to =
be
representative, small enough to be efficient.</span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.25in;mso-list:=
l2 level1 lfo2;
tab-stops:list .5in'><![if !supportLists]><span style=3D'font-family:Arial;
mso-fareast-font-family:Arial'><span style=3D'mso-list:Ignore'>&#8226;<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Second step: RANDOMLY SELECT INDIVIDUALS</p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span class=3DGramE>assign</span> each letter of the a=
lphabet
a number 1-26.<span style=3D'mso-spacerun:yes'>&nbsp; </span><span class=3D=
GramE>each</span>
letter corresponds to the first letter of the last name of players. <span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;</span>Using a calculator, generate a
random number used to select a letter.<span style=3D'mso-spacerun:yes'>&nbs=
p;
</span>Say, for instance, a 3 is given.<span style=3D'mso-spacerun:yes'>&nb=
sp;
</span>3 <span class=3DGramE>corresponds</span> to the letter C (the third =
letter
in the alphabet). <span style=3D'mso-spacerun:yes'>&nbsp;</span><span
class=3DGramE>evaluate</span> the number of players in that group.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Now say that there are 14 people i=
n the
NBA whose last name starts with C. <span style=3D'mso-spacerun:yes'>&nbsp;<=
/span><span
class=3DGramE>assign</span> them each a number 1-14 and use the same techni=
que to
choose a player.<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.25in;mso-list:=
l0 level1 lfo3;
tab-stops:list .5in'><![if !supportLists]><span style=3D'font-family:Arial;
mso-fareast-font-family:Arial'><span style=3D'mso-list:Ignore'>&#8226;<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>Third step: RECORD DATA</p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>After choosing all 33 players to represent our population, record pl=
ayer
height and free throw percentage <b>for the 05-06 <span class=3DGramE>seaso=
n</span></b>.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This restricted the varied data we=
 might
receive from players who have been in the league for 10 years versus players
who were in their first year.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>Basically, the point of this was to minimize bias.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Also, record player name so as to =
avoid
duplicate individual data.<b style=3D'mso-bidi-font-weight:normal'><o:p></o=
:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:10.0pt;
font-family:"Engravers MT";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-=
language:
EN-US;mso-bidi-language:AR-SA'><br clear=3Dall style=3D'mso-special-charact=
er:line-break;
page-break-before:always'>
</span></b>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>Exploratory d=
ata
analysis<o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1032" type=
=3D"#_x0000_t75"
 style=3D'position:absolute;margin-left:0;margin-top:.7pt;width:175pt;heigh=
t:485pt;
 z-index:3;mso-position-horizontal:left'>
 <v:imagedata src=3D"AdamBrianMikhail_files/image003.png" o:title=3D""/>
 <w:wrap type=3D"square"/>
</v:shape><![endif]--><![if !vml]><img width=3D233 height=3D647
src=3D"AdamBrianMikhail_files/image004.jpg" align=3Dleft hspace=3D12 v:shap=
es=3D"_x0000_s1032"><![endif]>The
data in the spread to the left is the height (in inches) and the free throw
percentage of 33 random players in the league.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Two things to notice:</p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'>-the tallest player (89 inc=
hes) has
an outstanding free throw percentage (89%) which is certainly an outlier.</=
p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>-someone
has a free throw percentage of 100%.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>For now, do not worry about these points.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>They will be addressed and explain=
ed
later in the report.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span class=3DGramE>the</span> faint graph shown below=
 is a
scatter plot of height v. free throw percentage.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Obviously, there is a relatively s=
trong
negative slope, although the individual data points do not necessarily lie
close to the regression line.<span style=3D'mso-spacerun:yes'>&nbsp; </span=
>The
correlation is .4558.<span style=3D'mso-spacerun:yes'>&nbsp; </span><span
class=3DGramE>it</span> is not a weak correlation, nor is it a strong one.<=
span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_i1026" type=
=3D"#_x0000_t75"
 style=3D'width:533.25pt;height:294pt' o:allowoverlap=3D"f">
 <v:imagedata src=3D"AdamBrianMikhail_files/image005.jpg" o:title=3D"STATS =
PROJECT"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D711 height=3D392
src=3D"AdamBrianMikhail_files/image006.jpg" v:shapes=3D"_x0000_i1026"><![en=
dif]></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The faint graph shown below is a new graph showing the
residuals (or the space between an individual point and the regression
line).<span style=3D'mso-spacerun:yes'>&nbsp; </span>The random scatter abo=
ut the
x-axis indicates that the regression line is an adequate and good model of =
the
data.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The high variance about=
 the
x-axis is indicative of a somewhat weak correlation.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This does not mean that the origin=
al
hypothesis is untrue.<span style=3D'mso-spacerun:yes'>&nbsp; </span>It simp=
ly
means that height is not at all a perfect predictor of free throw shot
percentage.</p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1031" type=
=3D"#_x0000_t75"
 style=3D'width:610.8pt;height:350.15pt;mso-position-horizontal-relative:ch=
ar;
 mso-position-vertical-relative:line' fillcolor=3D"none [4]" strokecolor=3D=
"none [1]">
 <v:fill color2=3D"none [0]"/>
 <v:imagedata src=3D"AdamBrianMikhail_files/image007.png" o:title=3D""/>
 <v:shadow color=3D"none [2]"/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D814 height=3D467
src=3D"AdamBrianMikhail_files/image008.jpg" v:shapes=3D"_x0000_s1031"><![en=
dif]></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><span class=3DGramE><b style=3D'mso-bidi-font-weight:n=
ormal'>analysis</b></span><b
style=3D'mso-bidi-font-weight:normal'> and conclusion</b></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'><span class=3DGramE>accordi=
ng</span>
to the study and the data produced therein, the original hypothesis (that b=
ig
men are not good free throw shooters and that little guys are) stood to be
generally true, but not in all cases.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>In fact, it is not true enough to be a predictor of free throw
percentage.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Looking at the
regression line, one could not predict accurately (or even within five
percentage points) a free throw percentage based on height.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>A possible explanation for this li=
es in
the possibilities of lurking variables.<span style=3D'mso-spacerun:yes'>&nb=
sp;
</span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'>One idea was conceived that=
 maybe
free throw percentage could more accurately be predicted by hand size.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Take shaquille o&#8217;neal, for
example.<span style=3D'mso-spacerun:yes'>&nbsp; </span>His hand is so large=
 that
shooting a basketball for him is much like an average person shooting a
grapefruit.<span style=3D'mso-spacerun:yes'>&nbsp; </span>It just so happen=
s that
bigger people will tend to have big hands, but small people can have large
hands, too.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Large people can =
have
small hands.<span style=3D'mso-spacerun:yes'>&nbsp; </span><span class=3DGr=
amE>it</span>
is a possibility that went unconsidered, and there is no easy way to conduc=
t an
experiment on it.<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'>Going back to the raw data,=
 there
was one extreme outlier.<span style=3D'mso-spacerun:yes'>&nbsp; </span><st1=
:place
w:st=3D"on"><st1:City w:st=3D"on">Yao</st1:City></st1:place> <span class=3D=
GramE>ming</span>,
a 7&#8217;5&#8221; center who shoots roughly 85% is living proof that free
throw percentage cannot be determined based on height.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>If the regression line were absolu=
te
truth, <st1:City w:st=3D"on"><st1:place w:st=3D"on">yao</st1:place></st1:Ci=
ty> ming
would shoot only 56%.<span style=3D'mso-spacerun:yes'>&nbsp; </span>this is=
 a
20.8% error.<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'>The other data point which =
may flaw
the data was a player who shot 100% accurately.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>It is likely that this is a player=
 who
does not receive much playing time, and took less than ten free throws all
year.<span style=3D'mso-spacerun:yes'>&nbsp; </span>This lurking variable d=
oes
not produce an accurate representation of that players true shooting ability
from the free throw line.</p>

<p class=3DMsoNormal><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>To
improve the study, playing time or free throw attempts should have been
considered.<span style=3D'mso-spacerun:yes'>&nbsp; </span>This would provid=
e a
more accurate representation of shooting accuracy.<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>More time would have allowed=
 for
more trials to be conducted and to verify that the regression line holds tr=
ue
for the entire NBa, rather than only the sample of 33 players.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:16.0pt'>A special thanks to:<o:p></o:p></s=
pan></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:16.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:16.0pt'>Nba.com<o:p></o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:16.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:16.0pt'>For providing the stats needed to =
make
this study possible.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Without =
them
I&#8217;d be lost.<o:p></o:p></span></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span style=3D'display:none;mso-hide:all'><o:p>&nbsp;<=
/o:p></span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

</div>

</body>

</html>

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