Question

In: Statistics and Probability

Use the “d_logret_6stocks” dataset to answer the questions. (General Motor: GenMotor)（using R） (1) Regress the return...

Use the “d_logret_6stocks” dataset to answer the questions. (General Motor: GenMotor)（using R）

(1) Regress the return of General Motor on the returns of Citigroup with intercept and without intercept, respectively. Report the estimated coefficients.

(2) Generate an ANOVA table to conclude if regression effects are significant.

(3) Compute the correlation of General Motor and Citigroup, and test if their correlation is

zero.

(4) Test if the proportion of returns of Citigroup greater than Pfizer is 0.6.

dataset below

Date   Pfizer   Intel   Citigroup   AmerExp   Exxon   GenMotor
1-Aug-00   -0.001438612   0.049981263   0.044275101   0.017410003   0.010224894   0.093294017
1-Sep-00   0.017489274   -0.255619266   -0.033536503   0.012656982   0.03798902   -0.032209239
2-Oct-00   -0.017046116   0.034546736   -0.011645582   -0.004897625   0.000330555   -0.019602167
1-Nov-00   0.012012934   -0.072550667   -0.022674793   -0.03827587   -0.00365002   -0.0948916
1-Dec-00   0.016278701   -0.102497868   0.010708311   0   -0.005252049   0.012461253
2-Jan-01   -0.008063083   0.090223122   0.03990062   -0.066129678   -0.014169243   0.022971579
1-Feb-01   -0.00042298   -0.11219423   -0.055096146   -0.030733152   -0.014046895   0.000824088
1-Mar-01   -0.040906294   -0.035702138   -0.038726816   -0.026380545   -0.000240008   -0.012105099
2-Apr-01   0.024190228   0.069994483   0.038511978   0.011868735   0.038897488   0.024082196
1-May-01   -0.002978787   -0.05826061   0.019333184   -0.002446047   0.002844256   0.020148775
1-Jun-01   -0.029781389   0.03463487   0.013258067   -0.03564197   -0.006813464   0.053440295
2-Jul-01   0.012504432   0.008168789   -0.022187219   0.017739418   -0.019481402   -0.005100405
1-Aug-01   -0.0306632   -0.027529477   -0.038475736   -0.044368019   -0.01460743   -0.061635162
4-Sep-01   0.01981548   -0.135934121   -0.053479798   -0.098043942   -0.008224146   -0.105946472
1-Oct-01   0.019063731   0.077211653   0.050835509   0.006689711   0.00061005   -0.016274333
1-Nov-01   0.015543895   0.126580684   0.02356606   0.048543672   -0.020726234   0.08521096
3-Dec-01   -0.036145791   -0.016421934   0.022871285   0.035242521   0.021578866   -0.009657415
2-Jan-02   0.019356687   0.046876533   -0.025940517   0.002871379   -0.002807817   0.022139216
1-Feb-02   -0.006050198   -0.088680731   -0.020151007   0.007237226   0.026948074   0.01967222
1-Mar-02   -0.013187975   0.027384065   0.039197815   0.050683167   0.025807264   0.057331233
1-Apr-02   -0.038640426   -0.026448085   -0.058277811   0.00137534   -0.037828005   0.025768635
1-May-02   -0.020012226   -0.014900615   0.000481346   0.015691714   -0.000118352   -0.010495544
3-Jun-02   0.00498962   -0.179572434   -0.046948457   -0.068454444   0.010640133   -0.065487824
1-Jul-02   -0.034159152   0.01226155   -0.062746165   -0.01186007   -0.0465282   -0.060041503
1-Aug-02   0.011452067   -0.051537916   0.022330581   0.009740522   -0.013050696   0.016998701
3-Sep-02   -0.056822917   -0.079127863   -0.043102044   -0.063162423   -0.045786933   -0.090010126
1-Oct-02   0.039382501   0.09536996   0.097624046   0.067951966   0.023357105   -0.068058029
1-Nov-02   -0.001620779   0.082000518   0.022127194   0.029514688   0.017231827   0.083238291
2-Dec-02   -0.013493147   -0.127500953   -0.043258124   -0.040869439   0.001739589   -0.032155007
2-Jan-03   -0.000914625   0.002562217   -0.008110182   0.002151752   -0.009860009   -0.006417575
3-Feb-03   -0.007697729   0.042681011   -0.012956568   -0.024428147   0.001227785   -0.025617995
3-Mar-03   0.01899439   -0.025156666   0.014203546   -0.004565156   0.011692992   -0.001942487
1-Apr-03   -0.005686915   0.053056729   0.056727624   0.057647618   0.003171011   0.030362391
1-May-03   0.005686915   0.054144721   0.021322255   0.041490099   0.01767084   -0.00280191
2-Jun-03   0.041784483   -0.000213046   0.018444872   0.001579917   -0.005981586   0.008214181
1-Jul-03   -0.010109859   0.077829522   0.023189447   0.024870758   -0.003990877   0.016906014
1-Aug-03   -0.045266311   0.06043443   -0.01419843   0.008620388   0.028166116   0.046380496
2-Sep-03   0.006546894   -0.016587184   0.021075597   0.000112293   -0.01291723   -0.001791893
1-Oct-03   0.017184425   0.078321576   0.020888904   0.018572284   -0.00024981   0.018169063
3-Nov-03   0.028255616   0.007861351   -0.003462108   -0.01144524   -0.001501884   0.006155458
1-Dec-03   0.022153888   -0.019719492   0.013782077   0.024270976   0.054151115   0.096343714
2-Jan-04   0.015748075   -0.021237664   0.011862818   0.03132587   -0.00221919   -0.031390331
2-Feb-04   0.002115176   -0.018679024   0.006780909   0.01301928   0.01712318   -0.009458693
1-Mar-04   -0.01928823   -0.030753805   0.012267738   -0.012145545   -0.006030469   -0.007941261
1-Apr-04   0.008607804   -0.024068646   -0.027843588   -0.024949111   0.009863444   0.001620126
3-May-04   -0.003063819   0.045791862   -0.015263851   0.015239967   0.00995531   -0.014176433
1-Jun-04   -0.013135825   -0.01478726   0.000692103   0.006594513   0.011450989   0.011337234
1-Jul-04   -0.030491723   -0.053760665   -0.019188415   -0.009580051   0.018083807   -0.03339934
2-Aug-04   0.011876253   -0.058250748   0.023904782   -0.002001822   0.000773627   -0.013614662
1-Sep-04   -0.02833205   -0.02581149   -0.023595125   0.012265109   0.020475586   0.012073829
1-Oct-04   -0.024200939   0.045251691   0.006452318   0.01438828   0.007945468   -0.042109935
1-Nov-04   -0.015356644   0.003157084   0.003644451   0.021085951   0.019898881   0.006031965
1-Dec-04   -0.01408469   0.019040089   0.032148678   0.005093112   8.64354E-05   0.016341604
3-Jan-05   -0.046516472   -0.017862074   0.00770161   -0.022982941   0.002842759   -0.036824626
1-Feb-05   0.039975516   0.030472706   -0.008076244   0.006507102   0.090927282   -0.00798521
1-Mar-05   -0.000338104   -0.013929818   -0.02606549   -0.02185412   -0.026194026   -0.083992068
1-Apr-05   0.014633051   0.00525287   0.023245386   0.011111802   -0.019130346   -0.042013994
2-May-05   0.014630589   0.060803225   0.001318328   0.009356124   -0.004194614   0.079608491
1-Jun-05   -0.005088825   -0.015344193   -0.008162243   -0.004091884   0.009725145   0.03275369
1-Jul-05   -0.017295755   0.018252426   -0.022110024   0.014246467   0.009586797   0.034619924
1-Aug-05   -0.014040733   -0.02213234   0.002713407   0.001894712   0.010547196   -0.02599387
1-Sep-05   -0.008682706   -0.01834345   0.016994806   0.016950229   0.025608232   -0.047977476
3-Oct-05   -0.060303366   -0.020818266   0.002497608   -0.003389887   -0.053831314   -0.048092196
1-Nov-05   0.002411637   0.058709923   0.03829912   0.024183203   0.031923551   -0.070676054

Solutions

Expert Solution

The R code is pasted below. Please store the data set that you have provided here in a file named "w_logret_3stocks.txt" and then only run the R program. Also, don't forget to change the path name of the .txt file in the first line of the R program to the path name of the .txt file where you have stored the data

# SETTING UP THE DATA
data = read.table("C:\\Users\\LAPTOP\\Desktop\\w_logret_3stocks.txt",header=T)
names(data)
attach(data)

# QUESTION 1, REPORTING THE REGRESSION COEFFICIENTS
# WITH INTERCEPT
model1 = lm(GenMotor ~ Citigroup,data)
model1
# WITHOUT INTERCEPT
model2 = lm(GenMotor ~ Citigroup - 1,data)
model2

# QUESTION 2, ANOVA TABLE TO CONCLUDE IF REGRESSION EFFECTS ARE SIGNIFICANT
summary(model1)
summary(model2)

# QUESTION 3, COMPUTING CORRELATION AND PERFORMING CORRELATION TEST
cor(GenMotor,Citigroup)
cor.test(GenMotor,Citigroup,alternative="two.sided")

# QUESTION 4, ONE SAMPLE PROPORTION TEST
prop.array = ifelse(Citigroup > Pfizer,1,0)
prop = sum(prop.array)
n = length(prop.array)
prop.test(prop,n,p=0.6,alternative="greater")

orchestra answered 2 years ago
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