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Advantages of Microsoft 77–888 questions studying with online meansOne of the options that has always been available in Excel's LINEST() worksheet role is the const argument, short for constant. The function's syntax is:

=LINEST(Y values, X values, const, stats)

where:

Setting the const argument to fake can easily Have major implications for the nature of the results that LINEST() returns. And there is a existent question of whether the const argument is a useful option at all. In fact, the question is not limited to LINEST() and Excel. It extends to the whole zone of regression analysis, regardless of the platform used to carry out the regression.

Some credible practitioners believe that it's distinguished to coerce the constant to zero in inescapable situations, usually in the context of regression discontinuity designs.

Others, including myself, believe that if setting the constant to zero appears to breathe a useful and informative option, then linear regression itself is often the wrong model for the data.

The exceed 2003 Through 2010 VersionsFigure 1 shows an sample of the disagreement between LINEST() results when the constant is calculated normally, and when it is forced to equal zero.

Figure 1 LINEST() returns the selfsame results, whether you exhaust exceed 2003 or exceed 2010.

In motif 1, the two sets of results are based on the selfsame underlying data set, with the Y values in A2:A21 and the X values in B2:D21. The first set of results in F3:I7 is based on a constant calculated normally (const = TRUE). The second set of results in F10:I14 is based on a constant that is forced to equal zero (const = FALSE).

Notice that not a single value in the results is the selfsame when the constant is forced to zero as when the constant is calculated normally.

Basing the Deviations on the MeansFigure 2 begins to demonstrate how this comes about.

Figure 2 The deviations are centered on the means.

In motif 2, cells G15:H15 contain the sums of squares for the regression and the residual, respectively. They are based on the predicted Y values, in L21:L40, and the deviations of the predicted values from the actuals, in M21:LM40.

The sums of squares are calculated by means of the DEVSQ() function, which subtracts every value in the argument's purview from the breathe distinguished of those values, squares the result, and sums the squares.

The value in cell G13, 0.595, is the R2 for the regression. One useful way to reckon that motif (and a useful way to deem of it) is:

=G15/(G15+H15)

That is, R2 is the ratio of the sum of squares regression to the total sum of squares of the Y values. The result, 0.595, states that 59.5% of the variability in the Y values is attributable to variability in the composite of the X values.

Notice in motif 2 that the statistics reported in G11:J15 are identical to those reported in G3:J7 (except that LINEST() reports the regression coefficients and their standard errors in the reverse of worksheet order). The former are calculated using Excel's matrix functions; the latter are calculated using the LINEST function.

Also notice in motif 2 that the correlation between the actual and the predicted Y values is given in cell H22. It is 0.772. The square of that correlation, in cell H23, is 0.595—that is of course R2, the selfsame value that you procure by calculating the ratio of the sum of squares regression to the total sum of squares.

There's nothing magical about any of this. It's everything as is expected according to the mathematics underlying regression analysis.

Changing the divergence Basis to ZeroNow examine the selfsame sort of analysis shown in motif 3.

Figure 3 The deviations are centered on zero.

Notice the values for the sum of squares regression and the sum of squares residual in motif 3. They are both much larger than the sums of squares reported in motif 2. The intuition is that the deviations that are squared and summed in motif 3 are the differences between the values and zero, not between the values and their mean.

This change in the nature of the deviations always increases the total sum of squares. (For the intuition that this is so, see Statistical Analysis: Microsoft exceed 2010, Que, 2011, Chapter 2.)

The change from centering the predicted values on their mean, and the errors in prediction on their mean, likewise changes the relative size of the sums of squares. It can occur that the sum of squares regression gets larger relative to the sum of squares residual, and the result is to enlarge the clear value of R2. Using the sums of squares shown in motif 2 and motif 3, for example:

Figure 2:

12870.037 / (12870.037 + 8742.913) = .595

(Compare with cells G5 and G13.)

Figure 3:

55879.198 / (55879.198 + 12875.802) = .813

(Compare with cells G5 and G13.)

So the suppression of the constant in motif 3 has resulted in an enlarge in the R2 from .595 to .813, and that's a substantial increase. But does it really breathe distinguished that the regression equation that's returned in motif 3 is more accurate than the one returned in motif 2? After all, the square root of R2 is the multiple correlation between the actual Y values and the composite, predicted Y values. The higher that correlation, the more accurate the prediction.

How the Deviations touch the R2We can test that accuracy by calculating the correlations, squaring them, and comparing the results to the values for R2 that are returned under the two conditions for the constant: present and absent.

Look first again at motif 2. There, the multiple R is calculated at .772, and the multiple R2 is calculated at .595 (cells H22 and H23). The value of .595 agrees with the value returned by LINEST() in cell G5, and by the ratio of the sums of squares in cell G13.

Now revert to motif 3. There, the multiple R is calculated at .684, and the multiple R2 is calculated at .468 (cells H22 and H23). But the value of .468 does not disagree with the value returned by LINEST() in cell G5, and by the ratio of the sums of squares in cell G13.

In sum, running LINEST() on the data shown in motif 2 and motif 3 has these effects on the clear accuracy of the predictions:

This is an inconsistency, even an clear contradiction. Regarded as a ratio of sums of squares, R2 is higher without the constant. Regarded as the square of the correlation between the actual and predicted Y values, R2 is lower without the constant.

The Constant and the DeviationsOf course, the problem is due to the fact that in omitting the constant, they are redefining what's meant by the term "sum of squares." As a result, we're dismembering the meaning of the R2.

When you involve the constant, the deviations are the differences between the observed values and their mean—that's what "least squares" is everything about. When you omit the constant, the deviations are the differences between the observed values and zero—that's what "regression without the constant" is everything about.

If the predicted values occur to breathe generally farther from zero than from their own mean, then the sum of squares regression will breathe inflated as compared to regression with the constant. In that case, the R2 will tend to breathe greater without the constant in the regression equation than it is with the constant.

A Negative R2?Finally, suppose you're still using a version of exceed through exceed 2002, and you Have used LINEST(), without the constant, on a data set such as the one shown in motif 4.

Figure 4 A negative R2 is viable only if someone has made a mistake.

Even the notion of a negative R2 is ridiculous. Outside the realm of imaginary numbers, the square of a number cannot breathe negative, and ordinary least squares analysis does not involve imaginary numbers. How does the R2 value of -0.09122 in cell F4 of motif 4 procure there?

For that matter, how does exceed 2002 near up with a negative sum of squares regression and a negative F ratio (cells F6 and F5 respectively in motif 4)? If the square of a number must breathe positive, then the sum of squared numbers must likewise breathe positive. And an F ratio is the ratio of two variances. A variance is an average of squared deviations, and therefore must likewise breathe positive—and the ratio of two positive numbers must likewise breathe positive.

How to procure a Negative R2The reply is poorly informed coding. Recall that, when the constant is calculated normally, the total sum of squares of the actual Y values equals the total of the sum of squares regression and the sum of squares residual. For example, in motif 2, the total sum of squares is shown in cell A23 at 21612.950. It is returned by Excel's DEVSQ() function, which sums the squared deviations of each value from the breathe distinguished of the values.

Also in motif 2, the sum of squares regression and the sum of squares residual are shown in cells G15:H15. The total of those two figures is 21612.950: the value of the total sum of squares in cell A23.

Therefore, one way to reckon the sum of squares regression is to subtract the sum of squares residual from the total sum of squares. Another method, of course, is to reckon the sum of squares regression directly on the predicted values. But if you're writing the underlying code in, say, C, it's much quicker to procure the sum of squares regression by subtraction than by doing the math from scratch on the predicted values.

When the constant is forced to zero, the sum of squares residual that's returned in everything versions of exceed equals the result of pointing SUMSQ(), not DEVSQ(), at the residual values. This is entirely correct, given that you want to coerce the constant to zero.

The sum of squares residual using the usual calculation of the constant is as follows:

Residual = Actual – Predicted

That is, find each of N residual values, which is the actual Y value less the predicted Y value (Ŷ). Subtract the breathe distinguished of the residuals () from each residual, square the difference, and sum the squared differences. Excel's DEVSQ() role does precisely this.

The sum of squares residual forcing the constant to zero is as follows:

or, more simply:

Excel's SUMSQ() role does precisely this.

The Mistake, Corrected—In PartNow, what LINEST() did in exceed version 2002 (and earlier) was to exhaust the equivalent of SUMSQ() to procure the sum of squares residual, but the equivalent of DEVSQ() to procure the total sum of squares. If you add SUMSQ(Predicted values) to SUMSQ(Residual values), you procure SUMSQ(Actual values).

But only in the situation where the breathe distinguished of the actual values is zero can SUMSQ(Predicted values) plus SUMSQ(Residual values) equal DEVSQ(Actual values).

The problem has been corrected in exceed 2003 and subsequent versions. But as late as exceed 2010, the problem lives on in exceed charts. If you add a linear trendline to a chart, call for it to coerce the constant to zero, and display the R2 value on the chart, it can still present up as a negative number. see motif 5.

Figure 5 A negative R2 can still show with a chart's trendline.

Notice in motif 5 that although exceed 2010 was used to yield the chart, the linear trendline's properties involve a negative R2 value. (The equation would breathe correct, though, if you chose to present it along with R2.)

ConclusionThis series of papers on how Microsoft has implemented LINEST() concludes with a discussion of Microsoft's extraordinary determination regarding how to ply extreme multicollinearity in the X variables.

Editor’s Note:To read more about spreadsheets, share a tip with other readers, or suggest a topic for Bill Jelen to cover in an upcoming column, click here to visit CFO.com’s Spreadsheet Tips page.

Reader Ray S. wins a copy of exceed for the CEO for this week’s question: “I am presented with a download of information in a PDF or Adobe format. This ‘data dump’ needs to breathe converted into either exceed or Access so as to breathe analyzed more easily. Can you provide best practices to accomplish this?”

Recommended Stories:Excel 2007 and exceed 2010 both support sending your exceed files to PDF. A constant frustration is Excel’s inability to later procure that data back into Excel. Here is a simple demonstration of the problem:

Figure 1 shows a simple table in Excel. In exceed 2010, exhaust File, deliver & Send, Create PDF/XPS Document as shown in motif 2. The table will breathe accurately rendered in the PDF document as shown in motif 3.

Fig. 1

Fig. 2

Fig. 3

Select the text in the PDF document by using Edit, Select All, or by dragging the mouse. Next, copy from the PDF document using Edit, Copy, or Ctrl+C. Then switch to Excel. Paste the copied PDF data to exceed and you will find that the original table is now unwound into a relatively useless single column as shown in motif 4 (below, left). How can it breathe that the Microsoft exceed team cannot round-trip a simple table from exceed to an Excel-created PDF and back to Excel? Is this simply the Microsoft exceed team being obstinate?

Fig. 4

Fails with PDF; Works with XPS

Notice that the Create PDF/XPS command actually offers to create either the market-dominant PDF format or the upstart XPS format. XPS is the modern format designed by Microsoft to compete with the PDF format. An unscientific search of Google indicates that PDF has a 98.5% market share compared with 1.5% for XPS. The exceed team smartly makes “PDF” the default choice. However, if you would instead deliver the file as XPS, copy the table from XPS, and paste back to Excel, you will see that the table retains its original shape, font color, and numeric formatting. Could it breathe that the exceed team is trying to boost the popularity of XPS instead of PDF?

One solution, then, is to start asking for your data in XPS instead of PDF. The downside is that 98.5% of your recipients won’t Have a clue how to yield XPS files.

The Microsoft Word Team Can procure It Right

If this truly is a case of Microsoft purposely doing a contemptible job dealing with Adobe PDF, the animosity is apparently not spread throughout the entire Microsoft Office team. If you copy the data from PDF and paste it to Word, the table appears in a row-and-column format, although the final zero in the august total wraps in that cell of the table, as shown in motif 5 (below).

Fig. 5

A seemingly ridiculous solution, then, is to copy the PDF, paste to Word, copy from Word, and paste to Excel. The final zero goes back into the august total cell. The result shown in motif 6 (below) is passable.

Fig. 6

Why Can’t exceed procure This Right?

For answers, I turned to Keith Bradbury of InvestInTech.com. Keith’s company is the inventor of Able2Extract, a program that can select PDF files and turn them back into exceed workbooks, Access tables, Word documents, and more. InvestInTech is the expert in the province of getting data from PDF to exceed or Access; I’ve been using its software to painlessly extract exceed data from PDF files since the early 2000s.

Keith’s team looked at my examples. They pointed out that each Copy (or Ctrl+C) in any program sends several formats of data to the Windows Clipboard such that the receiving program can select which to use. For example, copy some data from WordPad, and the application sends six versions of that data to the clipboard (text, RTF, UTF8, and so on).

When you copy from Adobe, the program sends two versions of the data, one in unostentatious text and one in flush text format. Keith’s team can only guess, but apparently, Microsoft Word is reading the flush text format from the clipboard and exceed is reading the unostentatious text, with less-than-stellar results.

Use a Third-Party Tool

Let’s breathe honest. I deem a lot of people transfigure their exceed files to PDF because they don’t want the recipient to breathe able to reuse the data in Excel. send me a 450 page document in PDF and they motif I won’t Have the time or inclination to select each page from PDF to Word and back to Excel. I actually had this exact problem once and converted the whole document back to an exceed database using Able2Extract. You can test out Able2Extract 7 with its free seven-day trial.

The software is simple to use. Open the PDF file with Able2Extract. The first step is to identify which area(s) you want to import. If the document contains titles or page numbers in the header, you could select to crop the page to ignore those sections of the document. Able2Extract offers to transfigure the data to Excel, Word, PowerPoint, Publisher, HTML, or AutoCad, as shown in motif 7.

The result is shown in motif 8. Able2Extract preserved the original font colors and numeric formatting. The process was not perfect; the font size changed from 11 point to 9 point and the right-justified headings moved back to the left. However, once I had the data in a table in Excel, it is effortless enough to fix those issues.

Able2Extract likewise offers a pro version that will exhaust OCR to recognize characters in PDF documents that Have been created using a scanner. Download a free trial from http://www.investintech.com/.

Best Practice?

It really should not breathe this hard to procure data out of a PDF file and back into Excel. If you Have a one-page table, the PDF-to-Word-to-Excel solution will work suitably well. If you Have a several-page document with many different tables or repeating headers, then going to a third-party solution such as Able2Extract makes sense.

Fig. 7

Fig. 8

Bill Jelen, a CFO contributing editor, runs MrExcel.com and is the author of 32 books about Microsoft Excel, including Charts & Graphs for exceed 2010. Post questions for future columns in the “Suggest a Topic” section of the Spreadsheet Community heart on the right.

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