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   0.4187682 21.85562
## 2   0.4198204 22.25516
## 3   0.4384998 23.53702
## 4   0.4415080 24.32732
## 5   0.4499001 24.33480
## 6   0.4542559 24.84911
## 7   0.4586317 25.17480
## 8   0.4605547 25.29029
## 9   0.4628981 25.33454
## 10  0.4630951 25.34201
## 11  0.4650503 25.43423
## 12  0.4666955 25.82773
## 13  0.4679183 25.83522
## 14  0.4680799 25.84349
## 15  0.4687343 26.25164
## 16  0.4721522 26.31380
## 17  0.4753764 26.33779
## 18  0.4755536 26.36996
## 19  0.4755609 26.44015
## 20  0.4761192 26.50048
## 21  0.4763156 26.52365
## 22  0.4773745 26.75871
## 23  0.4776392 27.16876
## 24  0.4795541 27.25791
## 25  0.4800191 27.36034
## 26  0.4802721 27.38144
## 27  0.4814444 27.45754
## 28  0.4817406 27.45774
## 29  0.4824500 27.46304
## 30  0.4829946 27.57895
## 31  0.4831609 27.58419
## 32  0.4839801 27.64397
## 33  0.4848601 27.73647
## 34  0.4857080 27.74604
## 35  0.4860954 27.77140
## 36  0.4869588 27.89602
## 37  0.4898791 27.99790
## 38  0.4900166 28.05146
## 39  0.4902873 28.12939
## 40  0.4906417 28.15538
## 41  0.4918099 28.28628
## 42  0.4919996 28.37581
## 43  0.4922364 28.37970
## 44  0.4944192 28.52086
## 45  0.4947193 28.58390
## 46  0.4950670 28.60089
## 47  0.4966789 28.68502
## 48  0.4977243 28.69572
## 49  0.5000804 28.73291
## 50  0.5006758 28.73879
## 51  0.5010848 28.85532
## 52  0.5013643 28.95295
## 53  0.5032812 29.04833
## 54  0.5033529 29.06260
## 55  0.5063580 29.09074
## 56  0.5072762 29.09399
## 57  0.5075754 29.15112
## 58  0.5087278 29.18424
## 59  0.5096686 29.20008
## 60  0.5099139 29.20761
## 61  0.5103375 29.20771
## 62  0.5110479 29.29588
## 63  0.5114544 29.37863
## 64  0.5118213 29.40148
## 65  0.5119524 29.41012
## 66  0.5125930 29.47979
## 67  0.5130911 29.55452
## 68  0.5135753 29.58196
## 69  0.5136972 29.75479
## 70  0.5138305 29.76444
## 71  0.5143989 29.77122
## 72  0.5150401 29.85656
## 73  0.5162612 29.86900
## 74  0.5165418 29.88545
## 75  0.5166593 30.21733
## 76  0.5178560 30.23505
## 77  0.5185988 30.26052
## 78  0.5189096 30.46656
## 79  0.5199353 30.53782
## 80  0.5207887 30.54848
## 81  0.5217440 30.78070
## 82  0.5218185 30.80894
## 83  0.5218656 30.98890
## 84  0.5219945 31.15572
## 85  0.5245615 31.17595
## 86  0.5246249 31.19124
## 87  0.5247061 31.31548
## 88  0.5247267 31.35637
## 89  0.5278204 31.42340
## 90  0.5279292 31.56937
## 91  0.5291936 31.65195
## 92  0.5301666 31.74646
## 93  0.5307717 31.77279
## 94  0.5308318 31.92401
## 95  0.5313977 32.00400
## 96  0.5314625 32.22800
## 97  0.5320042 32.33452
## 98  0.5322429 32.68769
## 99  0.5329229 32.73531
## 100 0.5344478 32.82088
## 101 0.5345620 32.88907
## 102 0.5346736 33.11366
## 103 0.5367753 33.12455
## 104 0.5373242 33.20630
## 105 0.5402137 33.28302
## 106 0.5403972 33.76023
## 107 0.5417864 33.83392
## 108 0.5419253 33.90662
## 109 0.5433870 34.41866
## 110 0.5460939 34.53339
## 111 0.5461246 34.66776
## 112 0.5498188 34.84734
## 113 0.5514522 35.01362
## 114 0.5533906 35.07977
## 115 0.5556062 35.22962
## 116 0.5575762 35.64598
## 117 0.5580334 36.12002
## 118 0.5589267 36.85615
## 119 0.5635037 37.31828
## 120 0.5645757 38.68931

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 
## -0.025736 -0.003255 -0.000809  0.004904  0.008739 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.228321   0.005216   43.77   <2e-16 ***
## h           0.009356   0.000175   53.47   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.006079 on 118 degrees of freedom
## Multiple R-squared:  0.9604, Adjusted R-squared:   0.96 
## F-statistic:  2859 on 1 and 118 DF,  p-value: < 2.2e-16

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