Final Exam Excel Statistics

8/16/2019 Final Exam Excel Statistics

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FINAL EXAM MA321 FIT M. KUDINOV

YOUR NAME__________________________________________________

Answer the questions in spaces provided in this firle and submit it here.

Pr1. Time Series.

The data in the table below represent the annual revenues(in billion of dollars)

of McDonald's Corporation over the 3!"ear period from #$% t& &&%.

X Y

Year C!e! Yr X"2 Re#e$%es MA &3'

#$% & & A

#$* . .

#$$ + .+

#$, 3 # .$

#$# + * .#

#,& % % . .

#, * 3* .% .%

#, $ +# ., .,

#,3 , *+ 3. 3.

#,+ # , 3.+ 3.+333333

#,% & && 3., 3.,

#,* +. +.3

#,$ ++ +.# +.#

#,, 3 *# %.* %.%333333

#,# + #* *. *.*****$

##& % % *., *.%333333

## * %* *.$ *.,*****$## $ ,# $. $.&*****$

##3 , 3+ $.+ $.*

##+ # 3* ,.3 ,.%

##% & +&& #., #.*

##* ++ &.$ &.*33333

##$ +,+ .+ .%

##, 3 %# .+ .3****$

### + %$* 3.3 3.3

&&& % *% +. +.33333

&& * *$* +.# +.,33333

&& $ $# %.+ %.,

&&3 , $,+ $. $.****$&&+ # ,+ # ,.,****$

&&% 3& #&& &.% A

a) Calculate a three!"ear movin- avera-e to the data (add a column to the table)

&COLUMN ADDED A(OVE'


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b) sin- a smoothin- coefficient of / 0 &.$%1 e2ponentiall" smooth the series

(add a column to the table1 use data anal"sis to smooth)

&COLUMN ADDED A(OVE'

c) lot the results from a) and b) with the time series.

d) Compute a quadratic trend forecastin- equation and plot the predicted result with the data a-ainst the co

4MMA56 7TT

Regression Statistics

Multiple 5 &.##$*$*33

5 4quare &.##%*&,%+#

Ad8usted 5 4quare &.##+#3++%

4tandard 9rror &.+&*+3*#3$*

7bservations 3

A7:A

df SS MS F

5e-ression #$.3*3#+3$$* +,%.*,#$,# #+&.#3

5esidual , +.*%3+$%%$# &.*%#,+

Total 3& #$%.#,$$+#3%%

Coefficients Standard Error t Stat P-value

;ntercept .3,%*3&+#,% &.&%%,,++3* *.$3#,*$,+3 .%*9!&&$

Coded 6r &.&+%#&+ &.&3$** .3+*#*3*, &.#&%+#


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e) Compute an e2ponential trend forcastin- equation and plot the predicted results with the data a-ainst the

4MMA56 7TT

Regression StatisticsMultiple 5 &.##&,#&%%

5 4quare &.#,3,#%

Ad8usted 5 4quare &.#,%3$&%

4tandard 9rror &.&%*+&$

7bservations 3

A7:A

df SS MS F

5e-ression +.%*&3#,$* +.%*&3#,$* %#+.%,+#

5esidual # &.&$$3+&& &.&&***#&3%

Total 3& +.3##++,,$

Coefficients Standard Error t Stat P-value

;ntercept &.3&%&&* &.&,&3,*# $.&%#3+%, *.9!&&,

Coded 6r &.&++*%*, &.&&&3*##$$ 3#.#3%3*$# *.**9!&$

b& 0 &=&.3 .3%&%3*,,

Y ) 1.341.1"X

b 0 &= &.&+ .&&&+#,$

f) Compute a second !order autore-ressive model1 test for the si-nificance of the second!order

autore-ressive parameter.

4MMA56 7TT


Multiple 5 &.##,%&,#$

5 4quare &.##$&,+,%

Ad8usted 5 4quare &.##*$,#3$,

4tandard 9rror &.3$,33+&%3

7bservations #

A7:A

df SS MS

5e-ression ,$,.#+* +3#.+%$3

5esidual * .**+*## &.&&,

Total , ,,&.#$#3&3+

Coefficients Standard Error t Stat

a& ;ntercept &.*+%+%, &.&$&*&3$ .&++*

a < :ariable .3&&+*,* &.#&$#% *.,+$3

a < :ariable !&.+#&3$*3&+ &.&++3%3%*# !.,$3


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p 0 Yi ) ,.11+1.3,Yi51 5 ,.2-*Yi52

tscore 0 a>4a 0 !.,$###

t critical ? #!@! .&*+

4ince t score of the a ! ., is less than the critical value ! .&*+ the initial assumption is

accepted. The third!order autore-ressive parameter is not si-nificantl" lar-e

and the contribution of its term to the model is not si-nificant

-) Compute a first!order autore-ressive model1 test for the si-nificance of the first!oder

autore-ressive parameter1 and plot the predicted results with the data a-ainst the coded "ears.

4MMA56 7TT


Multiple 5 &.##,%&+&3%%

5 4quare &.##$&&3&,,

Ad8usted 5 4quare &.##*#&3%3+

4tandard 9rror &.3+,#+#%

7bservations 3&

A7:A

df SS MS

5e-ression #%.,,*+&*3 #%.,,*

5esidual , .$$*+&*&3# &.#%$

Total # #,.*%,*****$


a& ;ntercept &.3+,%##*,* &.#%#3#* .3%+,+

a < :ariable .&$&%&$&$# &.&&$+*3 #*.*3&,3

p0 Yi ) ,.13+1.,6Yi51

tscore 0 a>4a 0 #*.*3&,*&

t critical ? 3&!@! .&%

critical value!.&*+

t0 ! .,


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4ince t score of the a #*.*3 is more than the critical value .&% the initial assumption is

re8ected. The first!order autore-ressive parameter is si-nificantl" lar-eand the contribution of its term to the model is si-nificant

Pr2 Sim7e Li$ear Reressi$.

The owner of a chain of ice cream store would lie to stud"

the effect of atmosperic temperature on sales durin- the summer season.

A sample of consecutive da"s is selected1 with the results stored in the table below

X Y

Tem7era/%re8 i$ !erees Saes8 i$ /9%sa$! : ; 9a/ ) 52.3- + ,.,


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4MMA56 7TT

Regression StatisticsMultiple 5 &.#*#%3+3,

5 4quare &.#3###*$,$

Ad8usted 5 4quare &.#3*,3,$$*

4tandard 9rror &.+*&$%##$

7bservations

A7:A

df SS MS

5e-ression *.3%+&%%#%## *.3%+&%*

5esidual # &.+&%*&,# &.&3+$+

Total & *.$%#*%$+#


b& ;ntercept !.%3+#,%#&+* &.#%3** !,.%,**$+

b Temperature1 in de-rees &.&*&$$#,*3 &.&&3%##+$+ $.%%$

Y9a/ ) 52.3- + ,.,


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&>RAP?ED IN SCATTER PLOT A(OVE'

b 0 &.&*

/hen the temperature outside increases b" a de-ree the sales that da" increase b" &.&* thousand dollars

b& 0 !.%3%

/hen the temperature outside is & de-rees the sales for that da" is !.%3% thousand dollars

(this statement doesn't mae sense)

Y9a/ ) 52.3- + ,.,


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alpha &.&% t critical !0 .

!0#

&

since t score of the slope $.% is -reater then the critical value . the initial

re8ected. The slope is si-nificantl" lar-er than Gero. 5elationship is stron-. ine

Pr3. A$#a $e :a0/r

;n order to test the stren-th of four brands of trash ba-s1

one!pound wei-hts were placed into ba-s1 one at a time

until the ba- broe.

A total of +& ba-s1 & of each brand1 were used. The data in the table below

-ives the wei-ht required to brea the trash ba-.

KRO>ER >LAD ?EFTY UFFSTUFF

3+ 3 33 *

3& + 3+ ,+& 3+ 3 &

3, 3* +& %

3* 3 +& &

3& +& 3+ &

3& 3* 3* $

+ +3 3+ ,

3* 3& 3 #

3, 3, 3+ &

4ample Mean < bar 0 3%.+ 3*.3 3+.# #.3

of the differences in the mean stren-th of the four brands of trash ba-s .

44/

KRO>ER (2 ! 2bar)= >LAD (2 ! 2bar)=

3+ .#* 3 ,.+#

3& #.* + 3.+#

a' sin- Data anal"sis>Anova1 test at the level of si-nificance &.&% for the evidence

critical value!.

critical value.

t0$.


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+& .* 3+ %.#

3, *.$* 3* &.

3* &.3* 3 ,.+#

3& #.* +& 3.*#

3& #.* 3* &.

+ +3.%* +3 ++.,#

3* &.3* 3& 3#.*#3, *.$* 3, .,#

Total *,.+ $*.

?EFTY (2 ! 2bar3)= TUFFSTUFF (2 ! 2bar+)=

33 3.* * ++.,#

3+ &., , .*#

3 ,.+ & &.+#

+& *.& % ,.+#

+& *.& & &.+#

3+ &., & &.+#

3* . $ %.#

3+ &., , .*#

3 ,.+ # &.

3+ &., & &.+#

Total $*.# $+.

SS@ ) +#%.%

44A

2bar n8@(2bar!2dbar)=

3%.+ %+.&%*%

3*.3 3.,&*%

3 3+.# $.3&*%

+ #.3 +,.3&*%

< Doublebar 3.+$% #,*.+$%

M4/ 0 44/>n!c M4A 0 44A>c!

M4/ 0 3.$*3,,,,,,#

M4A 0 **.%,3333333

F 0 M4A > M4/ F0 +,.&,3$%3$,+

column c! +!03

row n!c +&!+03* .,*


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Fu 0 .,*

&

Fu 0 .,*

4ince F calculated is more than Fu the M4A is si-nifi

That is the differences amon- -roup means are si-ni

(not random but due to the actual differences in qua

Anova? 4in-le Factor

4MMA56

Groups Count Sum Average Variance

H57E95 & 3%+ 3%.+ ,.$

EAD & 3*3 3*.3 #.%****$

I9FT6 & 3+# 3+.# ,.%++++++

TFF4TFF & #3 #.3 ,.333333

A7:A

Source of Variation SS df MS F

Jetween Eroups #,*.+$% 3 **.%,333333 +,.&,3$%

/ithin Eroups +#%.% 3* 3.$*3,,,,,,#

Total +,.#$% 3#

se Tue"!Hramer procedure. Means < bar

Absolute 3

air Difference 3%.+ 3*.3 3+.#

airs

&.#

3 &.%

+ *.

3 .+

+ $

3 + %.*

column 0 c +

=' ;f appropriate1 determine which brands differ in mean stren-th


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rows 0 n!c +&!+ 0 3*

Ku studentiGed 3.,

critical ran-e +.+*#,$*,*

*.

&.# $

&.% %.*

.+

differences

c.r.0+.+$

C$0%si$

There are several si-nificant differences ? between the fourth sample and all other samples (113). All oth

means which do not si-nificantl" differ one from another.


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_____

5= 0 ##.+#B 5= 0 #,.%B

ES &,.6' %a!ra/i0 &Y' E7$e$/ia La 1 La 2

.3,%*3&% & .3%&%3*# >A >A

.% .++$&%$# &.&$#, .+,%*3+ >A

.33$% .%+*3%* &.+*, .*3+*3# .

.*$% .*,,$,#* &.3&++# .$#$$%$$, .+ .

.,$3++ .,%$,,+ &.$,$%+ .#$$*&,+ .$ .+

.&*,3* .&*#3+$% &.3++3 .$%+%*#3 .# .$

.+&$ .3#&$ &.3#$#+ .3#3*+ . .#

.$&&+$ .*&*+%$*, &.++$%, .*3%&,*3 .% .

3.&&&&$ .#3%&3*# &.+#3* .,#%,$** ., .%

3.3&&&$ 3.#+&3 &.%3+$# 3.,%%,++ 3. .,

3.*$%&&$ 3.*#+%$$3 &.%$#$,+ 3.%&+$#$# 3.+ 3.

+.&*,$% +.3*&+# &.*3+# 3.,%+,%,+ 3., 3.+

+.*#,, +.*&,#3&% &.*#&#* +.+&%#% +. 3.,

%.3$3&+$ %.*+$ &.$+,,, +.**+$+3+ +.# +.

%.#,* %.*$*% &.$,%33 %.3+, %.* +.#

*.%$#%*% *.*3&** &.,3% %.*++$,&+, *. %.*

*.**#,# *.,,$*% &.,*&$% *.%&, *., *.*.##+$3 $.%%*+$ &.,%%, *.,3&$,3 *.$ *.,

$.#,, ,.%3#3&% &.,*#3 $.%+&,3*# $. *.$

,.&+#%3 ,.##*&+# &.##&$, ,.*%,%&* $.+ $.

#.3*3, #.$*#%$$3 &.##* #.$%# ,.3 $.+

&.3*%* &.%,+& .&#3,+ &.&&+, #., ,.3

.++ .+3*%&3$ .&%*#&% .&&3&,#$ &.$ #.,

.&,%3% .3*+%$$ .+ .&3,$$ .+ &.$

.##*3+ 3.%+&$ .3,% 3.3+$$# .+ .+

3.,##&, +.#3+$3 .%,, +.*+*,#% 3.3 .+

+.*+#$$ %.,, .$3,* *.+ +. 3.3

%.++ *.*,$# .,$% $.$+&+,# +.# +.

*.*, $.3+3%* .3##* #.+#$%* %.+ +.#,.+&$&3 ,.+%$&%, .$,$%+ .++$$$%3 $. %.+

#.#$*$* #.*&*3&% .3$%+ 3.%#3+$+# # $.


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ded "ears.

ignificance F

.#9!&33

Lower !" #pper !" ower !$% #pper !$%"

&.#*+%& .,&*$%#33 &.#*+%& .,&*$%#33

!&.&3# &.&$%$&&, !&.&3# &.&$%$&&,

&.&*$3$ &.&3# &.&*$3$ &.&3#

e

3%

5evenues

MA (3)

94 (&.$%)

& % &

&

%

&

%

&

%


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coded "ears.

ignificance F

*.$9!&$

Lower !" #pper !" ower !$% #pper !$%"

&.+* &.*$%+ &.+* &.*$%+

&.&3#,# &.&+3%3&%* &.&3#,# &.&+3%3&%*

E7$e$/ia M!e

F Significance F

+3+$. .+$9!&33

P-value Lower !" #pper !"Lower !$%" pper !$%"

&.3%& !&.&+&# &.3#$ !&.&+&# &.3#$

3.&9!&&$ &.##%# .*#+,3 &.##%# .*#+,3

&.3+, !&.**#*&% &.$,% !&.**#*&% &.$,%

& % & %

&

%

&

%

&

%


15/33

&

F Significance F

#33$.%* *.,9!&3$


&.,*%3+ !&.&*#+,#3 &.33,,*# !&.&*#+,#3 &.33,,*#

*.,9!&3$ .&+$+*%3% .,3* .&+$+*%3% .,3*

critical value.&*+

t 0 #*.*3


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&critical value.&%


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F Significance F

#$.*+#$ +.%,,9!&3


%.,9!&&, !3.%,#%3 !.#$&, !3.%,#%3 !.#$&,

+.*9!&3 &.&%33*&*% &.&*,% &.&%33*&*% &.&*,%

&%


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,% #& #% && &%

hat


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assumption is

r model is appropriate.

c 0 +

n8 0 &n 0 +&

%


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F 0 +,.&,

cantl" lar-er than M4/

ficant

lit" ).

P-value F crit

.9!& .,***%%%

+

#.3


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r samples have


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& % 3& 3%

5evenues

Kuadratic

92ponentia

l


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Final Exam Excel Statistics