# What exactly is the name of the type of regression analysis where you try to see if the model is significant over *multiple* start/end values?

I'm sure it's related to robust statistics. But I'm sure that there's a label more specific than that.

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Okay, so I tried to run regression analyses on global warming datasets over the last 10 years. What I wanted to show was that there was no significant warming trend over the last 10 years. However, because there are certain anomalous years, I wanted the argument to be more convincing, so I tried different start-year values. My point was to show that the premise behind the article (http://www.physorg.com/news/2011-07-global-linked-sulfur-china.html ) was basically correct. I'm not a climate change denier by any means as I work with climate scientists myself (I hate climate change deniers just as much as any other scientist) - however - the point is that China has released so much sulfur into the atmosphere that climate change had practically been stalled over the last 10 years (that being said, I have no doubt it will resume once again once China reduces the amount of sulfur-containing coal it uses)

I'll use the dataset from http://www.ncdc.noaa.gov/cmb-faq/anomalies.php - and particularly - the ftp://ftp.ncdc.noaa.gov/pub/data/anomalies/annual.land_ocean.90S.90N.df_1901-2000mean.dat dataset (the land+ocean anomalies), which is more scientifically rigorous

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Anyways, by performing regression analyses on this data...

For the 1997-2010 period, for the coefficient of x, I get a value of 0.00722 degrees per year. This is not statistically significant, as the p-value is .13

1998-2010: 0.00515 degrees per year/p-value of 0.19. Not statistically significant.

For the 1999-2010 period, for the coefficient of x, I get a value of 0.01182 degrees per year. This barely meets statistical significance, as the p-value is 0.0457

2000-2010: 0.0089 degrees per year/p-value of 0.17. Not statistically significant

2001-2010: 0.0016 degrees per year/p-value of 0.759. Not statistically significant

2002-2010: -0.00167 degrees per year/p-value of 0.784. But here we have a negative slope

2003-2010: -0.00141 degrees per year/p-value of 0.86. Again, negative slope

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Your question is unclear. Please give a short, reproducible example, preferably in R (but other languages work too). –  Zach Jul 13 '11 at 15:00
Okay I just edited –  InquilineKea Jul 13 '11 at 16:55
@Inq This sounds closely related to changepoint detection. The statistical technology is the same, and the same issues come up, but the purpose seems a little different. –  whuber Jul 13 '11 at 17:46
Ah okay thanks! Are changepoint detections related to rolling regressions? –  InquilineKea Jul 14 '11 at 0:50
@Inq Yes: Many changepoint methods apply a form of "rolling regression," searching for places where the coefficients suddenly jump. What they add to the process is a rigorous measure of statistical significance, which does not seem to be part of rolling regression. –  whuber Jul 14 '11 at 13:30

I still think you are looking for a rolling regression. Example:

Data <- read.table("ftp://ftp.ncdc.noaa.gov/pub/data/anomalies/annual.land_ocean.90S.90N.df_1901-2000mean.dat")
colnames(Data) <- c('Year','Anom')
Data <- Data[Data$Anom!=-999,] require(xts) Data <- xts(Data,ISOdate(Data$Year,1,1))
indexFormat(Data) <- "%Y"

GlobalWarming <- rollapply(Data, width = 10,
FUN = function(z) coef(lm(Anom ~ Year, data = as.data.frame(z))),
by.column = FALSE, align = "right")
plot(GlobalWarming)


As you can see, the stregth of the 10-year trend has declined over the past few years (and this isn't the first time this has happened)

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Oh wow - very nice - thanks! –  InquilineKea Jul 14 '11 at 0:50