[R] Correlations not in sync with r2 from regression

[Leeds, Mark (IED)]

I have two variables, minutereturnsa which can be thought of as my
independent variable and minutereturnsb which can be thought of as my
dependent variable. When I run correlations on the two variables,
depending on which of the three methods I use, I get values of between
-.15 through -.19.
 
Then, when I do a regression, I get an rsquared of .004 which is more in
line with my intuition. In other words, I think the cor
function is doing something very different from what a regression
calculates. In fact, when I use my full data set ( not
included here ), I get correlations at the level of -0.97 which is
extremely unreasonable given the two variables. So, I think cor is 
calculating something else in terms of what I  am used to ? Or, maybe
the scale of my variables is too small and this could be causing
something to go wrong ?

Has anyone else had this experience where their value from a corr is
extremely high and yet the x y plot of the data and the regression
itself do not reflect this. All the code is below the two data sets in
case anyone wants to run it in order to see better what
I mean. It's probably just an non understanding on my part of what the
cor function is actually doing ? Thanks a lot.


minutereturnsa<-c(-2.36264407318387e-05, -0.000114546483004574,
0.000480296012887571, 
-3.4370702667097e-05, -1.75028713567116e-05, -4.48227082969765e-05, 
2.90329205787643e-05, 0.000305825164510942, -5.03948020931233e-05, 
-0.000132337254829196, 0.000257366609910825, -0.000143416497692783, 
7.75575880389567e-05, -0.000390396184700492, 5.8463592766067e-05, 
-0.000166182789493874, 2.60897827946138e-05, -9.68285203182262e-05, 
0.000306300707090479, -0.000212593666131689, -2.05973305682505e-05, 
-0.000892262006425781, -7.65296399478643e-05, 9.29686476904834e-05, 
0.000400462742000229, -5.68981524482481e-05, 8.75374496889236e-06, 
-0.000325482754985451, -0.00026561900794686, 6.6048490682924e-05, 
5.22638320941127e-05, -9.67113649918971e-05, 2.9231547120645e-05, 
-5.85151902221526e-06, -6.50840736984293e-05, 3.34530686902923e-05, 
9.92970200188736e-05, 4.57716366808469e-05, 3.98160204646558e-05, 
-6.00275310205234e-05, -0.000182345705006526, -8.2237112582817e-05, 
8.49939625151563e-05, -3.54341054409346e-05, -0.000100100119395208, 
-0.000480874457688962, -5.96482127885878e-05, -1.57319826001867e-05, 
-0.000144679725631036, -0.000135114371429879, -4.7961402529495e-06, 
-0.000169457716609145, 3.99966377280236e-05, -5.124402520984e-05, 
0.000328975614625193, -0.00025080739315797, -0.000573125487459691, 
-7.7472898995623e-05, 3.44346931751005e-05, -3.06202186477478e-05, 
0.000370039560674940, 7.8350343693856e-05, -3.16439540668512e-05, 
-0.000160178561449342, -0.000396591758462961, -0.000210859243796158, 
0.000388855276420408, -0.000179700371241154, 4.16133481957459e-05, 
1.41192273312996e-05, 7.08468899466297e-05, -1.52706151546056e-06, 
3.67659444577839e-05, -0.000234283509586319, 0.000137243567309930, 
-5.20968533468391e-05, -0.000134271000559849, 0.00015686727434705, 
-1.20143299762177e-05, 0.000101875337767510, 3.65842929905824e-06, 
4.69929868991414e-05, 5.7532628616741e-05, -4.97275753463811e-06, 
-0.000170415848516292, 3.72182099566132e-05, -3.63157298233219e-05, 
6.5485377211516e-05, 1.70517614943577e-05, -0.00044266660425496, 
0.000117663889794173, -0.000156675474467072, -9.45186652945296e-06, 
0.000228093804488516, -0.000183465434343333, 8.7116036074697e-05, 
-0.000105286831582063, 3.77385685590426e-05, 0.000229830364734340, 
7.83212236301623e-05)

minutereturnsb<-c(8.4645336092315e-05, 0.000342545113518611,
0.000619138432391253, 
2.39224895137724e-05, -0.000105430737374235, -4.64094877949961e-05, 
0.000232692295488945, 0.000170343242044346, -0.000278101637244177, 
-2.39061360733928e-05, -0.000308615318143524, 0.00088876749136002, 
8.32424077339411e-05, -0.00055346752090557, 8.45076374274e-05, 
-0.00054551438959205, 0.000259390072846699, 0.000144324272249641, 
0.000180899432469239, 0.000288664295990948, 9.95638801164489e-05, 
0.00097571036608901, -4.60863646098986e-05, -0.00047897519405371, 
5.14178471453519e-05, 2.4281687986516e-05, 0.00036058584985188, 
0.000134937727959361, 0.000103280488242596, 2.88151877292364e-05, 
-0.000310955520890666, 0.000106216873712484, 5.52294891624783e-05, 
5.71829552473702e-05, 0, -4.24836809553852e-06, -0.000112243149114732, 
-0.000225054512974054, -0.000127369605538163, -4.718171803475e-06, 
0.000575331719490535, 0.000414750691947852, -2.48462938587934e-05, 
-0.000508280783423132, 0.000246095358950704, -0.000407474448815393, 
0.000288693409606466, -7.07108562671976e-05, -0.000794312866452707, 
-0.000106260214363552, 0.00028805175686486, 7.4386971687268e-05, 
-0.000298442739602223, 0.000194096767056173, -0.000298344525328176, 
0.000220745065718120, 0.000709521706545146, -0.000217011729104044, 
-1.82252827203300e-05, -0.000385731348574225, 0.000332978442621368, 
-8.95786863042147e-05, 0.000104547275809885, -0.000295648677070659, 
-9.6397420641381e-06, 0.000224064465289331, -0.000739358267871637, 
6.56478242859748e-05, 0.000815010958709728, -0.000107869047081266, 
-0.000304049331305123, 5.20322126815742e-05, -5.32009410303402e-05, 
-0.000167938227511044, -9.21891011866904e-05, -0.000266690878483189, 
3.64952404163787e-05, -4.46965899776330e-05, 4.25776509977993e-05, 
-7.80437967993208e-05, -2.12827088637013e-05, -7.09320471283803e-05, 
0.000148863850106373, -6.3806029690916e-05, 4.25559078296445e-05, 
-9.58063435172463e-05, 5.3209320157066e-05, -0.000546163217071793, 
-0.000351060356512889, 0.000162064277177798, -0.000384674967309095, 
-0.000199174847720585, -0.000216944813291597, 0.000101829147203247,
0.000105031807862588, -1.94459082898391e-05, 0.000271353813222852, 
-2.75323237151071e-05, 0.000581315536959615, -0.000348709449612628)


#-----------------------------------------------------------------------
---------

# CALCULATE VARIOUS CORRELATIONS

corpearson<-cor(minutereturnsa,minutereturnsb,method="pearson",use="pair
wise.complete.obs")  
print(corpearson)

corkendall<-cor(minutereturnsa,minutereturnsb,method="kendall",use="pair
wise.complete.obs")
print(corkendall)

corspearman<-cor(minutereturnsa,minutereturnsb,method="spearman",use="pa
irwise.complete.obs")
print(corspearman)

# EXLCUDE POSSIBLE Nas
# DO A REGRESSION
# PLOT FITTED VERSUS ACTUAL

options(na.action=na.exclude)
returnreg<-lm(minutereturnsb ~ minutereturnsa)
regsumm<-summary(returnreg)
print(regsumm)

plot(minutereturnsa,minutereturnsb)
lines(minutereturnsa,fitted(returnreg))
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