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Unformatted text preview: Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Chapter 15: Adjustment for Serial Correlation STAT 3022 Fall 2011 University of Minnesota November 11, 2011 Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Introduction Previous chapters have assumed independence . Response variables in regression are assumed to be independent of each other, after accounting for effects of explanatory variables. This assumption is sometimes inappropriate: if data collected over time (or space) if observations taken close together are related Time series deals with this type of problem. This chapter presents two extensions of regression methods to time series. Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Measuring Global Warming Example There have been several attempts at reconstructing mean temperature profiles over long periods of time. One example is given in Section 15.1.2 in the text. Data : temperature (degrees Celcius) averaged for the northern hemisphere over a full year. Series begins in 1880, runs through 1987. Measurements are expressed as differences from the 108year mean. Is the mean temperature increasing over the years? What is the rate of increase in global temperature over the past century? Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Graphical Summary > plot(TEMP~YEAR,pch=18) > lines(TEMP~YEAR,type="l") 1880 1900 1920 1940 1960 19800.40.2 0.0 0.2 YEAR TEMP Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Issues Why can’t we just perform regression of temp on year ? Can’t assume average temperature in 1962 was independent of temperature in 1961. Require independence assumption to estimate σ , the standard deviation of the response subpopulations. If estimate of σ is inaccurate, then so are the standard errors of regression coefficients. Confidence intervals, ttests, Ftests, etc., all become inaccurate. Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present Logging Practices and Water Quality Example In the Pacific Northwest, Douglas fir forests are logged by clearcutting sections of forest: practice involves stripping land of all vegetation burning what’s left before replanting rationale: regenerating Douglas fir seedlings thrive in full sunlight and low competition One consequence of practice is effect on water quality in streams – higher peak runoff, increased silt, higher water temperatures. Case Studies Comparing Means of Time Series Regression After Transformation Determining if Serial Correlation is Present The Data Example Response : Nitrate (NO 3N) levels (ppm), measured at 3week intervals at stream gauges over 5 years after logging.intervals at stream gauges over 5 years after logging....
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 Fall '08
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 Correlation, Regression Analysis, Standard Deviation, Errors and residuals in statistics, serial correlation, Undisturbed Watershed

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