Comments on: Using Excel's regression tools to determine the 95% confidence interval
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval/
Comments on Ask MetaFilter post Using Excel's regression tools to determine the 95% confidence intervalSun, 26 Jan 2014 12:48:05 -0800Sun, 26 Jan 2014 12:56:06 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Using Excel's regression tools to determine the 95% confidence interval
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval
MS Excel's regression tools provide 95% lower/upper confidence results but how does one properly interpret and then express those as a single ± (plus/minus) figure? <br /><br /> The in-house literature I am now required to read at work includes frequent references to linear trends, normally expressed as a trend per decade with a '±' figure identified as the confidence interval at 95%. The underlying datapoints used to calculate the liner trend are monthly measurements (1 per month).<br>
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I now have been requested to write a memo summarizing the "statistics" of the latest dataset of 120 months. At our office, the statistics part is accomplished using MS Excel. I have taught myself how to use the Data Analysis Tools in Excel to calculate the linear trend and other regression statistics. <br>
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So, I now have the Excel stats for the newest dataset but I am not sure how to properly express them in a way that avoids my looking like a statistics idiot (which I am). My main issue is I am not sure what to base the ± confidence interval on. The internal memos use a single number after the '±' (e.g. ±0.9) but the Excel regression analysis does not do it that simply;<br>
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Instead, Excel provides the following:<br>
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--------Coeff.---Std.Er.---Lwr95%-Upr95%-Lwr90%-Upr90%<br>
Intcpt -0.2394, 0.0266,-0.2918,-0.1871,-0.2833,-0.1955<br>
Data.X 0.0013, 0.0002,, 0.0009,, 0.0017 ,, 0.0009 ,, 0.0016<br>
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I know that the 0.0013 is the slope of the linear trend of monthly observations and to calculate a 10-year trend I would multiply by 120 (months). But it is not clear what numbers I would use to calculate a single '±' that is interpreted as the 95% confidence interval.<br>
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Are Excel's 'Lower' and 'Upper' 95% results the basis for the confidence interval? If so, which are the correct numbers to use, and would I then multiply that correct number(s) by 120 as done with the slope coefficient when expressed as a 10-year trend?<br>
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Thanks for clearing up an idiot's confusion on this. (Apologize for extra commas used to force columns of data to line up.)post:ask.metafilter.com,2014:site.255995Sun, 26 Jan 2014 12:48:05 -0800kartguystatisticsexcelconfidenceintervalregressionBy: Hollywood Upstairs Medical College
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval#3720148
If I am reading this correctly, you'd want to report the coefficient of Data.X as 0.0013±0.004, using the 95% interval. (Upper bound 0.0017- coefficient 0.0013 = .004, and also coefficient 0.0013 - lower bound 0.0009 = .004).comment:ask.metafilter.com,2014:site.255995-3720148Sun, 26 Jan 2014 12:56:06 -0800Hollywood Upstairs Medical CollegeBy: radsqd
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval#3720184
For 95%= 1.96*standard error is the +/- that you are looking for.<br>
That will change for 90% 1.645*standard error.<br>
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So for the Data X . 0013 +/- .0004. You get upper 95% by [1.96(~2)*.0002] or.004+0013=.0017,Lower 95% .0013-.0004 = .0009comment:ask.metafilter.com,2014:site.255995-3720184Sun, 26 Jan 2014 13:48:02 -0800radsqdBy: ROU_Xenophobe
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval#3720200
<i>For 95%= 1.96*standard error is the +/- that you are looking for.</i><br>
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Only for large N's (120 is large enough, but other work or projects might not be).<br>
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The more general way to get this from Excel output you gave is<br>
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Coeff +/- (Coeff-Lwr95%)comment:ask.metafilter.com,2014:site.255995-3720200Sun, 26 Jan 2014 14:10:08 -0800ROU_XenophobeBy: kartguy
http://ask.metafilter.com/255995/Using-Excels-regression-tools-to-determine-the-95-confidence-interval#3720892
Thanks, all. I was able to get my hands on an older dataset and then ran it through Excel. I then compared those regression results with previous internal memo confirming that indeed previous authors had expressed the confidence interval '±' using the same techniques suggested.<br>
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Your responses completely cleared my confusion and provided a needed comfort level.<br>
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One follow up question. If I multiply the slope coefficient by 120 to calculate an estimated 10-year trend, would I do the same for the '±' figure. Using example, ±0.004 would become ±0.48 - sound right?<br>
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Thanks again.comment:ask.metafilter.com,2014:site.255995-3720892Mon, 27 Jan 2014 09:54:04 -0800kartguy