Statistics: ANOVA, Regression Analysis and Frequency Distribution Table

This article covers ANOVA, Regression Analysis and Frequency Distribution Table in Statistics. It includes sample size, hypothesis testing, coefficient of determination, coefficient of correlation, ANOVA table, regression output and slope coefficient interpretation.

Statistics
Student Name:
Instructor Name:
Course Number:
8 September 2018

1. a. Construction of a frequency distribution table with cumulative frequencies and the
frequency percentages
answer
ro pg u re encf qu y
elati eR v
re encf qu y
c m lati eu u v
re encf qu y elati e c mR v u re enc% f qu y
50-59 3 0.15 3 0.15 15
60-69 2 0.1 5 0.25 10
70-79 5 0.25 10 0.5 25
80-89 4 0.2 14 0.7 20
90-99 6 0.3 20 1 30
b. construction of histogram
answer
T e i to ram trend p ard indicatin t at indi id al t dent per ormance a oodh h s g s u w s g h v u s u s’ f w s g
2. a ample i e or t e pro lem. s s z f h b
39+1=40
etermine et er or not demand and nit price are related eb. D wh h u . Us α = 0.05.
An ersw
e comp te t e t al eW u h -v u
t−value= coefficient
Standard error = 0.029
0.021 =1.3809
T e a ociated p al e i t i al e i reater t anh ss -v u s 0.399008; h s v u s g h 0.05, we therefore fail to reject
the null hypothesis and conclude that there is no relationship between the sales and
individual prices of the goods produced.
c omp te t e coe icient o determination and ll interpret it meanin e er peci ic. C u h ff f fu y s g. B v y s f .
Y=54.076+0.029x
55 60 65 70 75 80 85 90 95 More
0
1
2
3
4
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
i to ramH s g
re encF qu y
m lati eCu u v %
50
re encF qu y

R2= EE
TSS = 354.689
354.689+7035.262 = 354.689
7389.951 =0.047996
T e coe icient o determination i t i implie t at o t e ariation in t eh ff f s 0.047996; h s s h 4.7996% f h v h
dependent aria le i e plained t e independent aria le in t e modelv b s x by h v b h .
d omp te t e coe icient o correlation and e plain t e relation ip et een ppl and nit. C u h ff f x h sh b w su y u
price.
Coefficient of correlation= √ R2=R
Coefficient of correlation= √ 0.047996=0.2191
T e coe icient o correlation i t i o t at a ea po iti e relation ip e i th ff f s 0.21921; h s sh ws h w k s v sh x s s
et een demand and price T at i increa in demand o ld re lt to an increa e in t e priceb w . h s, s g w u su s h .
e Predict t e ppl in nit en t e nit price i. h su y ( u s) wh h u s $50,000
Y=54.076+0.029(50000)
=$1504.076
3. a on tr ction o A A ta le or t e increa e in prod cti it t ro pro ram A to. C s u f NOV b f h s u v y h ugh g s D
pot e e
hy h s s
H1 t e pro ram A to pro ram a e ot no i ni icant increa e in t e prod cti it o: h g s g D h v g s g f s h u v y f
cooperation line or er’s w k s
H2 t e pro ram A to pro ram a e ot i ni icant increa e in t e prod cti it o: h g s g D h v g s g f s h u v y f
cooperation line or er’s w k s
A A ta le
NOV b
Ano a in lev : S g
actorF
MMASU RY
ro p
G u s
o nt
C u mSu A era e
v g ariance
V
Pro ram Ag 5 725 145 525
Pro ramg B 5 675 135 425
Pro ramg C 5 950 190 312.5
Pro ramg D 5 750 150 637.5
A ANOV
o rce o
S u f
ariation
V
SS df MS
F P al e
-v u crit
F
et een ro pB w G u s 8750 3 2916.667 6.140351 0.00557 3.23887

it in ro pW h G u s 7600 16 475
Total 16350 19
(α=0.05)
Ad i eb. v s
ince t e comp ted i reater t an t e critical and t e p al eS h u F (6.140350877) s g h h F (3.238871517) h v u0.005569864 i le t ans ss h
0.05, e re ect t e n ll pot e i and concl de t at t ere i a i ni icantw j h u hy h s s u h h s s g f
increa e in prod ction rom t e pro ram applied e t ere ore ad i e t e compan to contin e its u f h g s . W h f v s h y u w h
t e pro ramh g s.
4. a at i t e e timated re re ion e ation o t e re re ion o tp t. Wh s h s g ss qu ? Sh w h g ss u u
oe icient
C ff
s
tandard
S rror
E
t tatS P al e
-v u o er
L w 95% pper
U 95%
nterceptI 3.5976 4.0522 0.8878 0.4248 -7.6532 14.8484
Price (x1) 41.3200 13.3374 3.0981 0.0363 4.2896 78.3505
Ad erti inv s g (x2) 0.0132 0.32759 0.0404 0.9697 -0.8963 0.9228
Sales=3.5976+41.3200( Price)+ 0.01324( Advertising)
etermine et er t e model i i ni icant o erall eb. D wh h h s s g f v . Us α = 0.10.
A ANOV df SS MS F
i ni ican
S g f
ce F
e re ioR g ss
n 2
45.3528
4
22.6764
2
6.71680
1 0.052644
e id alR s u 4 13.5043
3.37607
5
Total 6
58.8571
4
A can e een t e a o e ta le t e p al e or t e tati tic i a al e le t ans b s I h b v b , h -v u f h F-s s s s 0.0526 ( v u ss h α = 0.10),
t i lead to re ection o t e n ll pot e i and t e concl de t at t e o erall model ih s s j f h u hy h s s hus w u h h v s
i ni icant ats g f α = 0.10.
c. etermine i competitor price and ad erti in i indi id all i ni icantl related to ale eD f ’s v s g s v u y s g f y s s. Us α =
0.10.
ompetitor price ale
C
s vs s s
oe icient
C ff s tandar
S
t tatS P al e
-v u o er
L w pper
U

d rror
E
95% 95%
nterceptI 3.5818 3.6082 0.992676 0.366447 -5.69342 12.857
Price 41.6031 10.1552 4.096719 0.009385 15.49825 67.70786
Ad erti ement ale
v s vs s s
oe icient
C ff
s
tandard
S rror
E
t tatS P al e
-v u
o er
L w
95%
pper
U
95%
nterceptI 14.71053 3.108829 4.731854 0.005188 6.719026 22.70203
Ad erti ementv s 0.546053 0.459802 1.187582 0.288334 -0.63591 1.728011
ndependentl t e competitor price a ot a i ni icant relation ip on t e ale o ood a t eI y, h ’s h s g s g f sh h s s f g s s h
p al e ile t e ad erti ement a ot no i ni icant relation ip it t e ale o t ev u , 0.00938 wh h v s h s g s g f sh w h h s s f h
prod ct a t e al e i reater t an t e pot eticalu s h v u 0.28833 s g h h hy h 0.10
d. a ed on o r an er to part c drop an in i ni icant independent aria le and re e timate t eB s y u sw ( ), y s g f v b (s) - s h
model at i t e ne e timated re re ion e ation. Wh s h w s g ss qu ?
An ersw
T e in i ni icant aria le i t e ad erti ement and it i dropped t t e ne re re ionh s g f v b s h v s s hus h w g ss
e ation iqu s;
Y =3.581788+ 41.60305( Price)
e. nterpret t e lope coe icient o t e model rom part dI h s ff (s) f h f ( ).
An ersw
T e lope coe icient or t e competitor price i t i implie t at a nit increa e in t eh s ff f h ’s s 41.6031; h s s h u s h
competitor price o ld re lt to an increa e in t e ale made imilarl a nit’s w u su s h s s by 41.6031. S y, u
decrea e in t e competitor price o ld re lt to a decrea e in t e ale mades h ’s w u su s h s s by 41.6031.