3/29/05 251grass2-051
(Open this document in 'Page Layout' view!) Graded Assignment 2 Name:
Class days and time:
Student number:
Modify the data below as follows: Add the last digit of your student number to 7 in problem 1; Add the second to last number to the 9 in problem 2.
1) For the following joint probability table (i) check for independence, (ii) Compute and , (iii) Compute or and or, (iv) Compute and from the results in (ii) and (iii), (iv) Compute and using the formulas in section K4 of 251v2out or section C1 of 251var2. Note that .
2) For the following sample (i) Compute the sample mean and variance of , (ii) Compute or and or , (iii) Compute the sample mean and variance of from the results in (i) and (ii). (iv) Compute and using the formulas in section K4 of 251v2out or section C1 of 251var2. Note that .
9 / 24 / 4
6 / 2
2 / 5
1 / 7
1 / 6
3 / 5
10 / -3
————— 4/11/2005 6:37:46 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\2gr2-051.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\2gr2-051.MTW'
Worksheet was saved on Tue Feb 08 2005
Results for: 2gr2-051.MTW
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\1gr1-051ab.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\1gr1-051ab.MTW'
Worksheet was saved on Wed Feb 02 2005
Population Correlation Problem
Results for: 1gr2-051ab.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\1gr2-051ab.MTW";
SUBC> Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\1gr2-051ab.MTW'
MTB > echo
MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\251popcorr.mtb" 1.
Executing from file: C:\Documents and Settings\rbove\My Documents\Minitab\251popcorr.mtb
MTB > #251popcorr
MTB > # Computes population covariance and correlation
MTB > # Put x in C15, y in c17
MTB > # Put a joint probability table in c10 - c14
MTB > # Fill table with zeros to make it 5 by 5.
MTB > name k10 'varx'
MTB > name k11 'vary'
MTB > name k12 'Exy'
MTB > name k13 'covxy'
MTB > name k14 'corr'
MTB > name k15 'sdx'
MTB > name k16 'sumpx'
MTB > name k17 'sdy'
MTB > name k18 'sumpy'
MTB > name k25 'Ex'
MTB > name k26 'Ex2'
MTB > name k27 'Ey'
MTB > name k28 'Ey2'
MTB > execute 'marg973'
Executing from file: marg973.MTB
MTB > #marg973.mtb #part of 251popcorr Computes marginal probs
MTB > let c18=c10+c11+c12+c13+c14
MTB > let c16(1)=sum(c10)
MTB > let c16(2)=sum(c11)
MTB > let c16(3)=sum(c12)
MTB > let c16(4)=sum(c13)
MTB > let c16(5)=sum(c14)
MTB > let k16=sum(c16) #These are sums of x and y
MTB > let k18=sum(c18) #probabilities and should be 1.
MTB > print c10-c18
Data Display
Row C10 C11 C12 C13 C14 C15 C16 C17 C18
1 0.11 0.08 0.16 0 0 3 0.33 1 0.35
2 0.10 0.14 0.10 0 0 5 0.30 3 0.34
3 0.12 0.08 0.11 0 0 7 0.37 9 0.31
4 0.00 0.00 0.00 0 0 0 0.00 0 0.00
5 0.00 0.00 0.00 0 0 0 0.00 0 0.00
MTB > end
MTB > execute 'meany973'
Executing from file: meany973.MTB
MTB > #meany.973.mtb part of 251popcorr
MTB > print k16,k18
Data Display
sumpx 1.00000
sumpy 1.00000
MTB > let c20=c10*c17
MTB > let c20=c20*c15(1)
MTB > let c21=c11*c17
MTB > let c21=c21*c15(2)
MTB > let c22=c12*c17
MTB > let c22=c22*c15(3)
MTB > let c23=c13*c17
MTB > let c23=c23*c15(4)
MTB > let c24=c14*c17
MTB > let c24=c24*c15(5)
MTB > let c25=c15*c16 # xP(x)
MTB > let k25=sum(c25) # E(x)
MTB > let c27=c17*c17
MTB > let k27=sum(c27) # E(y)?
MTB > end
MTB > execute 'meanz973'
Executing from file: meanz973.MTB
MTB > #meanz973.mtb part of 251popcorr
MTB > let c27=c17*c18
MTB > let k27=sum(c27) #E(y)
MTB > end
MTB > execute 'exysq973'
Executing from file: exysq973.MTB
MTB > #exysq973.mtb part of 251popcorr
MTB > let c26=c15*c25 # xsqP(x)
MTB > let c28=c17*c27 # ysqP(y)
MTB > let k26=sum(c26) # E(xsq)
MTB > let k28=sum(c28) # E(ysq)
MTB > print c20-c28
Data Display
Row C20 C21 C22 C23 C24 C25 C26 C27 C28
1 0.33 0.4 1.12 0 0 0.99 2.97 0.35 0.35
2 0.90 2.1 2.10 0 0 1.50 7.50 1.02 3.06
3 3.24 3.6 6.93 0 0 2.59 18.13 2.79 25.11
4 0.00 0.0 0.00 0 0 0.00 0.00 0.00 0.00
5 0.00 0.0 0.00 0 0 0.00 0.00 0.00 0.00
MTB > print k25-k28
Data Display
Ex 5.08000
Ex2 28.6000
Ey 4.16000
Ey2 28.5200
MTB > end
MTB > execute 'xyvar973'
Executing from file: xyvar973.MTB
MTB > #xyvar973.mtb part of popcorr
MTB > let k10=k26-k25*k25 #variance of x
MTB > let k11=k28-k27*k27 #variance of y
MTB > print k10 k11
Data Display
varx 2.79360
vary 11.2144
MTB > let k20=sum(c20)
MTB > let k21=sum(c21)
MTB > let k22=sum(c22)
MTB > let k23=sum(c23)
MTB > let k24=sum(c24)
MTB > let k12 = k20+k21+k22+k23+k24 # E(xy)
MTB > print k20-k24, k12
Data Display
K20 4.47000
K21 6.10000
K22 10.1500
K23 0
K24 0
Exy 20.7200
MTB > end
MTB > execute 'cov973'
Executing from file: cov973.MTB
MTB > #cov973.mtb part of popcorr
MTB > let k13=k12-k25*k27 #Covariance
MTB > let k15=sqrt(k10) #St. dev of x
MTB > let k17=sqrt(k11) #St. dev of y
MTB > let k14=k13/k15
MTB > let k14=k14/k17 #Corr(x, y)
MTB > print k13-k18
Data Display
covxy -0.412800
corr -0.0737513
sdx 1.67141
sumpx 1.00000
sdy 3.34879
sumpy 1.00000
MTB > end
MTB > execute 'tb2973'
Executing from file: tb2973.MTB
MTB > #tb2973.mtb Part of 251popcorr
MTB > let k30=30
MTB > let k31=10
MTB > let k32=1
MTB > execute 'tb2s973' 5
Executing from file: tb2s973.MTB
MTB > #tb2s973.mtb Subroutine of tb2973
MTB > # Part of popcorr
MTB > let ck30=ck31
MTB > let ck30(6)=c16(k32)
MTB > let ck30(7)=c25(k32)
MTB > let ck30(8)=c26(k32)
MTB > let k30=k30+1
MTB > let k31=k31+1
MTB > let k32=k32+1
MTB > end
MTB > #tb2s973.mtb Subroutine of tb2973
MTB > # Part of popcorr
MTB > let ck30=ck31
MTB > let ck30(6)=c16(k32)
MTB > let ck30(7)=c25(k32)
MTB > let ck30(8)=c26(k32)
MTB > let k30=k30+1
MTB > let k31=k31+1
MTB > let k32=k32+1
MTB > end
MTB > #tb2s973.mtb Subroutine of tb2973
MTB > # Part of popcorr
MTB > let ck30=ck31
MTB > let ck30(6)=c16(k32)
MTB > let ck30(7)=c25(k32)
MTB > let ck30(8)=c26(k32)
MTB > let k30=k30+1
MTB > let k31=k31+1
MTB > let k32=k32+1
MTB > end
MTB > #tb2s973.mtb Subroutine of tb2973
MTB > # Part of popcorr
MTB > let ck30=ck31
MTB > let ck30(6)=c16(k32)
MTB > let ck30(7)=c25(k32)
MTB > let ck30(8)=c26(k32)
MTB > let k30=k30+1
MTB > let k31=k31+1
MTB > let k32=k32+1
MTB > end
MTB > #tb2s973.mtb Subroutine of tb2973
MTB > # Part of popcorr
MTB > let ck30=ck31
MTB > let ck30(6)=c16(k32)
MTB > let ck30(7)=c25(k32)
MTB > let ck30(8)=c26(k32)
MTB > let k30=k30+1
MTB > let k31=k31+1
MTB > let k32=k32+1
MTB > end
MTB > let c35=c18
MTB > let c35(6)=k18
MTB > let c35(7)=k25
MTB > let c35(8)=k26
MTB > let c36=c27
MTB > let c36(6)=k27
MTB > let c37=c28
MTB > let c37(6)=k28
MTB > print c30-c37
Data Display
Row C30 C31 C32 C33 C34 C35 C36 C37
1 0.11 0.08 0.16 0 0 0.35 0.35 0.35
2 0.10 0.14 0.10 0 0 0.34 1.02 3.06
3 0.12 0.08 0.11 0 0 0.31 2.79 25.11
4 0.00 0.00 0.00 0 0 0.00 0.00 0.00
5 0.00 0.00 0.00 0 0 0.00 0.00 0.00
6 0.33 0.30 0.37 0 0 1.00 4.16 28.52
7 0.99 1.50 2.59 0 0 5.08
8 2.97 7.50 18.13 0 0 28.60
MTB > write c30-c37.
Data Display (WRITE)
0.11 0.08 0.16 0 0 0.35 0.35 0.35
0.10 0.14 0.10 0 0 0.34 1.02 3.06
0.12 0.08 0.11 0 0 0.31 2.79 25.11
0.00 0.00 0.00 0 0 0.00 0.00 0.00
0.00 0.00 0.00 0 0 0.00 0.00 0.00
0.33 0.30 0.37 0 0 1.00 4.16 28.52
0.99 1.50 2.59 0 0 5.08 * *
2.97 7.50 18.13 0 0 28.60 * *
* NOTE * Column lengths not equal.
MTB > end.
MTB > execute 'tb3973'
Executing from file: tb3973.MTB
MTB > #tb3973.mtb final printout for 252popcorr
MTB > write c20-c24;
SUBC> replace.
Data Display (WRITE)
0.33 0.4 1.12 0 0
0.90 2.1 2.10 0 0
3.24 3.6 6.93 0 0
0.00 0.0 0.00 0 0
0.00 0.0 0.00 0 0
MTB > end
MTB > end
MTB >
Sample Correlation Problem
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\1gr2-051ab.MTW";
SUBC> Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\1gr2-051ab.MTW'
Existing file replaced.
MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\251samcov.mtb" 1.
Executing from file: C:\Documents and Settings\rbove\My Documents\Minitab\251samcov.mtb
MTB > #samcov Computes sample variances
MTB > # and covariances using 'var973'
MTB > #Input is x column in c40, y column in c42
MTB > # Example in Covex
MTB > name c40 'x'
MTB > name c41 'xsq'
MTB > name c42 'y'
MTB > name c43 'ysq'
MTB > name c44 'xy'
MTB > name k40 'sumx'
MTB > name k41 'sumx2'
MTB > name k42 'sumy'
MTB > name k43 'sumy2'
MTB > name k44 'sumxy'
MTB > name k45 'n'
MTB > name k46 'xbar'
MTB > name k47 'ybar'
MTB > name k48 'svarx'
MTB > name k49 'svary'
MTB > name k50 'scovxy'
MTB > name k51 'sx'
MTB > name k52 'sy'
MTB > name k53 'rxy'
MTB > name k54 'rxy2'
MTB > let c1=c40
MTB > execute 'var973'
Executing from file: var973.MTB
MTB >
MTB > #var973.mtb
MTB > #computes sample variance of data in C1.
MTB >
MTB > let k1=sum(c1)
MTB > let c2=c1 * c1
MTB > let k2=sum(c2)
MTB > let k3=count(c1)
MTB > let k4=k1/k3 #mean
MTB > let k5=k3*k4*k4
MTB > let k5=k2-k5
MTB > print k5
Data Display
K5 86.0000
MTB > name k1 'sum'
MTB > name k2 'sumsq'
MTB > name k3 'count'
MTB > name k4 'smean'
MTB > name k5 'svar'
MTB > name k6 'sdev'
MTB > name k7 'DF'
MTB > name k8 'sterr'
MTB > let k7 = k3 - 1
MTB > let k5 = k5/k7
MTB > let k6 = sqrt(k5)
MTB > let k8 = k5/k3
MTB > let k8 = sqrt(k8)
MTB > describe c1
Descriptive Statistics: C1
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
C1 8 0 4.50 1.24 3.51 1.00 1.25 3.50 8.25 10.00
MTB > print c1-c2
Data Display
Row C1 C2
1 9 81
2 4 16
3 6 36
4 2 4
5 1 1
6 1 1
7 3 9
8 10 100
MTB > print k1-k8
Data Display
sum 36.0000
sumsq 248.000
count 8.00000
smean 4.50000
svar 12.2857
sdev 3.50510
DF 7.00000
sterr 1.23924
MTB > end
MTB > let C41=c2
MTB > let k40=k1
MTB > let k41=k2
MTB > let k46=k4
MTB > let k48=k5
MTB > let k51=k6
MTB > let c1=c42
MTB > execute 'var973'
Executing from file: var973.MTB
MTB > #var973.mtb
MTB > #computes sample variance of data in C1.
MTB > let k1=sum(c1)
MTB > let c2=c1 * c1
MTB > let k2=sum(c2)
MTB > let k3=count(c1)
MTB > let k4=k1/k3 #mean
MTB > let k5=k3*k4*k4
MTB > let k5=k2-k5
MTB > print k5
Data Display
svar 70.0000
MTB > name k1 'sum'
MTB > name k2 'sumsq'
MTB > name k3 'count'
MTB > name k4 'smean'
MTB > name k5 'svar'
MTB > name k6 'sdev'
MTB > name k7 'DF'
MTB > name k8 'sterr'
MTB > let k7 = k3 - 1
MTB > let k5 = k5/k7
MTB > let k6 = sqrt(k5)
MTB > let k8 = k5/k3
MTB > let k8 = sqrt(k8)
MTB > describe c1
Descriptive Statistics: C1
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
C1 8 0 3.50 1.12 3.16 -3.00 2.00 4.50 5.75 7.00
MTB > print c1-c2
Data Display
Row C1 C2
1 2 4
2 4 16
3 2 4
4 5 25
5 7 49
6 6 36
7 5 25
8 -3 9
MTB > print k1-k8
Data Display
sum 28.0000
sumsq 168.000
count 8.00000
smean 3.50000
svar 10.0000
sdev 3.16228
DF 7.00000
sterr 1.11803
MTB > end
MTB > let C43=c2
MTB > let k42=k1
MTB > let k43=k2
MTB > let k45=k3
MTB > let k47=k4
MTB > let k49=k5
MTB > let k52=k6
MTB > let c44=c40*c42
MTB > let k44=sum(c44)
MTB > let k50=k45*k46*k47
MTB > let k50=k44-k50
MTB > let k50=k50/k7
MTB > let k53=k51*k52
MTB > let k53=k50/k53
MTB > let k54=k53*k53
MTB > Print c40-c44
Data Display
Row x xsq y ysq xy
1 9 81 2 4 18
2 4 16 4 16 16
3 6 36 2 4 12
4 2 4 5 25 10
5 1 1 7 49 7
6 1 1 6 36 6
7 3 9 5 25 15
8 10 100 -3 9 -30
MTB > Print k40-k54
Data Display
sumx 36.0000
sumx2 248.000
sumy 28.0000
sumy2 168.000
sumxy 54.0000
n 8.00000
xbar 4.50000
ybar 3.50000
svarx 12.2857
svary 10.0000
scovxy -10.2857
sx 3.50510
sy 3.16228
rxy -0.927971
rxy2 0.861130
MTB > end
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\1gr2-051ab.MTW";
SUBC> Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\1gr2-051ab.MTW'
Existing file replaced.
MTB >