*** Factor Analysis ***

Sums of squares of loadings:

  Factor1

 11.17569

 

The number of variables is 12 and the number of observations is 8144

 

Test of the hypothesis that 1 factor is sufficient

versus the alternative that more are required:

The chi square statistic is 209383.08 on 54 degrees of freedom.

The p-value is 0

 

Component names:

                                                                            

 "loadings" "uniquenesses" "correlation" "criteria" "factors" "dof" "method"

                                         

 "center" "scale" "n.obs" "scores" "call"

 

Call:

factanal(x =  ~ Jan + Feb + Mar + Apr + May + Jun + Jul + Aug + Sep + Oct +

          Nov + Dec, factors = 1, method = "mle", data = temp, scores = T, type

           = "regression", rotation = "varimax", na.action = na.omit, control =

          list(iter.max = 20, unique.tol = 0.0001))

 

Importance of factors:

                  Factor1

   SS loadings 11.1756931

Proportion Var  0.9313078

Cumulative Var  0.9313078

 

The degrees of freedom for the model is 54.

 

Uniquenesses:

        Jan         Feb        Mar        Apr        May       Jun       Jul

 0.01892805 0.005719193 0.01307799 0.03672961 0.04785991 0.1111591 0.1926561

       Aug       Sep        Oct        Nov        Dec

 0.1853478 0.1085326 0.05049321 0.02668542 0.02675484

 

Loadings:

    Factor1

Jan 0.990 

Feb 0.997 

Mar 0.993 

Apr 0.981 

May 0.976 

Jun 0.943 

Jul 0.899 

Aug 0.903 

Sep 0.944 

Oct 0.974 

Nov 0.987 

Dec 0.987 

 

 

 

          *** Linear Model ***

 

Call: lm(formula = Jan ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q Median     3Q   Max

 -3.412 -0.5115 0.1073 0.5432 2.326

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   18.7856    0.0425   442.1496    0.0000

          X    0.0094    0.0002    48.0693    0.0000

          Y   -0.1089    0.0003  -346.3161    0.0000

          H   -0.0058    0.0000  -313.0038    0.0000

 

Residual standard error: 0.7822 on 8140 degrees of freedom

Multiple R-Squared: 0.9784

F-statistic: 123100 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Feb ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q   Median     3Q   Max

 -3.459 -0.7212 -0.06065 0.8874 2.474

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   19.8705    0.0522   380.4316    0.0000

          X    0.0128    0.0002    53.6683    0.0000

          Y   -0.1099    0.0004  -284.2563    0.0000

          H   -0.0054    0.0000  -238.7685    0.0000

 

Residual standard error: 0.9617 on 8140 degrees of freedom

Multiple R-Squared: 0.9677

F-statistic: 81230 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Mar ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q   Median     3Q  Max

 -4.356 -0.8987 -0.03634 0.9442 2.54

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   22.4391    0.0647   346.7363    0.0000

          X    0.0157    0.0003    53.1081    0.0000

          Y   -0.0977    0.0005  -204.0777    0.0000

          H   -0.0049    0.0000  -172.4918    0.0000

 

Residual standard error: 1.191 on 8140 degrees of freedom

Multiple R-Squared: 0.9422

F-statistic: 44230 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Apr ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q   Median    3Q   Max

 -5.775 -1.075 -0.04361 1.054 3.571

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   26.5694    0.0780   340.5486    0.0000

          X    0.0182    0.0004    51.0019    0.0000

          Y   -0.0795    0.0006  -137.6631    0.0000

          H   -0.0047    0.0000  -138.3600    0.0000

 

Residual standard error: 1.436 on 8140 degrees of freedom

Multiple R-Squared: 0.9008

F-statistic: 24640 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = May ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min   1Q  Median    3Q   Max

 -6.097 -1.2 -0.1067 1.196 4.942

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   32.1349    0.0915   351.1204    0.0000

          X    0.0178    0.0004    42.4374    0.0000

          Y   -0.0856    0.0007  -126.4194    0.0000

          H   -0.0047    0.0000  -118.0734    0.0000

 

Residual standard error: 1.685 on 8140 degrees of freedom

Multiple R-Squared: 0.8762

F-statistic: 19210 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Jun ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q  Max

 -6.146 -1.396 -0.141 1.352 6.41

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   34.8016    0.1085   320.8258    0.0000

          X    0.0175    0.0005    35.1399    0.0000

          Y   -0.0702    0.0008   -87.4275    0.0000

          H   -0.0040    0.0000   -83.6996    0.0000

 

Residual standard error: 1.997 on 8140 degrees of freedom

Multiple R-Squared: 0.7831

F-statistic: 9796 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Jul ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q  Median   3Q   Max

 -6.996 -1.252 -0.1208 1.32 5.845

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   37.1428    0.1085   342.4558    0.0000

          X    0.0033    0.0005     6.6933    0.0000

          Y   -0.0592    0.0008   -73.7077    0.0000

          H   -0.0033    0.0000   -70.7046    0.0000

 

Residual standard error: 1.997 on 8140 degrees of freedom

Multiple R-Squared: 0.6766

F-statistic: 5677 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Aug ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q   Median    3Q   Max

 -6.663 -1.101 -0.09469 1.188 5.435

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   37.8662    0.0971   390.1477    0.0000

          X   -0.0070    0.0004   -15.8274    0.0000

          Y   -0.0654    0.0007   -91.0138    0.0000

          H   -0.0036    0.0000   -86.2519    0.0000

 

Residual standard error: 1.787 on 8140 degrees of freedom

Multiple R-Squared: 0.7328

F-statistic: 7440 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Sep ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q   Median    3Q   Max

 -4.602 -1.002 -0.08623 0.992 4.845

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   35.9729    0.0812   443.1123    0.0000

          X   -0.0095    0.0004   -25.5100    0.0000

          Y   -0.0765    0.0006  -127.2884    0.0000

          H   -0.0045    0.0000  -127.7968    0.0000

 

Residual standard error: 1.495 on 8140 degrees of freedom

Multiple R-Squared: 0.8485

F-statistic: 15200 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Oct ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q Median    3Q   Max

 -3.534 -0.7777 -0.062 0.812 3.522

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   32.4750    0.0601   540.7527    0.0000

          X   -0.0092    0.0003   -33.3128    0.0000

          Y   -0.0957    0.0004  -215.3039    0.0000

          H   -0.0053    0.0000  -201.0183    0.0000

 

Residual standard error: 1.106 on 8140 degrees of freedom

Multiple R-Squared: 0.9385

F-statistic: 41430 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Nov ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

   Min      1Q   Median     3Q   Max

 -3.11 -0.5231 -0.02225 0.5028 2.483

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   25.6353    0.0419   612.0896    0.0000

          X    0.0009    0.0002     4.5123    0.0000

          Y   -0.0943    0.0003  -304.2178    0.0000

          H   -0.0054    0.0000  -294.6120    0.0000

 

Residual standard error: 0.7711 on 8140 degrees of freedom

Multiple R-Squared: 0.9717

F-statistic: 93280 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Dec ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q  Median     3Q   Max

 -2.832 -0.3751 0.07327 0.4302 2.066

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   20.6484    0.0331   623.7464    0.0000

          X    0.0053    0.0002    35.0364    0.0000

          Y   -0.1041    0.0002  -425.0836    0.0000

          H   -0.0055    0.0000  -380.3688    0.0000

 

Residual standard error: 0.6095 on 8140 degrees of freedom

Multiple R-Squared: 0.9849

F-statistic: 177500 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Annual ~ X + Y + H, data = temp, na.action = na.exclude)

Residuals:

    Min      1Q   Median     3Q   Max

 -3.814 -0.8376 -0.09476 0.8347 3.754

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   28.7149    0.0646   444.5558    0.0000

          X    0.0062    0.0003    20.9890    0.0000

          Y   -0.0872    0.0005  -182.4550    0.0000

          H   -0.0048    0.0000  -169.6605    0.0000

 

Residual standard error: 1.189 on 8140 degrees of freedom

Multiple R-Squared: 0.9269

F-statistic: 34420 on 3 and 8140 degrees of freedom, the p-value is 0

 

 

 

 

 

 

 

 

          ***  Summary Statistics for data in:  temp ***

 

                      X             Y             H            Jan

     Min:     1.4113900     1.4100000  -163.9290000    -5.90212000

 1st Qu.:    74.8038000    46.5300000   850.0475000     2.43366000

    Mean:   115.1768288    71.8850688  1090.2850749     5.71972825

  Median:   119.9680000    74.7300000  1143.9400000     5.04532000

 3rd Qu.:   158.0760000    98.7000000  1406.4475000     8.39758750

     Max:   214.5320000   138.1800000  2429.1400000    20.04680000

 Total N:  8144.0000000  8144.0000000  8144.0000000  8144.00000000

   NA's :     0.0000000     0.0000000     0.0000000     0.00000000

Std Dev.:    50.8301856    32.1756258   486.5071226     5.32523646

 SE Mean:     0.5632521     0.3565399     5.3910123     0.05900924

LCL Mean:   114.0727109    71.1861595  1079.7173142     5.60405507

UCL Mean:   116.2809467    72.5839780  1100.8528355     5.83540143

Skewness:     0.2588505     0.1627976     0.4761794     0.47240357

Kurtosis:    -0.9914253    -0.9887940    -0.1875395    -0.05794020

                     Feb            Mar            Apr            May

     Min:    -5.66439000    -0.94550100     6.89741000    11.01200000

 1st Qu.:     4.09185750     8.44832000    14.43262500    19.33790000

    Mean:     7.52800970    11.92486740    17.82820460    22.89663509

  Median:     6.95584500    11.54665000    17.65935000    22.92070000

 3rd Qu.:    10.50157500    14.87257500    20.63337500    26.05440000

     Max:    20.63780000    23.55910000    27.48180000    32.72150000

 Total N:  8144.00000000  8144.00000000  8144.00000000  8144.00000000

   NA's :     0.00000000     0.00000000     0.00000000     0.00000000

Std Dev.:     5.34772651     4.95504839     4.55958522     4.78858757

 SE Mean:     0.05925845     0.05490716     0.05052502     0.05306260

LCL Mean:     7.41184800    11.81723533    17.72916267    22.79261884

UCL Mean:     7.64417140    12.03249946    17.92724654    23.00065135

Skewness:     0.33515668     0.34583928     0.23351528     0.05527923

Kurtosis:    -0.27776103    -0.38455190    -0.60397084    -0.74292367

                     Jun            Jul            Aug            Sep

     Min:    16.04490000    18.86440000    18.24900000    14.72990000

 1st Qu.:    24.31862500    26.97257500    25.71082500    21.49812500

    Mean:    27.45530340    29.63099917    28.38107251    24.45605980

  Median:    27.90635000    29.82315000    28.27930000    24.14200000

 3rd Qu.:    30.42340000    32.21305000    30.71985000    26.61167500

     Max:    36.51090000    37.93640000    37.28810000    33.67680000

 Total N:  8144.00000000  8144.00000000  8144.00000000  8144.00000000

   NA's :     0.00000000     0.00000000     0.00000000     0.00000000

Std Dev.:     4.28747016     3.51094459     3.45605482     3.83953092

 SE Mean:     0.04750969     0.03890497     0.03829673     0.04254605

LCL Mean:    27.36217227    29.55473549    28.30600113    24.37265867

UCL Mean:    27.54843453    29.70726284    28.45614389    24.53946093

Skewness:     0.19398277     0.14624119     0.11589627     0.34745294

Kurtosis:    -0.68639739    -0.53396346    -0.53278403    -0.62112398

                     Oct            Nov            Dec         Annual

     Min:     8.97122000     3.58916000    -2.99683000     7.50823000

 1st Qu.:    15.45972500     9.96218250     4.64599500    14.77695000

    Mean:    18.80784470    13.09712717     7.79430169    17.95610013

  Median:    18.19075000    12.24200000     6.90432500    17.67010000

 3rd Qu.:    21.05285000    15.09015000    10.16375000    20.40237500

     Max:    29.36290000    25.30180000    21.90420000    27.33200000

 Total N:  8144.00000000  8144.00000000  8144.00000000  8144.00000000

   NA's :     0.00000000     0.00000000     0.00000000     0.00000000

Std Dev.:     4.45906016     4.58562338     4.96601624     4.39841411

 SE Mean:     0.04941109     0.05081355     0.05502870     0.04873907

LCL Mean:    18.71098634    12.99751965     7.68643139    17.86055911

UCL Mean:    18.90470305    13.19673470     7.90217199    18.05164115

Skewness:     0.58348010     0.71044547     0.68827548     0.28638856

Kurtosis:    -0.45873329    -0.08252457     0.08532305    -0.53562163

                 Factor1

     Min: -2.398311e+000

 1st Qu.: -6.692942e-001

    Mean:  7.020143e-016

  Median: -9.802694e-002

 3rd Qu.:  5.373208e-001

     Max:  2.385710e+000

 Total N:  8.144000e+003

   NA's :  0.000000e+000

Std Dev.:  9.989848e-001

 SE Mean:  1.106981e-002

LCL Mean: -2.169965e-002

UCL Mean:  2.169965e-002

Skewness:  3.802592e-001

Kurtosis: -3.340496e-001

 

 

 

 

 

          *** Linear Model ***

 

Call: lm(formula = Annual ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -10.18 -1.989 0.6937 2.364 5.321

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   24.9524    0.0843   296.1206    0.0000

          H   -0.0064    0.0001   -90.9180    0.0000

 

Residual standard error: 3.099 on 8142 degrees of freedom

Multiple R-Squared: 0.5038

F-statistic: 8266 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Jan ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q  Median    3Q  Max

 -10.33 -2.725 -0.1945 3.579 6.19

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   14.3030    0.1006   142.1433    0.0000

          H   -0.0079    0.0001   -93.4064    0.0000

 

Residual standard error: 3.7 on 8142 degrees of freedom

Multiple R-Squared: 0.5173

F-statistic: 8725 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Feb ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q    Median    3Q   Max

 -11.48 -2.638 -0.003607 3.397 6.044

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   15.8035    0.1052   150.2260    0.0000

          H   -0.0076    0.0001   -86.1413    0.0000

 

Residual standard error: 3.868 on 8142 degrees of freedom

Multiple R-Squared: 0.4768

F-statistic: 7420 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

         

          *** Linear Model ***

 

Call: lm(formula = Mar ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -11.54 -2.317 0.2929 2.755 5.966

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   19.4012    0.0996   194.7121    0.0000

          H   -0.0069    0.0001   -82.1634    0.0000

 

Residual standard error: 3.664 on 8142 degrees of freedom

Multiple R-Squared: 0.4533

F-statistic: 6751 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Apr ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q  Max

 -12.05 -2.037 0.6346 2.288 5.77

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   24.8265    0.0904   274.7629    0.0000

          H   -0.0064    0.0001   -84.8126    0.0000

 

Residual standard error: 3.323 on 8142 degrees of freedom

Multiple R-Squared: 0.4691

F-statistic: 7193 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = May ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -12.44 -2.206 0.8766 2.521 6.518

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   30.0099    0.0975   307.7561    0.0000

          H   -0.0065    0.0001   -79.8800    0.0000

 

Residual standard error: 3.586 on 8142 degrees of freedom

Multiple R-Squared: 0.4394

F-statistic: 6381 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

 

          *** Linear Model ***

 

Call: lm(formula = Jun ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -11.37 -1.797 0.9838 2.464 6.281

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   33.4459    0.0912   366.8676    0.0000

          H   -0.0055    0.0001   -71.9550    0.0000

 

Residual standard error: 3.352 on 8142 degrees of freedom

Multiple R-Squared: 0.3887

F-statistic: 5178 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Jul ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -10.27 -1.505 0.9436 1.991 5.087

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   34.4715    0.0753   457.9269    0.0000

          H   -0.0044    0.0001   -70.4132    0.0000

 

Residual standard error: 2.768 on 8142 degrees of freedom

Multiple R-Squared: 0.3785

F-statistic: 4958 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Aug ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -9.582 -1.479 0.8501 1.853 5.041

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   33.4776    0.0708   473.0109    0.0000

          H   -0.0047    0.0001   -78.8528    0.0000

 

Residual standard error: 2.603 on 8142 degrees of freedom

Multiple R-Squared: 0.433

F-statistic: 6218 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Sep ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -9.423 -1.485 0.9001 1.825 4.776

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   30.6706    0.0722   424.6678    0.0000

          H   -0.0057    0.0001   -94.2240    0.0000

 

Residual standard error: 2.656 on 8142 degrees of freedom

Multiple R-Squared: 0.5216

F-statistic: 8878 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Oct ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q Median    3Q   Max

 -10.52 -1.763 0.6677 2.402 4.783

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   26.2034    0.0816   321.2898    0.0000

          H   -0.0068    0.0001   -99.2969    0.0000

 

Residual standard error: 2.999 on 8142 degrees of freedom

Multiple R-Squared: 0.5477

F-statistic: 9860 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Nov ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q  Median    3Q   Max

 -10.98 -1.947 0.09952 2.633 5.252

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   20.7830    0.0828   251.0490    0.0000

          H   -0.0070    0.0001  -101.6648    0.0000

 

Residual standard error: 3.044 on 8142 degrees of freedom

Multiple R-Squared: 0.5594

F-statistic: 10340 on 1 and 8142 degrees of freedom, the p-value is 0

 

 

          *** Linear Model ***

 

Call: lm(formula = Dec ~ H, data = temp, na.action = na.exclude)

Residuals:

    Min     1Q  Median    3Q   Max

 -10.96 -2.459 -0.1741 3.239 6.036

 

Coefficients:

                Value Std. Error   t value  Pr(>|t|)

(Intercept)   15.8738    0.0929   170.9063    0.0000

          H   -0.0074    0.0001   -95.2551    0.0000

 

Residual standard error: 3.415 on 8142 degrees of freedom

Multiple R-Squared: 0.5271

F-statistic: 9074 on 1 and 8142 degrees of freedom, the p-value is 0