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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 mistaken can easily absorb 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 entire belt of regression analysis, regardless of the platform used to carry out the regression.

Some credible practitioners believe that it's necessary to favor the constant to zero in certain situations, usually in the context of regression discontinuity designs.

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

The excel 2003 Through 2010 VersionsFigure 1 shows an specimen of the dissimilarity 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 consume excel 2003 or excel 2010.

In figure 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 figure 2, cells G15:H15 accommodate 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 compass from the express 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 artery to reckon that figure (and a useful artery 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 figure 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 benchmark errors in the transpose of worksheet order). The former are calculated using Excel's matrix functions; the latter are calculated using the LINEST function.

Also notice in figure 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 obtain 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 entire as is expected according to the mathematics underlying regression analysis.

Changing the deviation Basis to ZeroNow examine the selfsame sort of analysis shown in figure 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 figure 3. They are both much larger than the sums of squares reported in figure 2. The understanding is that the deviations that are squared and summed in figure 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 understanding that this is so, behold Statistical Analysis: Microsoft excel 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 befall that the sum of squares regression gets larger relative to the sum of squares residual, and the result is to augment the evident value of R2. Using the sums of squares shown in figure 2 and figure 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 figure 3 has resulted in an augment in the R2 from .595 to .813, and that's a substantial increase. But does it really express that the regression equation that's returned in figure 3 is more accurate than the one returned in figure 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 strike 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 figure 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 figure 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 harmonize 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 figure 2 and figure 3 has these effects on the evident accuracy of the predictions:

This is an inconsistency, even an evident 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 acceptation of the R2.

When you include the constant, the deviations are the differences between the observed values and their mean—that's what "least squares" is entire 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 entire about.

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

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

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

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

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

How to obtain a Negative R2The answer 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 figure 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 express of the values.

Also in figure 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 artery 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 obtain 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 entire versions of excel equals the result of pointing SUMSQ(), not DEVSQ(), at the residual values. This is entirely correct, given that you want to favor the constant to zero.

The sum of squares residual using the household 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 express 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 excel version 2002 (and earlier) was to consume the equivalent of SUMSQ() to obtain the sum of squares residual, but the equivalent of DEVSQ() to obtain the total sum of squares. If you add SUMSQ(Predicted values) to SUMSQ(Residual values), you obtain SUMSQ(Actual values).

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

The problem has been corrected in excel 2003 and subsequent versions. But as late as excel 2010, the problem lives on in excel charts. If you add a linear trendline to a chart, call for it to favor the constant to zero, and parade the R2 value on the chart, it can soundless demonstrate up as a negative number. behold figure 5.

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

Notice in figure 5 that although excel 2010 was used to bear the chart, the linear trendline's properties include a negative R2 value. (The equation would subsist correct, though, if you chose to demonstrate it along with R2.)

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

Editor’s Note:To read more about spreadsheets, partake a tip with other readers, or imply 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 excel 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 subsist converted into either excel or Access so as to subsist analyzed more easily. Can you provide best practices to accomplish this?”

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

Figure 1 shows a simple table in Excel. In excel 2010, consume File, reclaim & Send, Create PDF/XPS Document as shown in figure 2. The table will subsist accurately rendered in the PDF document as shown in figure 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 excel and you will find that the original table is now unwound into a relatively useless single column as shown in figure 4 (below, left). How can it subsist that the Microsoft excel team cannot round-trip a simple table from excel to an Excel-created PDF and back to Excel? Is this simply the Microsoft excel 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 recent format designed by Microsoft to compete with the PDF format. An unscientific search of Google indicates that PDF has a 98.5% market partake compared with 1.5% for XPS. The excel team smartly makes “PDF” the default choice. However, if you would instead reclaim the file as XPS, copy the table from XPS, and paste back to Excel, you will behold that the table retains its original shape, font color, and numeric formatting. Could it subsist that the excel 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 absorb a clue how to bear XPS files.

The Microsoft Word Team Can obtain It Right

If this truly is a case of Microsoft purposely doing a malign 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 majestic total wraps in that cell of the table, as shown in figure 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 majestic total cell. The result shown in figure 6 (below) is passable.

Fig. 6

Why Can’t excel obtain This Right?

For answers, I turned to Keith Bradbury of InvestInTech.com. Keith’s company is the inventor of Able2Extract, a program that can acquire PDF files and rotate them back into excel workbooks, Access tables, Word documents, and more. InvestInTech is the expert in the bailiwick of getting data from PDF to excel or Access; I’ve been using its software to painlessly extract excel 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 plain text and one in wealthy text format. Keith’s team can only guess, but apparently, Microsoft Word is reading the wealthy text format from the clipboard and excel is reading the plain text, with less-than-stellar results.

Use a Third-Party Tool

Let’s subsist honest. I deem a lot of people convert their excel files to PDF because they don’t want the recipient to subsist able to reuse the data in Excel. transmit me a 450 page document in PDF and they figure I won’t absorb the time or inclination to acquire each page from PDF to Word and back to Excel. I actually had this exact problem once and converted the entire document back to an excel 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 convert the data to Excel, Word, PowerPoint, Publisher, HTML, or AutoCad, as shown in figure 7.

The result is shown in figure 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 easy enough to fix those issues.

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

Best Practice?

It really should not subsist this hard to obtain data out of a PDF file and back into Excel. If you absorb a one-page table, the PDF-to-Word-to-Excel solution will drudgery suitably well. If you absorb 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 excel 2010. Post questions for future columns in the “Suggest a Topic” section of the Spreadsheet Community headquarters on the right.

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