Multiple Regression       

Indiuvidual regressors Descriptive V.I.F. Regression Equation Residual Analysis

 

Correlation Matrix

  Plant Ht Days to 50 Days to Flag Leaf Leaf Stomata Stomata Yield/
  cm Flowering Maturity Area cm² Thick mm Upper mm² Lower mm² Plant gm
Plant Height cm 1.000 0.113 0.299 -0.194 0.059 0.218 0.074 0.154
Days to 50% Flowering 1.000 0.630 -0.027 0.166 -0.221 -0.017 0.163
Days to Maturity 1.000 0.085 0.110 -0.134 -0.059 0.350
Flag Leaf Area cm² 1.000 0.199 -0.296 -0.320 0.334
Leaf Thickness mm 1.000 -0.176 -0.183 0.539
Stomata Upper mm² 1.000 0.634 0.041
Stomata Lower mm² 1.000 0.003
Grain Yield/Plant g               1.000
Significance Levels 0.05 0.01 0.005 0.001
If correlation r => 0.2542 0.33008 0.35782 0.41425

Individual Regressors

Yi Variable = Grain Yield/Plant gm  t Value Probability  
 Y1 = 7.749 +0.20057 x1 Plant Height cm 1.186 0.240
 Y1 = 2.375 +0.31808 x2 Days to 50% Flowerin 1.261 0.212
 Y1 = -57.854 +0.72635 x3 Days to Maturity 2.845 0.006  **
 Y1 = 8.257 +0.52458 x4 Flag Leaf Area cm*cm 2.696 0.009  **
 Y1 = -13.290 +194.173 x5 Leaf Thickness mm 4.869 0.000  ***
 Y1 = 19.461 +0.05796 x6 Stomata Upper mm*mm 0.312 0.756
 Y1 = 22.268 +0.00487 x7 Stomata Lower mm*mm 0.025 0.981  

Descriptive Statistics

Pooled n = 60   Lowest Highest Kurtosis Skewness Mean Std. Dev. Std. Error C.V. %
Plant Height cm X1 60.18 83.48 1.300 -0.103 73.395 4.060 0.524 5.53 %
Days to 50% Flower X2 57.00 70.00 0.045 -0.025 63.175 2.718 0.351 4.30 %
Days to Maturity X3 104.20 115.2 -0.525 -0.159 110.585 2.549 0.329 2.30 %
Flag Leaf Area cm* X4 19.43 33.67 -0.295 -0.342 27.094 3.366 0.434 12.42 %
Leaf Thickness mm X5 0.16 0.23 1.02 0.940 0.184 0.014 0.001 7.97 %
Stomata Upper mm² X6 40.34 59.45 0.886 -0.724 51.909 3.738 0.482 7.20 %
Stomata Lower mm² X7 32.38 47.77 0.229 -0.533 41.458 3.497 0.451 8.43 %
Grain Yield/Plant Y1 12.95 40.17 1.161 0.969 22.469 5.292 0.683 23.55 %

Variance Inflation Factor

Variable name R² Tolerance VIF F Test Prob LGT(F)
 1 Plant Height cm 0.208 0.792 1.263 2.320 0.898
 2 Days to 50% Flowering 0.460 0.541 1.850 7.509 0.519
 3 Days to Maturity 0.473 0.527 1.898 7.932 0.502
 4 Flag Leaf Area cm*cm 0.194 0.806 1.241 2.126 0.920
 5 Leaf Thickness mm 0.095 0.906 1.104 0.922 1.000
 6 Stomata Upper mm*mm 0.491 0.509 1.964 8.513 0.481
 7 Stomata Lower mm*mm 0.449 0.551 1.814 7.192 0.533

Multiple Regression

R² 0.4878 R²adj 0.4189
F 7.0751 Probability 0.0000  ***
RMS Error 4.0346 AIC 2.9134
  Beta Wt. R square Reg. Coeff. Std.Err. t-value t Prob.  
INTERCEPT a 0.000 -113.679 26.343 4.315 0.000  ***
Plant Height cm 0.044 0.007 0.057 0.145 0.392 0.697
Days to 50% Flowerin -0.096 -0.016 -0.186 0.263 0.707 0.483
Days to Maturity 0.346 0.121 0.717 0.284 2.527 0.015  *
Flag Leaf Area cm² 0.291 0.097 0.458 0.174 2.634 0.011  *
Leaf Thickness mm 0.504 0.271 181.603 37.600 4.830 0.000  ***
Stomata Upper mm² 0.171 0.007 0.242 0.197 1.227 0.225
Stomata Lower mm² 0.096 0.000 0.145 0.202 0.716 0.477
bu   = plant height cm 0.154            

Residual Analysis

Durbin Watson d 2.4085 p -0.2042
Theil Nagar (Small Sample) p -0.1898
Runs 29 (+)28 (-)32 Runs Mean 30.8667
Runs' 95% Confidence Limits 23.3743 < to > 38.3591

 

No. Est.Y Residual Std.Res. No. Est.Y Residual Std.Res. No. Est.Y Residual Std.Res. No. Est.Y Residual Std.Res. No. Est.Y Residual Std.Res.
1 27.06 -3.06 -0.76 13 27.69 -0.03 -0.01 25 18.87 1.56 0.39 37 22.53 1.14 0.28 49 29.65 10.52 2.61
2 15.83 4.57 1.13 14 20.29 -3.06 -0.76 26 25.80 -2.64 -0.65 38 22.36 0.14 0.03 50 21.89 -5.48 -1.36
3 20.98 0.98 0.24 15 15.88 -0.70 -0.17 27 18.42 -0.54 -0.13 39 21.12 0.40 0.10 51 19.24 -4.30 -1.07
4 29.69 0.23 0.06 16 24.70 3.73 0.92 28 21.80 -4.07 -1.01 40 20.40 1.24 0.31 52 22.13 -3.56 -0.88
5 26.70 -5.31 -1.32 17 25.88 -2.37 -0.59 29 27.61 -5.14 -1.27 41 22.87 2.73 0.68 53 22.42 -2.31 -0.57
6 18.50 4.85 1.20 18 22.43 3.51 0.87 30 24.41 1.37 0.34 42 20.48 2.32 0.57 54 15.82 -2.87 -0.71
7 23.75 -1.97 -0.49 19 29.63 3.81 0.94 31 27.22 -3.01 -0.75 43 22.03 -2.96 -0.73 55 25.41 0.58 0.14
8 14.94 3.13 0.78 20 22.22 -3.21 -0.80 32 20.73 1.28 0.32 44 25.61 -3.49 -0.86 56 26.77 6.82 1.69
9 21.88 -5.82 -1.44 21 20.15 -1.18 -0.29 33 18.58 3.49 0.87 45 20.95 -1.85 -0.46 57 24.54 -2.60 -0.65
10 24.81 -1.11 -0.28 22 23.20 -1.38 -0.34 34 16.16 -0.45 -0.11 46 23.16 2.97 0.73 58 30.83 0.63 0.16
11 21.04 8.06 2.00 23 21.68 -0.24 -0.06 35 20.33 7.50 1.86 47 24.56 9.96 2.47 59 22.25 -3.01 -0.75
12 19.49 -3.19 -0.79 24 21.39 -4.05 -1.00 36 16.71 0.80 0.2 48 23.37 -4.58 -1.13 60 21.42 1.16 0.29