Obtener funciones que describan el comportamiento del experimento

AFA = Área foliar en agraz h = altura de la planta

AFA = sort(rnorm(n = 120,mean =  0.5,sd =  0.03))
h = sort(rnorm(120, 30, 3))

df = data.frame(AFA, h)

df
##           AFA        h
## 1   0.4113183 22.38840
## 2   0.4247499 23.30641
## 3   0.4259421 23.42059
## 4   0.4303283 23.74115
## 5   0.4304196 24.21625
## 6   0.4396560 24.80154
## 7   0.4405909 26.09932
## 8   0.4408983 26.10097
## 9   0.4516983 26.12827
## 10  0.4524313 26.16559
## 11  0.4527746 26.30233
## 12  0.4537002 26.40341
## 13  0.4603466 26.46963
## 14  0.4612595 26.55662
## 15  0.4623332 26.65861
## 16  0.4629827 26.71829
## 17  0.4631156 26.72388
## 18  0.4631207 26.75798
## 19  0.4649297 26.80343
## 20  0.4667558 26.86325
## 21  0.4668520 27.09873
## 22  0.4680147 27.21957
## 23  0.4714014 27.22781
## 24  0.4720451 27.30073
## 25  0.4720754 27.30483
## 26  0.4740940 27.38343
## 27  0.4747902 27.43549
## 28  0.4762998 27.44326
## 29  0.4770680 27.50962
## 30  0.4775327 27.62642
## 31  0.4777620 28.03189
## 32  0.4778005 28.09838
## 33  0.4780933 28.17106
## 34  0.4797380 28.19918
## 35  0.4811469 28.21253
## 36  0.4821968 28.38848
## 37  0.4826838 28.41527
## 38  0.4827510 28.54037
## 39  0.4830549 28.84369
## 40  0.4834412 29.08966
## 41  0.4834963 29.13774
## 42  0.4843052 29.23301
## 43  0.4849206 29.24748
## 44  0.4856313 29.33206
## 45  0.4861096 29.33844
## 46  0.4866382 29.40827
## 47  0.4867073 29.46512
## 48  0.4868666 29.51607
## 49  0.4872189 29.60414
## 50  0.4882686 29.61634
## 51  0.4883168 29.64321
## 52  0.4897993 29.92032
## 53  0.4898761 29.96653
## 54  0.4904325 30.01603
## 55  0.4929598 30.12002
## 56  0.4941504 30.16024
## 57  0.4942496 30.19615
## 58  0.4943924 30.23790
## 59  0.4953565 30.25546
## 60  0.4957453 30.28476
## 61  0.4959762 30.32689
## 62  0.4965405 30.33424
## 63  0.4977025 30.39084
## 64  0.4977981 30.52694
## 65  0.4983940 30.54443
## 66  0.4994044 30.62662
## 67  0.4996011 30.68053
## 68  0.5001781 30.83944
## 69  0.5007844 30.85788
## 70  0.5019611 30.94105
## 71  0.5020261 30.94943
## 72  0.5025610 30.99084
## 73  0.5027868 31.03787
## 74  0.5034435 31.13714
## 75  0.5038202 31.21283
## 76  0.5069241 31.23357
## 77  0.5093677 31.24163
## 78  0.5093958 31.36091
## 79  0.5101636 31.36116
## 80  0.5105951 31.41245
## 81  0.5118224 31.47176
## 82  0.5119412 31.48521
## 83  0.5120586 31.50475
## 84  0.5134599 31.67005
## 85  0.5135777 31.72969
## 86  0.5138602 31.73557
## 87  0.5142063 31.74389
## 88  0.5144057 31.80315
## 89  0.5146699 31.80917
## 90  0.5160224 31.85049
## 91  0.5163535 31.86006
## 92  0.5167202 31.97703
## 93  0.5167244 32.18165
## 94  0.5173623 32.18239
## 95  0.5177656 32.24256
## 96  0.5192892 32.44815
## 97  0.5193572 32.45285
## 98  0.5197945 32.46512
## 99  0.5198711 32.62501
## 100 0.5199283 32.67660
## 101 0.5205768 32.75772
## 102 0.5238420 32.81520
## 103 0.5246196 32.98139
## 104 0.5264906 33.13910
## 105 0.5276797 33.45738
## 106 0.5311222 33.64116
## 107 0.5338435 33.82218
## 108 0.5353842 33.89297
## 109 0.5354009 33.92468
## 110 0.5356189 33.96473
## 111 0.5369104 34.04519
## 112 0.5405430 34.17263
## 113 0.5440528 34.48904
## 114 0.5502102 35.15656
## 115 0.5520258 35.81156
## 116 0.5534044 36.02108
## 117 0.5534718 36.15706
## 118 0.5551058 36.56395
## 119 0.5611106 36.80139
## 120 0.5658307 37.14207

Gráfica

plot(h, AFA, pch = 16, main = "Área vs Altura")
grid(10,10)
abline(h = mean(df$AFA), col = "red", lwd = 3, lty = 2)
abline(v = mean(df$h), col = "red", lwd = 3, lty = 2)

xy = expand.grid(x = seq(0, 100, 10), y = seq(0,100, 10))
plot(xy, pch = 8, cex = 1.8)
grid(11,11)

rechazo Ho Ecuación del modelo \[ AFA = 0.216 + 0.009(h)\]

mod1 = lm(AFA ~ h, data = df)
summary(mod1)
## 
## Call:
## lm(formula = AFA ~ h, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0140548 -0.0020068 -0.0000251  0.0021107  0.0080682 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.1890055  0.0031968   59.12   <2e-16 ***
## h           0.0101780  0.0001056   96.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.003455 on 118 degrees of freedom
## Multiple R-squared:  0.9874, Adjusted R-squared:  0.9873 
## F-statistic:  9282 on 1 and 118 DF,  p-value: < 2.2e-16

rechazo Ho Ecuación del modelo \[ AFA = 0.216 + 0.009(h)\]