By Cory Doctorow at 7:17 am Tue, Jan 1, 2013
Redditor Jasonp55 has a neat demonstration of the perils of confusing correlation with causation, and his well-chosen example makes this a potentially useful chart for discussing this issue with friends who won't vaccinate themselves and their kids.
/r/skeptic, I was practicing GraphPad and I think I may have discovered the 'real' cause of autism... (imgur.com)
(Thanks, Fipi Lele!)
Of course, since there’s no correlation between vaccination rates and autism, your false logic is flawed!
If we played loose enough with the numbers we could make it look like there was. Consider, the first well documented case of autism was in 1747, and European countries started inoculations right around that time.
Of course, the autism case was in Scotland and the inoculations were happening in England and France, but don’t let facts get in the way of being frightened.
“No correlation between X & autism” : that was the point. It’s a perfectly common rhetorical device. You might want to read about analogies, straw men & reductio ad absurdum.
But there is a correlation between child illness and not getting vaccinated, since there is no known cause for Autism spectrum disorder, the data is random.
The data are random.
My favorite example is from my first statistics class. The professor said that when ice cream sales went up, so did cases of polio. Nobody thought ice cream caused polio, though.
My prof used ice cream sales and sexual assault…both increase in the summer in Winnipeg for some reason…
The thing is, that example is actually a case where there *is* a connection, albeit via a third factor (summer). In some alternate universe where the causes of polio were totally unknown, that correlation could still be a useful clue to someone trying to solve the problem, even if a naive investigator would be misled.
this is correct, i agree that is a very flawed example. there is a mutual causality to the shared correlation. just because the data set and factors are incomplete doesn’t mean that the shared correlation is meaningless.
time for those professors to go back to school. :-)
while it is true you cannot infer causality to correlations, it doesn’t mean you shouldn’t investigate them or should consider them meaningless.
in the above graph, there could just as easily be a mutual third factor. if the perceived toxicity of conventionally grown food due to pesticides and fertilizers is driving the movement to purchase organic goods, that same factor might be affecting autism. not saying that it is, just reinforcing that these relationships while not necessarily directly connected can indeed be meaningful.
Actually I do seem to recall there was exactly such a scare (ice cream causing polio) for a time.
This is just going to make Jenny McCarthy not eat organic food now too.
Perhaps she should stop eating food altogether.
Then she’d become tragedy fodder on the nightly entertainment news.
People who do not eat and people who are dead correlate very strongly. And there is causality.
People who are dead do not eat and make no choice.
People who choose not to eat are alive.
It does appear that the act of choosing keeps us alive Or…. :)
That’s nonsense – all he’s shown is that autistic people buy more organic food.
Beat me to it. I knew something was driving the increasing demand for organic food, but I hardly would have guessed this connection. I wonder what other products should be pitched to the autistic among us.
Done. It apparently works, too.
Temple is awesome, we love her.
Wait. Are you saying that vaccinations are a plot by the organic food industry to create more autistic organic food buying customers?
Way back in the beginning of the drug wars, one of the cries was that something like 50% of all heroin users had tried marijuana at some time before they switched to heroin. One researcher noted that in America 99% of all heroin users and drunk milk before starting on heroin, yet that didn’t make milk a gateway drug.
“yet that didn’t make milk a gateway drug.”
Listen buddy, I had a chance in this life before I started glugging back the white stuff. Pretty soon I couldn’t even drink tea or coffee without a top-up. I been Chasing the Teat ever since. Tried to kick with UHT a few times, but that just left me cold and shivering in the calcium-sick dawn.
You’re another one of those stereotypical men; you look at a cow and all you see is an udder.
Well, bucko, I’m here to tell you it’s 2013. That cow is more than a milk machine. She has a mind of her own. She can be an engineer, a corporate CEO, a small business owner. She will lactate IF she chooses and WHEN she chooses.
Now let’s crash the Dairy Board meeting and throw milk-coloured paint.
Indeed. I’ve worked with quite a few bovine engineers.
Can she be a steak or a burger, because that’s what I’m after.
It’s true. Name another mammal that drinks milk into adulthood – let alone another animal’s milk. Total addition.
My cat is fond of the occasional tipple. Then again, she was eating chicken necks yesterday. No concept of risk you see. Maybe she’s autistic? After all, she doesn’t like hugs and is totally self-centred.
I’ve never had a dog that wouldn’t eagerly lap up milk.
Would only be useful in arguing against anti-vaccine folks if the primary basis for their refusal were some similar graph comparing vaccination and autism rates. I’m thinking that’s likely not the case.
Actually, it’s dual use. I see a lot of team organic blaming GMOs for autism (and a range of other health issues).
Well, to play devil’s advocate, I’d point out that the graph doesn’t do anything to knock down that hypothesis – initial appearances notwithstanding. If we assume that the consumption of organic food was and remains at a very low level compared to all food consumption (probably true, organic food sales are only about $40 billion annually), then showing a nice exponential increase over time pretty much tells us nothing about changes in consumption of GMO food over time. More generally, the graph is mostly just a way of baiting anti-vaxers – it really doesn’t show a damn thing, which is sort of the point, but on the other hand it doesn’t provide a way to convince even a rational person of anything.
the point was “correlation != causation” and taking something obviously not the cause of autism like organic food, and showing it correlates with rates of autism helps illustrate why you shouldn’t confound the two things.
Sadly, the anti-vaccine folks are not persuadable. Doesn’t matter what tack you take, confirmation bias will trump any facts you provide. And if you press the issue, they just decide you’re a big meanie and dig their heels in further.
I wish I could just mock them and the Morgellans for being idiots, though in the latter case it’d be their mental illness acting up and I’d feel bad :(
Bill gates just stopped 200 a year out of a billion in India from getting polio with vaccines right, but 27,000 kids die a day of curable diseases . How come people like boing boing and you don,t write about that . Where is your humanity, you don,t have to be very smart to work this out ,bigoted name calling like you did is unnecessary.
A Victory, Not A Conspiracy: Bill Gates And Ending Polio http://www.forbes.com/sites/matthewherper/2012/01/12/bill-gates-and-polio-victory-not-conspiracy/
The long-term payoff if you can entirely eliminate an infectious killer like polio or smallpox is huge; comparing annual deaths doesn’t tell the whole story. But even if I disagreed with Gates’ priorities (which you seem to, though I can’t fully parse your comment), I’d hardly be inclined to call him out, since he’s still doing more than most of us.
There is also a fascinating TED talk about sanitation and disease and evolution. I wish I could remember who it was by. Basically, it showed that the harder you made it for a disease to spread, the milder the disease became. I think the example they used was cholera.
Basically, basic sanitation removed cholera’s preferred vector. If everyone is drinking water from a source that is easily contaminated, the disease’s best vector to spread is explosive diarrhea. Bam. Someone else drinks contaminated water. It doesn’t matter if it kills the person or not, the disease colony has already accomplished what it needs to do to spread. With better sanitation the disease has a harder time spreading. The versions that tend to spread slowly become the less virulent varieties, because killing your host tends to immobilize them pretty quickly. The milder varieties of the disease, the ones that make you less sick, tend to spread faster than the severe versions. The result is a double whammy. Countries with good sanitation not only have fewer incidence of water borne diseases, but they tend to have milder strains. (On top of that, they have better treatment, which turns the double whammy into a triple play.
Of course, immunization works a little differently, although not entirely. Flu vaccines do tend to make the flu that you do get less severe. The big thing with vaccines though is the herd immunity idea (which actually might respond to the same pressures- the more people are immune, the more mild the strains that do hit the un-immunized might have to evolve to be to spread at all.) The system falls apart when you get anti-vaxers though. :(
i apologize , obviously saving 200 a year from polio outweighs the lives of 27,000 children who”are dieing every day of cheaply curable illnesses lol ok fine sir ,The number a people who get polio is just a few hundred each year , its not Ebola k , was just a simple question i researched and got a eye opener when i seen the numbers i did provide a link right , my bad for expecting intelligence here i guess .
Now i just happen to be fascinated that everyone here demonizing me as anti vaccines, when my numbers are stupidly easy to find , you should have another look , Take care k
The only bigotry is in your head, bub. The fact is that the anti-vax movement is based entirely on lies and represents a clear and present danger to public health. And Morgellon’s is without question a manifestation of mental illness.
I’m pretty skeptical of the ‘clear and present danger’ part. A lot of pro-vaccine folks underestimate the extent to which sanitation, refrigeration, and improved hygiene helped obliterate infectious disease. That is, they assume that without vaccines, we would be dying by the millions of diseases that were pandemic in the 19th century. But in most cases vaccines were the icing on the cake. The measles deaths graph that anti-vaxers like to use http://www.whale.to/m/measlesdeaths1.html , while it does not actually say what they think it does, makes an important point about the history of public health. Huge progress was made before vaccines delivered the coup de grâce. Even without them, the additional mortality in this day and age would be fairly small.
A lot of pro-vaccine folks underestimate the extent to which sanitation, refrigeration, and improved hygiene helped obliterate infectious disease.
Massively false. Sanitation, etc. has vastly reduced the incidence of many diseases. But not the ones for which we vaccinate. You’ve conflated foodborne illnesses with airborne illnesses.
Also, “pro-vaccine folks” sounds disturbingly like “round-earth folks”.
How then do you explain the graph? Measles is not food-borne. But in any case, it appears that reducing the overall incidence of disease results in a virtuous circle, probably because the human immune system has limited resources. Eliminate one pathogen from the environment and suddenly people are more robust against others.
Anyway, measles is far from the only example. Infant tuberculosis mortality (USA) dropped 95% from 1900 to 1960, no vaccine involved. Pertussis death rates likewise dropped about 90% between 1918 and 1948.
In the case of measles and pertussis, it’s worth reiterating that further significant gains were made after the introduction of the vaccine. But in both cases, over 90% of the reduction in mortality appears to have been accomplished without any vaccine involvement. Further, there is no special reason to think that the factors that drove down the mortality rates prior to the introduction of the vaccine have been static. In other words, it’s unlikely that suddenly abolishing pertussis vaccination (for example) would result in a return to the mortality rates of 1948.
Interesting. I believe the existence of other people is also a clear and present danger to public health. I think I would be far less likely to catch a disease, and my children would be much safer, if all the other people in the world were “Sanitized for Your Protection.” By which I mean rounded up and put in special camps where your filthy germs can’t terrorize my precious darlings.
It’s the only Scientific course of action, so if you don’t agree, you’re just promoting woo.
Note to the irony impaired: The above is a rhetorical technique called “extension” not an actual call to action. Anti-anti-vaxers have a tendency to facism that needs to be highlighted in this sort of discussion.
Anti-anti-vaxers have a tendency to facism that needs to be highlighted in this sort of discussion.
Frustration and hyperbole are even more highly correlated than organic food sales and autism. If you’ve ever tried to convince an anti-vaccination person of some very basic facts you can understand the frustration.
And you clearly understand the concept of sarcasm so I’m really not sure why you’re throwing “fascism” around. Is it your experience that accusing people of “fascism” makes for a calmer and more enlightening discussion?
Is your argument based merely on profound ignorance, or is it the bad faith indicated by your link to whale.to? For example, someone that knew what they were talking about would be aware that the introduction of antibiotics effective against tuberculosis in the early 50s drastically reduced death rates from that disease. Likewise, the availability of effective antibiotics and improved supportive care reduced the death rates from diseases like pertussis and measles without having much of any effect on their incidence. Plenty of children who would have died in earlier years ended up permanently disabled instead (one of my great-aunts among them).
Boris is conflating mortality with morbidity.
“You cannot reason someone out of a position they were not reasoned into.
I don’t know about that. I’ve been “reasoned out of” plenty of positions, when someone showed me facts and good arguments. And a lot of those times, my initial position was a default, an idea from instinct/culture/something other than reason.
And if that could happen to me, it would be arrogant for me to think that it couldn’t happen to other people.
But would it be arrogant for you to think that there are some people for whom it could not happen? Of course not; there are seven billion people in the world — it would be a bizarre statistical anomaly if they all turned out to be as reasonable as you are.
No problem is helped by pretending all human beings are rational. Let’s be realistic, here. Some people simply don’t choose what they believe on the basis of facts and good arguments. It would be silly of me to think otherwise.
Yeah, you meet someone, you start a running estimation of their reasonableness, and it goes up and down with each new piece of evidence. They repeat bunkum? Not a good sign. They learn something new and change their mind? Great sign.
I like starting that estimation pretty high, even though it’s wrong most of the time, just because I think it stops me from underestimating people and missing opportunities. And it helps me keep a better attitude. But I know what you mean.
Possible correlation: since the figures are for the diagnosis of autism, rather than the occurrence, would it not be reasonable to suppose that an increased awareness of the condition coincided with an awareness in the (supposed) benefits of organic produce? So that what we’re actually plotting here is an ‘enlightenment’ curve. Just a thought.
Yuppies: the hidden factor
Well, I’m not sure about “enlightenment”, but people who can afford organic fruit are going to be more likely to afford the psychological care.
Bingo, Zero! There is little if any evidence for a real increase in autism. The increase is in diagnoses, which is related to several known factors, including better ascertainment, broader diagnostic criteria, increased social awareness, and increase in services.
There’s a web site that will take your graph and match perfectly to another data set, like Indonesian earthquakes of the 21st century and 19th century herring catches.
Sounds fun, do you have a link?
Correlation does not imply causation.
No, I didn’t miss the point of the column, I simply linked directly to an explanation.
This attempt to show that correlation does not equal causation will confuse idiots into thinking hippie food causes autism. His point will not be made.
There may be a connection.
I suspect some (not all!) autism may be the product of the way we rear children to expect constant praise, freedom from frustration, and instant gratification. One aspect of this over-protectiveness is obsession with health risks, such as vaccination and food. Vaccination doesn’t cause autism. But fretful parents who fear vaccination just might.
So your personal hobbyhorse somehow is suspect in autism? Personally I think you need to familiarize yourself with the etiology of autism before starting down this road. At least then your handwaving bullshit might be more elegant.
Are the hobby horses genetically modified?
Oh God, are they fed organic food?
Are you French by any chance? Because the rest of the developed world acknowledges that autism has a neurological basis, not a psychological one.
I’m pretty sure that, in order to properly diagnose autism, the child has to show symptoms before two years of age. That’s actually pretty early, developmentally speaking, for things like “constant praise, freedom from frustration, and instant gratification” to have much effect on behavior. Self-esteem (which could be damaged by anything that could be called “constant praise”), the ability to handle frustration (whether prevented or encouraged), and the ability to delay gratification are all skills that develop much later than two years of age. According to my pediatrician (who I think is very aware of autism research results), has said that, almost always, she has suspicions of autism as early as 9 months (also, corresponding confidence about its absence).
All that to say that there is a high degree of certainty that parenting styles do not “cause” autism. However, there is a high degree of certainty that your attitude indicates you might be a jac…
“I suspect some (not all!) autism may be the product of the way we rear children to expect constant praise, freedom from frustration, and instant gratification”
I suspect you have no clue what autism is.
Back in the real world, actual doctors have determined that the symptoms of autism can be detected as early as six weeks of age. So no, your personal hobbyhorse has nothing at all to do with it.
Perhaps we should look closely at what the mother consumed during the pregnancy. It would be far more useful, although difficult to collect truthful results.
Long ago in Astounding Science Fiction there was an article “The Great Tomato Conspiracy”, Everything bad correlated with the consumption of or proximity to tomatoes. Criminals locked up in penitentiaries had eaten tomatoes. Teen age delinquents had eaten tomatoes. A very good send-up of sloppy reasoning.
That was very good, I remember it. Another good one was Richard Feynman’s “Cargo Cult Science” concept that he illustrated in a commencement speech at Cal Tech — it can be read here:
I don’t have strong feelings one way or the other but it seems to me if vaccinations work and you get vaccinated you would not have to worry about those that choose not to get vaccinated. BTW I was in the military and got vaccinated for everything under the sun and still got sick, even conntracted hepatitis which I had been vaccinated. My point, who cares if you don’t want to get a shot, on the other hand children are a different story. The CDC should be doing more testing and I do believe there is danger when giving many vaccinations to a child all at once. Just saying…
That’s not how vaccines work. A better model (but I am still simplifying) would be that being vaccinated might reduce your chance of developing the disease (if exposed) from 70% to 10%. In such a case, a population of vaccinated people would, while not utterly immune to the disease, make it impossible for it to spread to any significant degree. It would always tend to fizzle out. Meanwhile it would obviously be rather easy for it to spread like wildfire in an entirely unvaccinated population. The CDC has complex models that suggest a threshold percentage of vaccinated people which establishes this herd immunity. It varies from case to case, because different vaccines have different levels of effectiveness.
Hey, that was really good. It’s very rare to see a cogent BB post that uses the phrase “herd immunity” in any context whatsoever.
“it seems to me if vaccinations work and you get vaccinated you would not have to worry about those that choose not to get vaccinated.”
Not that I expect you to follow up on your guesses.
My sister’s cousin-in-law’s friend gave her two-year-old an organic banana. Some time after that, the kid had a temperature and seemed irritable. Some time after that, the kid was diagnosed with autism. QED.
I’d just like to bounce through and point out that this long, populous comment thread started with numerous people inexplicably acting as if there were actually two real/legitimate sides to a “debate” over vaccination, and tapered to a close with a clear supernatural miracle: a howler monkey with a typewriter, while getting repeatedly beaten over the head, accidentally produced a grammatically correct series of English words that, were this random howler monkey an intentional being, would express an (alleged) belief that autistic traits can have something to do with being a spoiled child. Fortunately, no such comment was actually made by a functioning human mind, so we don’t have to abandon ‘autistic’ as a word suddenly and summarily stripped of all meaning.
Protip: those of you who are capable of processing basic communicated ideas, and ergo are presumably here to argue against “anti-vaxxers” (personally, I find this usage a shameful insult, purely on principle, to the venerable Greek prefix ἀντι-), seriously just give it up. Neither the stats, nor common experience, nor theory of delusion-based group behavior, support any reasonable expectation that you’re doing anything substantial here, other than wasting calories and moments of attention on (albeit eventually/occasionally dangerous) morons, and feeding/exercising your useless-outrage muscles.
Just not worth it. If nothing else, the ongoing collapse of our supply (as a species) of effective antibiotics puts you, your children, and any future children you might have/know at more than enough serious, lately-unprecedented disease risk to make some deranged rabble gnawing at the edges of herd immunity totally inconsequential.
Your verbal effluvia does produce an extraordinary increase in self-confidence and condescending outlook in those that share your bias, that much is granted.
So we’re wasting our time, but your long comment was a worthwhile use of yours? Gotcha.
“Protip: those of you who are capable of processing basic communicated ideas, and ergo are presumably here to argue against “anti-vaxxers” (personally, I find this usage a shameful insult, purely on principle, to the venerable Greek prefix ἀντι-), seriously just give it up”
It’s essentially arguing religion with fundamentalist hippies.
So wait, DOES organic food cause autism? I was led to believe that it was the vaccines that were responsible. Has anyone thought that maybe vaccines lead to an increase in organic food consumption? What about those water fluoridation nuts? As if our government would continue to put fluoride in the water if it makes us dumb…mer…
Actually, there is a third factor that causes both. The idiots that pay more money for organic food with no proven benefits are the same people who refuse to immunize their kids. The number of these people is increasing.
Nice troll hat.
Well, there probably is some correlation between Autism an dorganic food sales. There’s a true-story book and TV movie called “Son Rise” about a family with a seemingly-autistic son who, IIRC, dramatically changed their diet and lifestyles (ie: natural, organic foods only, no tv, etc) and saw their son go from “unreachable” to “normal” (again, IIRC).
Today’s science doesn’t really blame things like food additives for autism, but when you’re a parent of an autistic child and searching for answers, it’s certainly one more thing to try.
I really don’t see the point in this at all. Organic food and autism? If anything, organic food improves neurological function.
No one is saying organic food is bad. The point here is that correlation does not equal causation.
Sometimes people produce trend charts like this with closely matched lines, and then point to the correlation and blame one of the trends for the other. Such as the autism/vaccination correlation mentioned above. Or the “violence in schools/video game sales” correlation that is currently all the rage. Just because two trends have similar curves doesn’t mean one is causing the other.
See also this chart implying that global warming is caused by a lack of pirates: http://www.venganza.org/about/open-letter/
Steady on, me hearty… it’s all well and good to point out the pitfalls of spurious correlation, but let’s not drift into pirate-climatecaust denial (aka piratical revisionism).
That sort of anti-Piratism should be a thing of the dim and unenlightened past: the link between the near-extinction of pirates and the rise in global temperatures is a thing that transcends statistical analysis.
One need only look at what has happened since our brave pirate brethren in Somalia began their careers as modenr privateers: global warming stopped (about 15 years ago), thus enabling us to rejoice at the failure of the 2000 prediction (by David Viner of CRU) that “Children just aren’t going to know what snow is” (implying a global absence of snow… and probably of pirates too). That statement was reported in the Independent of March 20th 2000.
Thankfully, UK kiddies have been enjoying abundant snow thanks to the unsung efforts of our Somali chums.
TL;DR: climate models are statistically less robust – and follow more of a “do what’s required to get the answer we want” paradigm – than any economic model of which I am aware. Aaargh, me hearties.
Interesting debate. Of course there would be a million datasets similar to above, which is an exponential that sees the y-axis quadruple after about 10 observations – either curve is the (1+p/100)^n variety (where p is a compound percentage – around 15% i reckon. So anything that has grown at a compound rate of about 15% over 10 years will have a curve like this. There may be a connection but on random datasets, of which there would be many of this type, the starting point, without a hypothesis, is coincidence.
What you’re sneaking up on is the problem of spurious correlation when data are not stationary: that is, when data are integrated of order > 0 (meaning that they have a non-stable mean in sub-samples).
Generally, a phenomenon related to population will, in equilbrium, grow broadly in line with population. (e.g., long-run behaviour of the labour force). Things that grow in line with aggregate expenditure will – again, as a measure of tendency rather than in every observation – grow at “m-n-beta” (the rate of growth of the money supply, less population growth, less technological change). which is the theoretical equilibrium rate of growth of nominal quantities.
If you have two quantities that are both growing exponentially (even at divergent rates), you will always find an affine transformation of one quantity that will generate a large correlation coefficient (and therefore a relatively large coefficient of determination).
If the two series are growing linearly, the transformation is trivial (multiply either series by the ratio of the slopes) and the coefficient of determination will approach unity… it won’t actually BE 1 unless both series exhibit (a) zero; or (b) perfectly correlated; noise around their respective linear growth paths.
This is why trained statisticians (and econometricians – of which I am one) test data for stationarity, make sure that regressors are of the same order of integration as the dependent variable (so that the regression has a stable steady state), and if required take differences (or even log differences) of data to reduce the regression to one involving only stationary quantities.
TL;DR: statistics is sufficiently complex that a layman or autodidact is likely to get it wrong in ways that aren’t amusing to anybody who finished high school with decent marks in maths.
The graph shows that the more autism is prevalent and diagnosed, people reach for petrochemical free foods. As for vaccinations, I’ve always wondered why the incidence of Autism is so gender lopsided since both genders equally receive the same vaccinations….
I don’t think it can be said that “the graph shows” that. That’s the point of this article, isn’t it? And I was unaware that autism is “gender lopsided”. (off to do a little research on that…)
You’re right, I’m just trying to say it’s not actually a negative graph as it was meant to be. Yes, autism is much more prevalent in males…
Autism is diagnosed about 4.5 times more often in boys than in girls.
Now here’s something interesting I found (I’ll quote two paragraphs that seemed particularly salient):
In epidemiological research Wing (1981) found that among people with high-functioning autism or Asperger syndrome there were as many as fifteen times as many males as females. On the other hand, when she looked at people with learning difficulties as well as autism the ratio of boys to girls was closer to 2:1. This would suggest that, while females are less likely to develop autism, when they do they are more severely impaired.
Attwood (2000), Ehlers and Gillberg (1993) and Wing (1981) have all speculated that many girls with Asperger syndrome are never referred for diagnosis, and so are simply missing from statistics. This might be because the diagnostic criteria for Asperger syndrome are based on the behavioural characteristics of boys, who are often more noticeably “different” or disruptive than girls with the same underlying deficits. Girls with Asperger syndrome may be better at masking their difficulties in order to fit in with their peers, and in general have a more even profile of social skills.
So, as usual, it’s “not quite that simple,” apparently. Here’s the link to that page:
The real question is: Why do people with autism like organic food so much?
Sheesh… come on Cory – even Americans don’t try to regress non-stationary variables against one another, surely?
OLS is efficient and consistent (and hence unbiased – hence BLUE) only when the Gauss-Markov conditions hold, and they will NEVER hold for anything growing geometrically… at the very least there is a problem with autocorrelation, and almost certainly heteroscedasticity.
And as we all know, the coefficient of determination (R^2) is the square of the Pearson correlation coefficient – whichin turn is cov(x,y)/var(x).var(y) (why can’t we do LaTeX up in this bitch, yo?); using R^2 as a goodness of fit measure assumes that OLS is BLUE for the problem under consideration.
It is highly unlikely that two I(1) or I(2) series will have stable variances.
Model that shit with ARIMA and the correlation will disappear, I bet.
gt you is my hero
This will be a great way to help me explain to patients (as I do everyday) the difference between association and causation.
anti-vax correlation is not causation Funny happy mutants infographic not food reddit woo
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