we hypothesized that a linear regression to determine if some probesets behaved unexpectedly in one cell type compared to the other might be a reasonable approach to identify as exons. figure 3description of the reap algorithm comparing exon array signal estimates from hcns - scns and cyt - es ( a ) histogram of pearson correlation coefficients computed from median signal estimates for probesets between cyt - es versus hcns - scns for genes ( blue bars ). genes were required to have more than five probesets localized within the exons in the gene. red bars represented pearson correlation coefficients computed from exons with shuffled signal estimates. ( b ) each probeset contained probeset - level estimates from three replicates each, ( a, b, c ) in cyt - es and ( d, e, f ) in hcns - scns. the five points summarizing the log2 probeset - level estimates are indicated by black filled circles. ( c ) each probeset was summarized by five points. scatter plots of signal estimates for probesets that were present in at least one cell type ( cyt - es or hcns - scns ) for the ehbp1 gene. probesets were considered present if the dabg p - value was < 0. 05 for all three replicates in the cell type. a regression line derived from robust linear regression with mm estimation is indicated. points above the line represent probesets within exons that were enriched in cyt - es and points below represent exons that were enriched in hcns - scns. points close to the regression line are not significantly different in cyt - es versus hcns - scns. boxed points represented the five - point summary of a probeset that was significantly enriched in cyt - es but was skipped in hcns - scns. ( d ) histogram of studentized residuals for points from the scatter plot in ( c ) in ehbp1. ( e ) the histogram of studentized residuals for all points for all analyzed probesets ( 100 bins ). ( f ) the scatter plot of studentized residuals generated from comparing cyt - es versus hcns - scns and hcns - scns versus cyt - es of 5, 000 randomly chosen probesets. here, a possible representation of the data was explored. if we had n replicates in one condition and m replicates in the other, we could consider n * m points if we analyzed every possible pairing. for instance, three replicate signal estimates for every probeset per cell line, such as signal estimates a, b, and c in hescs and d, e, and f in hcns - scns, would translate to pairing every signal ( d, a ), ( d, b ), ( d, c ) … ( f, a ), ( f, b ), ( f, c ) for linear regression ( figure 3b ). instead, pairing the signal estimates of all replicates in one condition to the median of the other would only require n + m − 1 points and would capture the variation of the signal estimates of each probeset. for example, we considered ( d, b ), ( e, a ), ( e, b ), ( e, c ), and ( f, b ) points where b and d were the median intensities for the replicates in cyt - es and hcns - scns, respectively ( figure 3b ). a scatter plot of all probesets of the ehbp1 ( eh domain binding protein, refseq identifier nm _ 015252 ) is shown in figure 3c in the format described. each probeset was represented by 5 points of log - transformed ( base 2 ) values; and each point on the scatter plot reflected the extent of inclusion of an exon in hescs and in hcns - scns ( figure 3c ). a classical linear regression model could be proposed to fit the response variable yij, the log2 expression of probeset i in cell - type j ( for example, j is cyt - esc ) to explanatory variables xik, and the log2 expression of probeset i in cell type k ( for example, k is hcns - scns ). however, classical linear regression by least - squares estimation is biased because the least squares predictions are strongly influenced by the outliers, leading to completely incorrect regression line estimates, masking of the outliers, and incorrect predictions of outliers. therefore, we applied m - estimation robust regression to estimate the line, which is less sensitive to outliers. fitting was performed using an iterated, re - weighted least squares analysis. our assumption was that most of the points were “ correct, ” i. e., that most of the exons were constitutively spliced. thus, robust regression would find the line that was least dependent on outliers, which would be potential as exons. this assumption was substantiate d by our observation that, using publicly available ests and mrnas, a minority of human exons ( 7 % ) have evidence for exon - skipping, the most common form of as. using robust regression, the regression line for cyt - esc versus hcns - scns in the ehbp1 gene is illustrated in figure 3c. the boxed points belonged to a probeset that was enriched in hescs but depleted in hcns - scns, which was suspected to be due to as. the difference between the actual and regression - based predicted value, normalized by the estimate of its standard deviation, is called the studentized residuals. studentized residuals were computed for all probeset pairs in ehbp1, and the histogram depicting their distribution is illustrated in figure 3d. as expected, the mean of the distribution was close to zero, and the distribution was approximated by a t - distribution with n - p - 1 degrees of freedom, where n was the number of points on the scatter plot, and the number of parameters p was 2. the boxed points had studentized residuals of 1. 829, 3. 104, 2. 634, 3. 012, and 2. 125 with p - values of 0. 034, 0. 00119, 0. 00477, 0. 00158, and 0. 01780, respectively, computed based on the t - distribution ( figure 3c ). at a stringent p - value cutoff of 0. 01, four of the five studentized residuals were designated as significant “ outliers, ” indicating that the probeset was “ unusual. ” rt - pcr confirmed that the exon, represented by the probeset, was indeed differentially included in hescs and skipped in hcns - scns ( figure 7b ). applying this approach to all gene models revealed that, as expected, the majority of studentized residuals are centered at zero ( figure 3e ). thus far in the example, our analysis was based on regression of hescs ( y - axis ) versus hcns - scns ( x - axis ) ( figure 3b – 3d ). however, robust regression as described was not symmetrical, i. e., parameter estimation of y as a function of x was not the same as that of x as a function of y. the negative slope revealed that probesets enriched in hescs versus hcns - scns ( positive valued ), were expectedly depleted when hcns - scns was compared to hescs ( negative valued; figure 3f ). as our method for predicting candidate alternative exons was based on identification of outliers using robust regression, we named the method reap. identification and removal of false positivesin the process of experimentally validating our predictions, we encountered three main sources of false positives ( fp ) from robust regression. first, we identified genes with probeset signal estimates that were poorly correlated and were not amenable to our method. as an example, the median probeset signal estimates in hescs and hcns - scns of the fip1l1 gene ( gene identifiers bc011543, al136910 ) had a pearson correlation coefficient of 0. 38, and the distribution of points was not amenable to robust regression ( figure 4a ). to avoid inappropriate application of reap and generating false predictions, we empirically determined that a gene had to have a pearson correlation coefficient cutoff of 0. 6 before being amenable to reap analysis. next, we managed two additional sources of fps, namely “ high - leverage ” and “ high - influence ” points, which we were able to identify by computing the following metrics. for every point, we computed ( i ) the studentized residual ( as described above ), ( ii ) the influence, and ( iii ) the leverage ( see materials and methods for more details ). leverage assessed how far away a value of the independent variable was from the mean value; the farther away the observation the more leverage it had.