Using the spreadsheet program recorded

26 Jun Using the spreadsheet program recorded

Question
11, 2009
31, 2011

ent #5: Quantitative Structure Activity Relationship (QSAR)
ent #8: Quantitative Structure Activity Relationship (QSAR)
h student needs to turn in their own work in their own words,
ether! To ensure properRebeccaownBroyer in their must words, even if
student needsProfessorinownership of ideas, you own list the
to turn
their M. work
classmate(s) that you worked ideas, you appropriate field. name(s) of
ensure properProfessor Matthew R. in the must list the full
ownership of with Pratt
Department of Chemistry
you worked with in the appropriate field.
u will explore the concepts of drug structure and its effect on
Last updated October 26th, under
sing the spreadsheet program provided 2014 the laboratory
will explore the concepts of drug structure and its effect on biological
se, you will graph data to determine drug structure activity
Laboratory Assignment #7: QSAR
readsheet program provided under the laboratory please
need extra help with using the spreadsheet functions, links for each
hChapter determine drugthat each student needs text for moreown work in their own words, even if you
data to 18 Remember structure Chemistry to turn in their need
of your Medicinal activity relationships. If you
work together! To ensure your TA.
e
R. spreadsheet functions, please ask proper ownership of ideas you must list the full name(s) of your
classmate(s) that you worked with in the appropriate field.

In this laboratory, you will explore the concepts of drug structure and its effect on biological
se #1.
#1.
activity. Using the spreadsheet program recorded
under the
of cholesterol in the blood serum of 12 women wereprovided together laboratory links for each exercise,
cholesterol in the blood serum of 12 women drug structure activity relationships. If you need extra help
you will graph data to determine were recorded
ges:
with using the spreadsheet functions, please ask your TA. Remember that the order of
operations in the spreadsheet matters for the calculation.

1

2

3

4

5

6

7

41

43

66
71
47
67
45
51
58
The 53
concentrations of 49
cholesterol in the blood serum62 12 women were recorded together with
of

Exercise #1 (8 Points)

8

9

10

11

12

their ages:

151

180

216

175

238

Case

165

202

1

246

2

158

3

208

4

216

5

188

6

7

8

9

10

11

12

art of this problem, you will calculate the linear66 53 that 47 49 67 45 51 58 62
equation 71
Age (years)
41
43
a and prepare a graph showing the data plotted.
his problem, you will calculate the linear equation that best fits the
Cholesterol (mg/
151 180 216 175 238 165 202 246 158 208 216 188
100 mL)
graph showing the data plotted.
quares regression is what is mostly used to fit a straight line

lso known as “regression”, “linear regression” or “trend line.”
Use these data to determine if there line to data; it
gression is what is mostly used to the slope (see below) by is also
gets its name because it estimates fit a straight is a correlation between age and amounts of cholesterol. To
accomplish “trend line.” The the linear equation
”, “linear regression” orthis, you will calculatemethod gets its that best fits the data and prepare a graph
e sum of the squares (least squares) between the data and name
showing the data plotted.
he slope (see below) by minimizing the sum of the squares (least
Linear least squares regression is what is most commonly used to fit a straight line to data; it is
data and the model.
also know as “regression”, “linear fact a simple
he straight line that fits best a model is inregression”, or “trend line.” This method gets its name

because it estimates the slope by minimizing the sum of the squares (least squares) between the
data and a model straight line.
line that fits best a model is in fact a simple process.
he equation y Calculating the straight line that fits a model best is in fact a simple process. All you need to do is
= a + bx,
on y = a + bx, fit the data to the equation:
y = a + bx
First, you will calculate the slope of the line, which is the term “b”, by using the following
equation:
n

[(

)(

ate the slope
# xi " x yi " y
ulate the slope b = i=1 n
!
!
!
2
#$ x i " x ‘
&
)
%
(
!

x average and y =
!

i=1

(

)]

)

n

"y
i=1

n

i

is the y average.

s, the x average is the sum of all the x data (in this
d by the number of data points (12) and similarly, the
of all ! data (cholesterol) divided by the number of
y

[ [
]

i
i
‘
$
oy. Using proper ownership program their you will explore laboratory ‘ of drug structure$ and its2 ‘ 2 ‘ on biological
ensure turn in their In this ideas, provided words,the $ if concepts
you own list
needs to the spreadsheet oflaboratory, must under itsyou worked with in the appropriate $ i i effect
own work in classmate(s) the
n
the
you #1. explore the concepts for drug structure 12thatevengraph biological n Activity drugx istructure activity
of each Assignment women were ) )
ise will
x
e #1.
entrations cholesterol indata blood serum of of have ntoneffect" recorded together= i=1 #&#&"xx " ) )
cholesterollinks toappropriatejust and n will x& x ix" data toslope bi=1" x yn % y % i ( (
in the your list You12 name(s) of on thethe
exercise, structurecalculate the concepts of x "y field. x
& explore slope # ( x
#5: to iactivity (
b
just have nwill %
ntrations of of worked ideas, Laboratoryserumfield.womencalculaterecordeddetermine)"Relationship (QSAR) n effect on
thetheblood You drug you Quantitative Structure =#i ( xn (drug i structure andn its
were
exercise, you will graph in you must laboratory, you %
determine
e(s) that
(
proper ownership of with
"2
In
i
activity. Using If the
ol in their ages:in the blood serumwerewomenfullwere #x ii=1 linksi"yyprovided spreadsheet ) y’ 2 ‘
cholesterol program serum of wereyou need # recordedx yy" yy
the blood
i=1 laboratory
eofspreadsheetserumwithLaboratory 12 women laboratory"xpleaseusing thei=1under i the)(i=1functions, links (for" xeach( y
provided nthisrecorded together i" yy i i each
fin the blood serum blood12 womenofunder spreadsheet#"x i x withfor"Structure Activity "xx " )
cholesterol
x program
with need in the n of of relationships. therecorded extrannihelp together
#i=1calculate
please
# x
you
help n12 womenn biological thewere#8: Quantitative slope = i=1 # provided under (QSAR) (
using
spreadsheethavencalculate xi the
functions,
ges: with inextraappropriate field.the12Assignment torecorded"the"slope b = b program$#i$Relationshipthe #i ( xi )"yxi )"
n
n x
n
x
ked
just have Using the spreadsheet
& &
ages: data thedetermine drug structureYouactivity.i=1 todetermineyou needtheir nown work relationships.bIf effect on bi
exercise,In TA.xthat "justbbstudent needsyour concepts to ndrug 2structure and words,
youxwill the slopeyou= i=1 explore drug structure Chemistry text for i=1 laboratory
data =
to
i=1
% % i )slope b
laboratory,relationships.
graphthe concepts have asktoyourthisYougraphChapter i=118x ofmore You justjust havecalculatein’ their(slopeits= youn need
to You of drugto calculate"theits)eachy== bi=1will for If tothe Medicinal ofactivity’y 2the(the) own=more
activity ) on x
You
to calculate
You just have calculate i the)See yyi )" exercise,
You 18just yourRemember fortheeffect "yni n ni
to to calculate ( slope
You just have Medicinal xi "yeach
calculate slope
See
plore Chapter just ofxhavestructure andChemistryb text"yyou will turn in data to determine drug structure activity
# ( ( xi ( slopen n n i i 22 2graph have $(nxi=1"xx" TA.
#
n
$ y
" i=1i)" x i )
links
2
2′
i x i helpi=1 i=1 using the spreadsheet$functions, please ask i your ) )
ng the
your
information5
2
8
providedn
laboratory& $
needs 10 program 12 own work is ( you y average.$ even ‘
turn
i
"
QSAR.havecalculatei=1 functions, activity.naskeach7the =spreadsheet"’help inownershipyof spreadsheet functions,#%( x i )"(x
spreadsheet calculate extraevenunder work together! = i=1 ensure xxx’average #&#%( undertheir must words, x i & x fo
program the slope please QSAR. Ifxyou needxextra average andi=1 % i=1 i=1 ii=1( inthethe own list the please
provided with that6where TA. x To$ 9x isi the
= = n
ust have to to 1
the slope b 4 b if you Using student i=1$#theto ‘ 11
ou just spreadsheet i=1 3Rememberonthe laboratoryi=1 ##i$i"xxxxproper theirand= &= ideas,istheaverage. #%( links )
" i"12 )) with using the y
relationships.29 =biologicalthe y(average. y y
is %%
y
i=1 x && &&
where y12 #%% 11is the y(average. " "
)
ore 1 where 3 =of = 7is the 6 averageeffect classmate(s) that n) ( worked nwith in ithei appropriate field. i=1 i=1
concepts 6 4
3 the 4 2 5 x x drug structure x average and" x10 i is
5 is 8 x and its 8 2 ‘ 11n n "
(
where
full drug 7 #$"you To on =n proper 18 ! !
name(s) 10your Seei i=1data
you of your n Medicinal Chemistry fulln for more
exercise, ( )" xwill
structure activity relationships. If o
n
you work 9together! TA. ensure i=1ni=1 to determine drug nn
will graph data to determinethe ask$( x iofxxiand ‘y graphChapterownership of ideas, younmust list the text name(s) yo
structure activity n n i=1
n
n
#! your )49 i=1
n n 1. points) 71 Exercise)
& where (
&
n
% with
et help with provided 1. 66 n(8 points)help where= xi=1 67i eachthe51 average 62y "iyy y i=1 is ask y average.
the laboratory) links x n 45
n (8
x ifunctions, i=1x
yi x
Exercise please
)ra program 41
"n n
xercise #1. using 43 nspreadsheeti=1 % i=1!47 that" x=forn isspreadsheet58" x and="= iifield.thethe y average. y" yy
the under 53 information( on #1.inworked withxin the appropriate
extrafunctions, xusing n n is
rcise #1.
your classmate(s) #1. " the nthe x average and " y i please is your TA.i " x ii " i
you
"
# x "
!
51
51 "
"49ix activityx relationships. QSAR.needis =average y = of
o 6641 n of 43 7166 structureiChemistrynwhereofwomenyouthethe terms, average.i=1drugwomen y average.effectxon (in (in
i
women were
n
In serum text67 of and issimpleib blood !
and
wherein the "just 6747 nlaboratory,more simple y58 the the x average. i=112is x average recorded
whereYoux 71x have4549calculate i=1" yrecorded blood serum=
! blood ithe average and ! 62explore thetogether
! The this to average cholesterol ithe is concepts
x 12 women
more slope
= 45
is y average.
ons of 53n your Medicinalbloodis the of ofwhereyouthewerein yaverage andaverage12is thethe xwereallitsandx ydatais thethis
12 cholesteroly
r determine drug 4753 The"ixconcentrationsfor58! = will "" recorded wherexx=ofi=1 ofis structure of of all ythei=1 together a
18 cholesterol ! in ! the" concentrationsIn xIn xi=1Ifwere isi terms, 62 ywhere yx= i=1is the the averagethe = = data y
serum
s of cholesterol simplei=1i=1i=1isserumtheyaveragemorei=1 thexin xthei=1y theandaverage thethe sum i=1 recordedi=1 is the
is sum b = and
" functions, simple their the y"averageUsing=ntheYou dividedaverage.numberthe this points i " x y in" yn
In i In more x xi=1 = ask thethe238their andthe yyi=1 spreadsheetallthex 188 data slope !#the nand similarly,
morewhere= x 216terms,x average caseis the divided208 ythe number n data under
of
average
sumhave to the x
this
where= = togetherx TA. points) 202 246 sum isthe! thecalculate n of data
is 1. xx averageand is
dsheet x" x i wherepleaseterms,is "average ages:n =age)i=1#1.the!yof ynaverage. n ‘of(in (in points ! x(12) and similarly,
biologicalipoints) Exercise= i=1 isjust the 216 data
the
the all $
x x case and
l (mg/100ml) 151
175 with i 165 Exercise is is y average.
eir ages:i=1 where x 180 with isisyourthei=1activity.and yythe=age)terms,byxbyprogramn2providedsum all(12) laboratory ‘ (in the
1. = 202!is! more 188#1.n the (12)average.similarly,
i=1
In nandby(8 (8isnumber158 explore 216 thetheaverage is structurenof ofits effectxonxbiologica
this= yi=1158 ! the youywill of nn n158 concepts of similarly, the and thethe x " 2
In208y average.208
more simple data
terms,
x
In
x and
thi
n nand 246laboratory,numbersimplepoints y188dataaverage thethe drug structure$ activity this
n links ages: the! the 216 data will points (12)x!"drug is sumthe i=1 all # data (in
e 216 x case the the 165 dividedis thethe
x x average
=
here = 180 the age) 202 y 165 by average y average thethe sumn all ! data (cholesterol) divided by by datanumbe
iswhere age)
x
) x 151 175is 238the 175 238
246andaverage. is graph
of
case216average divided xeach y average Youisjust the of to calculate the slope b = divided& thethe )
!
!
for nconcentrationsis cholesterolof andblood (cholesterol) women werenumber o
exercise, you sum naverage.to data) serum of
y
all
havein in & iy determineof of thethexand similarly, the to
% moreis serum of theall i x(12)yweresimilarly, al
(data pointswomen data is2 for of o
n n
n concentrations of of divided thethe blood simple terms, laboratory "links recorded
the issimpleof sum 12 the " data isy the sum each
n )( and this (
! ! activity. TheIncase thethe age)terms, by byInthe numberthe data all 12xaverage%(ini) (inthe sumth
divided
simple
xi=1
this
The ! data spreadsheet helpx averageby of sum the x x average recorded
! y average is thethe sum Usingmoredata points (12).dividedaverageytheunder 8 of offunctions, please12
!
! more age)terms, thethe x number ynumber (
the simple (12).
provided
terms, #
all x calculate 9 2extra program 12iIn"xx i i"spreadsheet 9(12) 10 i
of all Incase 1needis cholesterol #i=1more thenumber points age)
xxthe
If data
you is
5 "
of
the number xdata
1 Inaverage is4 Case5terms, will !yy averagedivided 3sum 4ofnndataithedata(cholesterol)(12) and$similarly, the of o
2more3 simple sum oftogetherdata(cholesterol)alltheall !usingdata"(in this age)case similarly, the
10
11
or the firstyInIn Inmoresimplerelationships.average (cholesterol)ofwiththeythedataage)(in bthis thethe#byage) If data points
part more simple terms,6youxwillthe8age)theisdivided of dividedxxtheydata (in thisi=1by thethe by"the ‘you need
you !y 7 x xgraph the thethe have theallbythe6age)(in this
n
In Inmore simpleterms,thecasexwith pointsages:determinethe!(in xxthey7 (in this dividedn & the11 ) points (1
the is
of slope
points
number
average tosum of of ynumberthe data activity n number
more simple terms,n thetheaverage their thethe by by toxcalculatethis case this = divided by x iof data
terms, thethecaseaveragesumthe equation thatof(cholesterol)by divided
Inof this problem, with thexyx averageage)thesumsumall case xdatadatapoints caseand number x (
more simple terms,theiraverage isYoulinearsum # all datastructure the (12)relationships.of number
average isjust
divided
is
sum
all the
(in
more simple linear equation
of drug thedata divided
ages:
exercise,
i=1
part the you divided xbyxtheanumbershowinglinearChapterand(inofyi=1!!n case(cholesterol) isallsum$by theall more
roblem,the points prepare 12 just of thewere recordedthedatathat = !yythe(cholesterol) isjust have textof ynumber
will terms, TA.averagedata slope
case
sum
datathethe theaverage is yourbytheof all points andpoints this ally and average sum y calculate the slope
ore fit of this bloodnnumber of thecalculatedata Seethe12).xSimilarly,btheyour theaverage Chemistrysum allfor y of of b =
terms, serum average the thesum the ( xequationof all all x
more simple terms, (12). 12data points (in thisof thatiisthedata pointsdata y isis Youdivided ! !
terol data problem, younumberhave !datapointsthe (12).similarly, average y similarly,ofdivided the % y i
You
calculate
y
just by
st in in datawillthethe(12).askwomenbythe number"(12)slopepoints (12) Medicinal the the ofdatay data2 ‘(cholesterol) div
and
#
rol simpleof thispointsthe ofdividedis!werecalculatethedataisumthisfunctions, similarly, sumthe y bytoof" (cholesterol)
of divided have tonumber theplotted. of
recordedx of) ydata
average
dividedcalculateyou willbywiththe theis(12)data"18b =! naverage theisask of TA. xi=1
points
data data sum(in
case problem, extra help i sumusing the oftogether similarly,i and 2the the
case age) divided by theaverage all spreadsheet (12) and please
age) women ythe points nlinearx(equation
all
case aby theYou divideddataonTo Toof dataofb, youthe nthat for each (x , (x ) pair on on n table,
the numbergraphx oftoythe(12) calculate b, youthe data similarly, , y ) pair the i " table,
and
numbersimilarly, simply best each y
irstthethedividedcase age)age) divideddatanumberandandpoints )(12).(12)(12) averagethe the yourall45 &datanumbermakedivide
part!blood serumtheAgeinformationdataQSAR.of(12).similarly, 53 "y71$ forfitssimilarly,thethe# (the x ) )make thethe s
calculateplotted. data points simply
2’
i
‘ i 49
ata age) prepareby theto" x y i of yof slope points (12).43 151 258 i=1 62$ points (12). ii 6 i67 7
are a graphdivided graph number data data != points (12). 66
plotted. number(12)
the 49 b 67
the and You43(cholesterol)showingCase !pointsi=141 45
sum
se
age) !showingx i 53 data " the points ! calculate
by calculate 47
51
71 i=1
! y have is calculate of ofy! data # of that best fits3 by x 47 number
data
data
m, you41 aycalculatewillisisis sumsumoflinearydatan (cholesterol)y divided %byi"the5number of i=1 %= y 9 ( 58 10y62 11
f prepare !graphaverage lineardata by bydatadata (cholesterol) = (12).%&xthethe(average of y 8 i=1 is the averag
this problem, (cholesterol)the sum plotted. equation " wheredividedthe is4thenumber of and
will yjustyou ! !the(years)the allallthat number dataypoints i=1#& thepoints (12). of
average thethe divided all the y (cholesterol)i " points # by "xx )
y average
x the
x2
dataaverage datathe (cholesterol)the bestthe the datayof dividedisi the x)(average.
data 66wheredata divided thedivided byi number x"of data
(cholesterol) equationall number fitsofand divided (12). number
sum
(cholesterol) = x i
the of
showinginformation,isisymostlyindividualfit a productsbelow y "yythe sum n use theinby by the sum al
x average ‘on nstraightby
y that you
xsimply for for eachcolumn)A,number the i=1linemakespreadsheet,you" first the sum of o
= is whatthe dataninall y , ytopair on areax "xx " the " ! that divide
rage is is squares of ythis you simply of all ,(x ) pair and the n table, make y
sum Usingall y
averagethe the 1. of all b, you (cholesterol) divided by $individual the table,
sum
i=1
near least calculate pointsplotted.n
used
To To calculate b,(12).
sum divide
i
To To of i=1 b," b, products i=1each (x
calculate i
make
) pair
data points
the (12). data points (12). 1.
aing theYou justdataregression(8 points)eachcalculate iyou) simply foris i the x xii, (xiii) pairand on= table,is the ythethe sum
graph isregression
calculate (mg/100ml)to(xi#1.ix180x you simply for each y , yitheon thethe table, make sum
pointsslope data the ndata 1.(12).mostly usedcalculatestraightsimply for line.”, (x), pairyouyou thenfori i=1 208 thethe )average.
ta pointsdatab = known (12). is to fitn nslope 10#regression” or= x i nToeach y average simplyy 158make
(12).plotted.
Exercise " b, i " line 175 To ii
ression showinghaveis$as used2 ‘ thea Exercise #! youyou216"for each2(xcalculate b, on simply each (xi, (x)isumpair the th
squaresis4also 5is2166towhat(8 points) straight 151i&#1. 12simply“trend2188 i 165yb,202 the table, for each yi , pair 188 on t
what points 175“regression”, 202 b = fiti=1 %158 y)208y2 216 n 238
mostly 7 2388 165To “linear line ( where x i=1 n calculate i) pair 246 "table, make 216 i sum
a
xb,n x 41( 43
Cholesterol
calculate11 thatproducts x "by y
on you " divide 45 y sum of
To yindividual that you divide by the thatof all divide by the sum of all
data; it all all
0ml) 3 of of 180 individual products 9 of xallxallyindividual products66 xx "53 "yysum thatof 49 y i 67 by the51 on 58 a
151
246y" y $
Age for n"
(years)
" sum you x
" y y
calculate b,products " xeachiline.”# pair"on ‘!x xx"xi . the i 71yof 47 women n
(x
i
n
x b, x simply regression”the slope more i the is thethat x
"
i=1
x= divide x
as methodTo as “regression”,youmostly "allindividualii)squares onix"table, ii)byxmakeyyouyouof allxallwere)"recordedallyou
“regression”, itsnto iswhere“linear oriforofofeachii, (x ,straight )in the"table,y )"individual sum of werethe( y )average. the
known individual b,you isthesimplyifor= individualixInyou i=1 simple make )thethe dividei=1 (isindividual ) allyou divid
“linear regression” itxx iis allto ncholesterolline.” nblood xindividualsumsum all x
talsoYou just To calculate iThe yousimplyusedeachiorwherepairinthethexiblooditserum!thewomen individualsum oftogether=
what ! slope eachindividual)squares
hesquares regression calculate you! "ofi“trendxof(xaveragepairlinebelow)of"make the1212sum i=1by"by"yrecordedthatand yd
getsTon calculate The(simply x #eachof ,cholesterol (thetoxofyy i terms, theandproducts x i )the y "of of
name you )concentrations" (x y“trendand ( "2. all all make sum x=
individualii)"yy)products table, i make sum =
that
Tohave " x %moreb,concentrationsthextable,%)make(seeisi the)(ntable, isy alsoaverage. (n i thethexyiaverageall
calculate eachyou(xi), pairestimates fit) a(x&,pairpair the "isidata; yaverage theaverage is xisum that
To simply&forb,b,(xi,simplypair forthe"xy i(,makei)) xon on 2(table, (make ofwhere yxdivide is (the sum
calculatebecauseyi)i=12on bfor table, (xy,products on the" y serum theproducts
table, of all the data (in this y
n
i
pair
simplyon i by
y sum
b, products is mostly slope 2(seeatheireachx i also the sumalso
for
olculateits mostlycalculate xx aystraightwithisto data; iitbyi below) by isi=1 individual y average. .n .
calculateyouyoubecause it togetherthatforthedivide$y i average n the x
b, simply In
regression Toestimateswhere" xy= =i=1youbelow) byline thedata;2xof"individual squares number
what is name“linearxxregression” to fitindividualaveragetheon theall sum ! average.
what of i with ythat the squares) Thei and x
used
straightsquares 2and y
i=1
me becauseisproductsthefiteach"For(leastyou(partx58i=1squaressum=age). willi the)(ysquares linear2of data points (12) and
slope
yi
"
wherex x x x divide"(see to151 180
is
case
“regression”,of71squares estimates linei=1 theages: is equationall =.xi=1by is175nameyaverage
nimizingof53 itallproblem, thea.simple 45.first51ythey "thissumxof"yit dataterms, xtheisum 165 202 equation that
the sum ni=1 ito"you used" or terms, i=1yof the 62 you simple
squares .
3gets individualindividual 49 xiwillxcalculatethe line.” between youi divide (by"thebyxthe all all 2 is the sum of!all the x d
66 individual squares their ages:"xx " x xlinear "that’ ithe you and calculate of
n x
rstYou justproductsallx47i" )"yproductsthe“trenddivideaveragesum"divide #divided ysquares "all".x ) . 246 158 208 216
part where all #individualixiyaveragenandindividual"thatproblem,2divide the the sumthe ( x )
this x to individual y"yproducts= youxthesquaressum"xxyou . gets is the 238 of (all
ofof of#n(caseorxithei"67Cholesteroly(mg/100ml)iythexymethodall216individual(12)) !of xi
yname( andthat nnby by squares i
allcalculate )“trend)methodThe yandthethethatof)divideindividual sum ofand similarly, the
#squaresaveragedata points allfromyxay = y ofbx use the thethe linebyto
In dataaverage. i=1 its sum
iy
i "
individual the “trend " (theThethat youindividualyythe “Apply” link.
all sum
individualor =i=1 (line.” products theibetweeni &the x ( all
products
x pushing i that a
products divide " %by! gets .x
by i=1 the’
the prepare the squares
egression”y(leasti=1 toindividual! squares) byTheto icalculateya iyouaits) name the (least a values (because
n”,the sloperegression”is thebetweennb minimizingitsisnumberisof calculated fromall
“linear bb slope (see below) line.”have= byinterceptis of !then the sum
he squares havesquaresxxi(least age)byindividualixmethod moreithen bHint: to add of the = data"(cholesterol) divided hat
emodel.of theinput i calculate )slopedivided n" intercept (the)slope is calculatedthe data " bx A (because line has
squares) ( "Youthatthe ixgets and!2 sum ! of = showing
i The
just2 data$ plotted.
e x idata( y i " prepare nxni graph showing the data n Incase the age)terms, by the numberthe data of all (12) data s
ate"the and ) == !2 y 2
te x ) slope
estimates
data "!
graph n
(e of this problem," nai$a.will the22”best fitthe2 linearxequationsquareswilldivided x the linearplotted. that 11 fits
of sum
and
For the first2 x .
this 1 y
problem, you
calculate average equat…