Overview

This document covers output from five regression models run against four major age classes in this river. The regression models are:

  • Sibling
  • log(Sibling)
  • LogY(Sibling)
  • LnR vs. LnR
  • Ricker

The first three forecast models are based on linear regressions of sibling relationships. Below are the sibling relationships that are relevant for each of the four major age classes that we are forecasting:

Forecast Age Sibling
Age.12 Age.11
Age.22 Age.21
Age.13 Age.12
Age.23 Age.22

Table output

Each model output consists of a table and two graphs. The table shows the most recent 10 years of observed returns for the age being forecast (‘Observed Return’) and the relevant sibling return (‘Sibling Return’) shown in bold black text. Brood and return years are shown in blue text. Two regression model statistics (R-squared and P-value of the slope) are shown in red. Model forecasted returns are shown in bold black text with a yellow highlight. Error measurements are shown in green text. Error measurements shown are absolute deviation (AD), absolute percent error (APE), percent error (PE) and arc tan percent error (AAPE).

Absolute deviation (AD) is defined as

\[\ AD = O - F\] where

O = Observed Return

F = Forecasted Return

Absolute Percent error (APE) is defined as

\[\ APE = ABS(1 - F/O)\] Percent error (PE) is defined as

\[\ PE = 1 - F/O\] Arctangent percent error (AAPE) is defined as \[\ AAPE = arctan(abs((O - F)/O))\]

Graphical output

For each model the data being regressed is shown in a scatterplot. The second graph shows the regression residuals.

age.12

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2007 1,542,520 0 0.515 0 1,748,672 206,152 0.13 -0.13 0.13
2012 2008 2,679,158 0 0.518 0 1,741,590 937,567 0.35 0.35 0.34
2013 2009 740,947 0 0.516 0 1,772,727 1,031,781 1.39 -1.39 0.95
2014 2010 6,053,034 3,046 0.519 0 2,454,585 3,598,449 0.59 0.59 0.54
2015 2011 2,846,209 4,589 0.501 0 2,909,401 63,192 0.02 -0.02 0.02
2016 2012 8,590,994 21,302 0.501 0 6,804,771 1,786,223 0.21 0.21 0.20
2017 2013 3,713,931 2,616 0.528 0 2,474,247 1,239,684 0.33 0.33 0.32
2018 2014 4,484,065 9,832 0.525 0 4,229,603 254,462 0.06 0.06 0.06
2019 2015 5,730,177 4,227 0.527 0 2,896,111 2,834,066 0.49 0.49 0.46
2020 2016 NA NA 0.517 0 NA NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2007 1,542,520 0 0.433 0 682,409 860,111 0.56 0.56 0.51
2012 2008 2,679,158 0 0.417 0 729,402 1,949,756 0.73 0.73 0.63
2013 2009 740,947 0 0.375 0 804,680 63,733 0.09 -0.09 0.09
2014 2010 6,053,034 3,046 0.389 0 2,825,989 3,227,045 0.53 0.53 0.49
2015 2011 2,846,209 4,589 0.397 0 3,108,066 261,857 0.09 -0.09 0.09
2016 2012 8,590,994 21,302 0.400 0 3,961,297 4,629,697 0.54 0.54 0.49
2017 2013 3,713,931 2,616 0.420 0 2,923,050 790,881 0.21 0.21 0.21
2018 2014 4,484,065 9,832 0.425 0 3,673,497 810,568 0.18 0.18 0.18
2019 2015 5,730,177 4,227 0.433 0 3,215,880 2,514,297 0.44 0.44 0.41
2020 2016 NA NA 0.440 0 NA NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2007 1,542,520 0 0.242 0.002 1,415,729 126,791 0.08 0.08 0.08
2012 2008 2,679,158 0 0.243 0.001 1,419,906 1,259,252 0.47 0.47 0.44
2013 2009 740,947 0 0.235 0.001 1,450,164 709,217 0.96 -0.96 0.76
2014 2010 6,053,034 3,046 0.241 0.001 1,642,835 4,410,199 0.73 0.73 0.63
2015 2011 2,846,209 4,589 0.225 0.001 1,829,663 1,016,546 0.36 0.36 0.34
2016 2012 8,590,994 21,302 0.224 0.001 4,087,831 4,503,164 0.52 0.52 0.48
2017 2013 3,713,931 2,616 0.255 0.000 1,703,331 2,010,600 0.54 0.54 0.50
2018 2014 4,484,065 9,832 0.248 0.000 2,486,131 1,997,934 0.45 0.45 0.42
2019 2015 5,730,177 4,227 0.252 0.000 1,906,743 3,823,435 0.67 0.67 0.59
2020 2016 NA NA 0.243 0.000 NA NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2007 1,542,520 0 0.221 0.003 1,704,110 161,590 0.10 -0.10 0.10
2012 2008 2,679,158 0 0.222 0.002 1,682,744 996,414 0.37 0.37 0.36
2013 2009 740,947 0 0.219 0.002 1,539,324 798,378 1.08 -1.08 0.82
2014 2010 6,053,034 3,046 0.223 0.002 2,086,585 3,966,449 0.66 0.66 0.58
2015 2011 2,846,209 4,589 0.223 0.001 1,542,373 1,303,836 0.46 0.46 0.43
2016 2012 8,590,994 21,302 0.217 0.001 2,167,135 6,423,860 0.75 0.75 0.64
2017 2013 3,713,931 2,616 0.215 0.001 1,547,749 2,166,182 0.58 0.58 0.53
2018 2014 4,484,065 9,832 0.204 0.002 2,372,479 2,111,586 0.47 0.47 0.44
2019 2015 5,730,177 4,227 0.208 0.001 3,153,115 2,577,063 0.45 0.45 0.42
2020 2016 NA NA 0.220 0.001 2,458,726 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2007 1,542,520 0 0.139 0.016 1,915,008 372,489 0.24 -0.24 0.24
2012 2008 2,679,158 0 0.138 0.015 1,874,588 804,570 0.30 0.30 0.29
2013 2009 740,947 0 0.142 0.012 1,628,936 887,989 1.20 -1.20 0.88
2014 2010 6,053,034 3,046 0.133 0.014 2,483,816 3,569,217 0.59 0.59 0.53
2015 2011 2,846,209 4,589 0.132 0.013 1,623,202 1,223,007 0.43 0.43 0.41
2016 2012 8,590,994 21,302 0.138 0.011 2,563,164 6,027,830 0.70 0.70 0.61
2017 2013 3,713,931 2,616 0.134 0.011 1,598,306 2,115,626 0.57 0.57 0.52
2018 2014 4,484,065 9,832 0.142 0.008 2,809,287 1,674,779 0.37 0.37 0.36
2019 2015 5,730,177 4,227 0.141 0.007 3,572,217 2,157,961 0.38 0.38 0.36
2020 2016 NA NA 0.137 0.008 2,871,589 NA NA NA NA

age.22

sibling

Below are model outputs using data from 1972

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 1,197,115 0 0.624 0 2,545,156 1,348,041 1.13 -1.13 0.84
2012 2007 6,972,782 24,305 0.626 0 4,457,935 2,514,847 0.36 0.36 0.35
2013 2008 1,247,528 2,520 0.624 0 2,775,711 1,528,184 1.22 -1.22 0.89
2014 2009 9,725,832 11,611 0.626 0 3,460,694 6,265,137 0.64 0.64 0.57
2015 2010 13,231,078 87,386 0.611 0 9,706,769 3,524,309 0.27 0.27 0.26
2016 2011 2,573,729 43,953 0.617 0 6,328,002 3,754,273 1.46 -1.46 0.97
2017 2012 397,153 3,702 0.612 0 2,980,939 2,583,787 6.51 -6.51 1.42
2018 2013 38,269 2,155 0.614 0 2,780,356 2,742,086 71.65 -71.65 1.56
2019 2014 71,251 4,883 0.615 0 2,924,316 2,853,065 40.04 -40.04 1.55
2020 2015 NA 0 0.617 0 2,446,644 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 1,197,115 0 0.360 0 311,855 885,260 0.74 0.74 0.64
2012 2007 6,972,782 24,305 0.345 0 3,731,602 3,241,180 0.46 0.46 0.44
2013 2008 1,247,528 2,520 0.355 0 2,241,240 993,712 0.80 -0.80 0.67
2014 2009 9,725,832 11,611 0.353 0 3,160,973 6,564,858 0.67 0.67 0.59
2015 2010 13,231,078 87,386 0.359 0 5,341,752 7,889,326 0.60 0.60 0.54
2016 2011 2,573,729 43,953 0.374 0 4,731,617 2,157,888 0.84 -0.84 0.70
2017 2012 397,153 3,702 0.372 0 2,529,400 2,132,247 5.37 -5.37 1.39
2018 2013 38,269 2,155 0.357 0 2,116,144 2,077,875 54.30 -54.30 1.55
2019 2014 71,251 4,883 0.307 0 2,327,385 2,256,134 31.66 -31.66 1.54
2020 2015 NA 0 0.269 0 323,937 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 1,197,115 0 0.331 0 978,020 219,095 0.18 0.18 0.18
2012 2007 6,972,782 24,305 0.332 0 1,379,402 5,593,380 0.80 0.80 0.68
2013 2008 1,247,528 2,520 0.321 0 1,070,039 177,489 0.14 0.14 0.14
2014 2009 9,725,832 11,611 0.322 0 1,218,442 8,507,389 0.87 0.87 0.72
2015 2010 13,231,078 87,386 0.303 0 3,602,141 9,628,937 0.73 0.73 0.63
2016 2011 2,573,729 43,953 0.313 0 2,076,519 497,210 0.19 0.19 0.19
2017 2012 397,153 3,702 0.314 0 1,195,348 798,195 2.01 -2.01 1.11
2018 2013 38,269 2,155 0.317 0 1,132,867 1,094,598 28.60 -28.60 1.54
2019 2014 71,251 4,883 0.306 0 1,069,588 998,337 14.01 -14.01 1.50
2020 2015 NA 0 0.302 0 924,063 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 1,197,115 0 0.018 0.215 1,378,063 180,948 0.15 -0.15 0.15
2012 2007 6,972,782 24,305 0.020 0.204 1,236,002 5,736,780 0.82 0.82 0.69
2013 2008 1,247,528 2,520 0.012 0.244 1,281,089 33,561 0.03 -0.03 0.03
2014 2009 9,725,832 11,611 0.013 0.235 1,021,967 8,703,864 0.89 0.89 0.73
2015 2010 13,231,078 87,386 0.002 0.310 2,262,992 10,968,086 0.83 0.83 0.69
2016 2011 2,573,729 43,953 0.000 0.325 1,157,502 1,416,227 0.55 0.55 0.50
2017 2012 397,153 3,702 -0.002 0.344 2,389,722 1,992,569 5.02 -5.02 1.37
2018 2013 38,269 2,155 -0.002 0.338 1,037,439 999,170 26.11 -26.11 1.53
2019 2014 71,251 4,883 0.007 0.266 2,293,323 2,222,072 31.19 -31.19 1.54
2020 2015 NA 0 0.004 0.289 4,136,214 NA NA NA NA

age.13

sibling

Below are model outputs using data from 1972

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 2,701,997 3,663,815 0.339 0.000 1,332,570 1,369,427 0.51 0.51 0.47
2012 2007 1,852,364 1,542,520 0.315 0.000 1,096,757 755,607 0.41 0.41 0.39
2013 2008 1,930,847 2,679,158 0.300 0.000 1,266,532 664,315 0.34 0.34 0.33
2014 2009 1,001,605 740,947 0.292 0.000 1,037,815 36,211 0.04 -0.04 0.04
2015 2010 5,545,200 6,053,034 0.296 0.000 1,713,813 3,831,387 0.69 0.69 0.60
2016 2011 2,168,999 2,846,209 0.244 0.001 1,399,643 769,356 0.35 0.35 0.34
2017 2012 2,635,003 8,590,994 0.240 0.001 2,303,522 331,482 0.13 0.13 0.13
2018 2013 2,789,273 3,713,931 0.264 0.000 1,562,926 1,226,347 0.44 0.44 0.41
2019 2014 2,065,407 4,484,065 0.258 0.000 1,715,752 349,655 0.17 0.17 0.17
2020 2015 NA 5,730,177 0.261 0.000 1,924,980 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 2,701,997 3,663,815 0.361 0 1,369,154 1,332,843 0.49 0.49 0.46
2012 2007 1,852,364 1,542,520 0.370 0 911,523 940,842 0.51 0.51 0.47
2013 2008 1,930,847 2,679,158 0.359 0 1,225,841 705,007 0.37 0.37 0.35
2014 2009 1,001,605 740,947 0.362 0 649,860 351,744 0.35 0.35 0.34
2015 2010 5,545,200 6,053,034 0.355 0 1,873,428 3,671,772 0.66 0.66 0.58
2016 2011 2,168,999 2,846,209 0.380 0 1,345,773 823,227 0.38 0.38 0.36
2017 2012 2,635,003 8,590,994 0.383 0 2,459,153 175,850 0.07 0.07 0.07
2018 2013 2,789,273 3,713,931 0.400 0 1,578,049 1,211,225 0.43 0.43 0.41
2019 2014 2,065,407 4,484,065 0.406 0 1,782,124 283,283 0.14 0.14 0.14
2020 2015 NA 5,730,177 0.412 0 2,049,578 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 2,701,997 3,663,815 0.205 0.004 1,039,987 1,662,010 0.62 0.62 0.55
2012 2007 1,852,364 1,542,520 0.202 0.004 844,512 1,007,852 0.54 0.54 0.50
2013 2008 1,930,847 2,679,158 0.190 0.005 980,460 950,387 0.49 0.49 0.46
2014 2009 1,001,605 740,947 0.185 0.005 809,420 192,184 0.19 0.19 0.19
2015 2010 5,545,200 6,053,034 0.184 0.004 1,443,031 4,102,169 0.74 0.74 0.64
2016 2011 2,168,999 2,846,209 0.202 0.002 1,057,343 1,111,656 0.51 0.51 0.47
2017 2012 2,635,003 8,590,994 0.198 0.002 2,102,608 532,396 0.20 0.20 0.20
2018 2013 2,789,273 3,713,931 0.218 0.001 1,199,550 1,589,723 0.57 0.57 0.52
2019 2014 2,065,407 4,484,065 0.216 0.001 1,343,428 721,979 0.35 0.35 0.34
2020 2015 NA 5,730,177 0.220 0.001 1,581,073 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 2,701,997 3,663,815 0.066 0.078 952,244 1,749,754 0.65 0.65 0.57
2012 2007 1,852,364 1,542,520 0.061 0.082 959,484 892,880 0.48 0.48 0.45
2013 2008 1,930,847 2,679,158 0.059 0.083 972,938 957,909 0.50 0.50 0.46
2014 2009 1,001,605 740,947 0.056 0.086 944,457 57,148 0.06 0.06 0.06
2015 2010 5,545,200 6,053,034 0.056 0.082 1,102,624 4,442,576 0.80 0.80 0.68
2016 2011 2,168,999 2,846,209 0.057 0.077 981,287 1,187,713 0.55 0.55 0.50
2017 2012 2,635,003 8,590,994 0.052 0.085 1,170,912 1,464,092 0.56 0.56 0.51
2018 2013 2,789,273 3,713,931 0.054 0.077 1,000,231 1,789,043 0.64 0.64 0.57
2019 2014 2,065,407 4,484,065 0.045 0.093 1,242,346 823,061 0.40 0.40 0.38
2020 2015 NA 5,730,177 0.048 0.084 1,427,834 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2006 2,701,997 3,663,815 0.300 0 1,166,903 1,535,094 0.57 0.57 0.52
2012 2007 1,852,364 1,542,520 0.303 0 1,137,569 714,796 0.39 0.39 0.37
2013 2008 1,930,847 2,679,158 0.307 0 1,142,758 788,089 0.41 0.41 0.39
2014 2009 1,001,605 740,947 0.312 0 1,021,691 20,086 0.02 -0.02 0.02
2015 2010 5,545,200 6,053,034 0.314 0 1,453,279 4,091,921 0.74 0.74 0.64
2016 2011 2,168,999 2,846,209 0.303 0 1,058,229 1,110,770 0.51 0.51 0.47
2017 2012 2,635,003 8,590,994 0.309 0 1,526,764 1,108,240 0.42 0.42 0.40
2018 2013 2,789,273 3,713,931 0.308 0 1,038,601 1,750,672 0.63 0.63 0.56
2019 2014 2,065,407 4,484,065 0.314 0 1,627,946 437,461 0.21 0.21 0.21
2020 2015 NA 5,730,177 0.314 0 1,781,269 NA NA NA NA

age.23

sibling

Below are model outputs using data from 1972

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2005 1,754,061 4,527,248 0.357 0 571,368 1,182,693 0.67 0.67 0.59
2012 2006 746,641 1,197,115 0.332 0 389,879 356,762 0.48 0.48 0.45
2013 2007 2,379,818 6,972,782 0.328 0 774,961 1,604,857 0.67 0.67 0.59
2014 2008 679,005 1,247,528 0.304 0 445,870 233,135 0.34 0.34 0.33
2015 2009 1,396,254 9,725,832 0.302 0 1,006,296 389,958 0.28 0.28 0.27
2016 2010 851,679 13,231,078 0.309 0 1,251,159 399,480 0.47 -0.47 0.44
2017 2011 491,950 2,573,729 0.304 0 542,461 50,511 0.10 -0.10 0.10
2018 2012 143,170 397,153 0.306 0 400,390 257,220 1.80 -1.80 1.06
2019 2013 32,085 38,269 0.312 0 367,746 335,660 10.46 -10.46 1.48
2020 2014 NA 71,251 0.320 0 357,737 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2005 1,754,061 4,527,248 0.527 0 548,811 1,205,250 0.69 0.69 0.60
2012 2006 746,641 1,197,115 0.526 0 292,730 453,911 0.61 0.61 0.55
2013 2007 2,379,818 6,972,782 0.515 0 731,258 1,648,561 0.69 0.69 0.61
2014 2008 679,005 1,247,528 0.522 0 316,034 362,970 0.53 0.53 0.49
2015 2009 1,396,254 9,725,832 0.515 0 933,312 462,942 0.33 0.33 0.32
2016 2010 851,679 13,231,078 0.527 0 1,119,489 267,810 0.31 -0.31 0.30
2017 2011 491,950 2,573,729 0.531 0 471,479 20,471 0.04 0.04 0.04
2018 2012 143,170 397,153 0.532 0 179,092 35,922 0.25 -0.25 0.25
2019 2013 32,085 38,269 0.539 0 52,380 20,295 0.63 -0.63 0.56
2020 2014 NA 71,251 0.579 0 68,613 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2005 1,754,061 4,527,248 0.323 0.000 297,217 1,456,844 0.83 0.83 0.69
2012 2006 746,641 1,197,115 0.298 0.000 231,868 514,773 0.69 0.69 0.60
2013 2007 2,379,818 6,972,782 0.281 0.001 402,779 1,977,039 0.83 0.83 0.69
2014 2008 679,005 1,247,528 0.271 0.001 254,098 424,907 0.63 0.63 0.56
2015 2009 1,396,254 9,725,832 0.260 0.001 552,312 843,941 0.60 0.60 0.54
2016 2010 851,679 13,231,078 0.267 0.001 780,714 70,965 0.08 0.08 0.08
2017 2011 491,950 2,573,729 0.275 0.000 301,398 190,552 0.39 0.39 0.37
2018 2012 143,170 397,153 0.272 0.000 251,852 108,682 0.76 -0.76 0.65
2019 2013 32,085 38,269 0.279 0.000 238,914 206,828 6.45 -6.45 1.42
2020 2014 NA 71,251 0.286 0.000 222,818 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2005 1,754,061 4,527,248 0.177 0.009 269,134 1,484,927 0.85 0.85 0.70
2012 2006 746,641 1,197,115 0.154 0.013 332,702 413,939 0.55 0.55 0.51
2013 2007 2,379,818 6,972,782 0.152 0.012 324,797 2,055,021 0.86 0.86 0.71
2014 2008 679,005 1,247,528 0.136 0.015 340,259 338,746 0.50 0.50 0.46
2015 2009 1,396,254 9,725,832 0.134 0.015 312,805 1,083,449 0.78 0.78 0.66
2016 2010 851,679 13,231,078 0.121 0.018 448,519 403,160 0.47 0.47 0.44
2017 2011 491,950 2,573,729 0.124 0.016 331,741 160,209 0.33 0.33 0.31
2018 2012 143,170 397,153 0.122 0.015 458,212 315,042 2.20 -2.20 1.14
2019 2013 32,085 38,269 0.115 0.017 314,153 282,067 8.79 -8.79 1.46
2020 2014 NA 71,251 0.119 0.015 439,788 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2011 2005 1,754,061 4,527,248 0.087 0.053 291,607 1,462,454 0.83 0.83 0.69
2012 2006 746,641 1,197,115 0.096 0.041 385,560 361,081 0.48 0.48 0.45
2013 2007 2,379,818 6,972,782 0.101 0.035 369,915 2,009,903 0.84 0.84 0.70
2014 2008 679,005 1,247,528 0.106 0.030 388,301 290,703 0.43 0.43 0.40
2015 2009 1,396,254 9,725,832 0.110 0.025 341,619 1,054,634 0.76 0.76 0.65
2016 2010 851,679 13,231,078 0.118 0.020 541,218 310,461 0.36 0.36 0.35
2017 2011 491,950 2,573,729 0.119 0.018 362,786 129,164 0.26 0.26 0.26
2018 2012 143,170 397,153 0.123 0.015 548,920 405,750 2.83 -2.83 1.23
2019 2013 32,085 38,269 0.117 0.016 332,663 300,577 9.37 -9.37 1.46
2020 2014 NA 71,251 0.091 0.030 520,773 NA NA NA NA