Los datos de la producción producción de trigo trigo en toneladas y el precio precio del kilo de harina harina en peset en la década de los 80 en e n España fueron:
Producc Producción ión de trigo trigo
Precio Precio de la harina harina
30
25
-39.04
28
30
28.84
32
27 Beta 1
-1.35367545
25
40 Beta 0
74.1151179
25
42
25
40
22
50
24
45
35
30
40
25
28.6
35.4
286
35 4
Precio de la harina = 74.116 74.11 6 - 1.3536 (producción de trigo)
En la tabl tabla a siguie siguiente nte se se presen presentan tan las las punt puntuaci uacione oness obteni obtenidas das en en el examen examen de de ingreso ingreso a la la Un (promedio escolar) por ocho e studiantes universitarios. Estime la relación entre GPA y ACT empleando MCO; es decir, obtenga las estimaciones para l este caso, el intercepto una interpretación útil? Explique, ¿que tanto mas alto será el GPA pr ¿Cuál es el valor que se predice para el GPA si ACT = 20? ¿Qué tanto de la variación en el GPA de estos ocho estudiantes es explicada por el ACT ? .Expl
Y
X
0.7265625
Estudiante
GPA
ACT
1
2.8
21
Beta 1
0.1021978
2
3.4
24
Beta 0
0.56813187
3
3
26
4
3.5
27
5
3.6
29
6
3
25
7
2.7
25
8
3.7
30
25.7
20 7
3.2125
25.875
7.109375
20 Estime la relación entre GPA y ACT empleando MCO; es decir, obtenga las estimacione este caso, el intercepto una interpretación útil? Explique, ¿que tanto mas alto será el G
GPA = .5681 + .1022 ACT ; GPA = 0.5681, si x => La intersecc cciión no tiene una in intterpre GPA = .5681 + .1022 (35) = 4.14505 ¿Cuál es el valor que se predice para el GPA si ACT = 20? GPA = .5681 + .1022 (20) = 2.61 ¿Qué tanto de la variación en el GPA de estos ocho estudiantes es explicada por el AC
Alrede Alr ededo dorr de 57, 57,7% 7% de la la varia variació ción n en en el GPA GPA se expl explica ica por ACT en esta esta peq pequeñ ueña a mu
Utilice los datos de EJ2 para analizar si existe una relación inversa entre las horas de sueñ variables puede usarse como la variable dependiente (sleep corresp correspond onde e a minuto minutoss de de su minutos de trabajo por semana). Formule el modelo Sleep = 3,586.4 – 3,586.4 – .151 .151 totwrk Obtenga el β0 y β1 ; la R2.¿Que significa el intercepto de la ecuación? La intersección implica que el importe i mporte estimado de sueño por semana para alguien que ser alrededor de 8,5 horas por noche.
Si totwrk aumenta 2 horas, .cuanto se estima que disminuirá sleep?. Le parece que este Si alguien alguien trab trabaja aja dos más hora horass por sema semana na a cont continua inuación, ción, Δtot Δtotwrk wrk = 120 120 (porqu (porque e tot sólo unos pocos minutos cada noche. Si alguien fuera a trabajar una hora mas en cada Como R2 es el 10%, el modelo no se puede puede considerar.
sleep
t otw r k 3 11 3
3438
-135132.793
2 92 0
5020
2 67 0
2815 Beta 1
896428.104 -0.15074582
3 08 3
3786 Beta 0
3586.37695
3 44 8
25 80
4 06 3
12 05
3 18 0
21 13
2 92 8
36 08
3 36 8
23 53
3 01 8
28 51
1 57 5
64 15
3 29 5
3 70
3 79 8
24 38
3 00 8
26 93
3 24 8
25 26
3 68 3
29 50
3 20 1
30 03
2 58 0
40 11
3 42 0
23 00
3 09 0
15 43
2 76 0
34 73
2 88 0
32 76
3 47 0
25 06
2 67 3
26 51
2 82 0
45 80
2 87 3
35 88
1 90 5
34 18
2 92 6
22 50
2 60 3
26 38
3 23 8
31 73
3 88 8
34 46
2 71 6
35 88
3 24 5
29 61
3 15 8
27 78
3 10 5
30 80
3 51 5
35 56
3 33 0
27 88
4 15 3
11 00
2 95 5
31 16
2 20 0
25 06
2 88 5
27 63
3 34 5
30 48
2 76 5
25 11
3 92 8
32 68
2 83 3
32 42
3 75 0
25 50
3 32 8
31 88
3 79 5
15 55
3 36 3
27 43
2 28 0
50 43
4 15 1
35 70
3 26 6
28 83
3 57 0
23 98
2 88 5
26 63
2 87 9
23 63
2 79 0
18 00
2 79 9
27 00
3 17 3
30 31
3 30 8
24 38
3 30 5
26 20
2975
2698
3316
2970
3226
2430
3635
2250
3233
2888
3348
1345
2630
2925
2858
3976
3203
2205
3451
1208
3008
2905
2821
3825
3525
2348
3150
1825
3113
2563
2816
2576
3105
2275
3605
3595
3611
2575
3128
2843
3213
2188
3860
0
4275
2248
3076
2876
4313
2758
2885
2578
3165
2163
3105
4075
3063
2388
3368
2048
3415
2935
3508
2400
2788
2325
3180
2108
3123
2483
3388
1913
3610
1738
3351
3671
2653
3225
3413
4058
3218
2713
3045
2982
3433
3025
3730
2213
2970
2125
3475
2313
3430
3140
2910
625
3570
2350
3060
2745
3495
2038
2970
2880
3008
3331
3428
1175
3288
1605
2400
3146
3070
3135
2250
4065
3323
2968
3023
2791
3505
2398
3503
1588
3370
2611
3120
2948
3308
3038
3398
1655
3333
2560
2728
1175
3256
1350
3250
3598
2915
2638
4170
3230
3030
3311
3668
2218
2303
3699
3618
3569
3316
1775
3601
283
2413
400
2771
3533
3383
2638
3808
1175
3363
2426
3675
2113
3120
2477
3536
2375
3253
2813
2885
2625
2560
3018
2985
4335
3095
3105
2985
3194
2243
2713
2838
2338
3375
938
3355
3151
3743
0
2701
3695
2943
2575
3463
2380
2723
2781
3875
2088
3115
2892
2756
1188
3398
2088
3098
3480
2991
2588
3215
2688
3611
1445
3305
3050
3367
2250
2618
2763
3475
3008
3618
2941
3460
650
3250
2700
2648
2775
3045
2313
3065
3003
2875
2301
3090
1806
2798
2366
3610
2466
3403
2648
3656
2010
3348
1760
3130
3135
3213
1485
3855
2463
3138
2351
3203
2975
2930
1283
2448
2488
3556
826
3660
2575
2536
2326
2828
2700
3103
1350
3730
1175
2840
2353
3210
1563
3650
600
2708
2501
3530
2250
4695
1533
3639
2513
2335
2896
2813
2550
3088
2747
3710
2127
3293
1125
3261
1125
3540
3692
3176
2225
3060
2375
3590
2100
2923
2243
3020
2275
3110
2393
3898
2408
2841
2413
3278
2420
3151
1263
3165
2765
3720
2100
3675
2425
3300
3213
2250
1200
3298
2276
3245
2475
2770
2300
3383
2188
3338
2313
3330
2300
3098
2828
3158
2200
3404
3748
3038
2681
3115
1860
2623
4325
3013
2313
2895
3411
1485
2075
2770
2587
3308
2975
3210
2125
3116
2628
3183
2388
3330
2866
3113
2173
2880
2450
3308
1613
3428
3150
3998
1350
3965
700
3515
2250
3345
1955
3638
2125
2655
938
2618
3869
3450
2450
3188
2353
3390
2563
3108
1863
3825
2143
3778
1571
3046
2571
3333
1818
4575
0
3263
2250
3113
2313
4545
835
3880
2830
3303
2226
3388
2325
3278
2140
3376
2592
2895
2313
3216
2263
2930
2100
3150
1075
3248
2238
3983
1168
3218
1900
2803
2376
3038
1800
3150
2965
3405
3466
3548
1538
3670
2600
2961
1675
3530
1113
2668
2400
3233
2288
3750
2226
3203
2001
2948
2480
3621
2588
3630
1213
3631
1650
2836
2263
2940
2163
3943
958
3378
3185
4140
0
2888
2931
3030
1138
3705
2363
3795
1298
3160
3103
3075
3261
2678
2755
4113
2488
3293
2058
2760
2695
3720
2113
3840
1538
3338
1323
4373
0
2928
2735
3090
3225
2740
2375
2496
1762
3098
2601
2933
2513
3195
1755
3213
2288
3015
2640
3698
2518
3488
1880
3335
2438
2965
2551
3823
2300
3443
2996
3560
2513
3461
2300
3178
2656
3435
1920
3211
1275
3635
465
3378
1125
3780
1050
2715
2850
3436
2250
3285
2451
3203
2463
3683
2150
3135
2325
3213
3273
3365
2203
3278
1853
3150
3616
3750
1963
3418
1126
2910
2450
3683
1125
2311
3996
3368
3071
3453
2325
3870
2253
2921
2263
3438
2206
3775
2711
2945
1263
3270
1960
3405
1470
3533
2980
3320
2085
3030
2270
3563
3391
3470
1660
3130
2450
3660
1163
4113
1288
2661
2485
2115
2050
3240
1038
3480
1213
4048
1558
2956
1175
2985
0
2745
0
3405
2460
3158
2325
3138
2488
3143
2288
2865
2251
3853
1173
3435
2946
3221
1150
3320
2193
2633
2663
3158
2413
3353
2475
3350
2050
2580
2575
3633
2170
3955
1763
4215
2525
2733
3226
3270
0
3128
2173
3515
2843
4068
2568
3885
913
3410
1497
3641
2686
4091
75
2708
2325
2640
2538
2918
2038
2983
2025
3420
2205
3322
1838
3553
1570
3945
1125
3018
2388
2870
1830
2891
2163
3323
1370
3155
3075
4110
2505
3328
2146
3015
1975
3195
1650
2710
2775
2890
2380
3578
1321
2708
2458
4100
3170
3818
360
3060
750
3765
2100
2710
2368
3753
1325
3943
2451
3505
1993
3693
2533
3150
1671
2780
1950
2955
1313
2948
1813
3045
2049
3595
1963
2985
0
3346
2288
3195
2195
3073
2088
3608
2100
2928
2606
3525
1875
3953
2351
3218
2300
3848
2126
3740
515
3570
2560
3218
2026
3255
2100
3363
1673
3286
2275
3255
2750
3548
2178
3181
1208
3188
1175
3318
0
4030
2193
2746
2288
3410
0
3943
2013
2423
2138
3388
2233
3280
1905
3376
375
3458
1538
3710
788
3196
2293
3206
838
2881
2866
3113
2031
3128
1738
3203
1525
3330
330
4180
2570
3368
1093
3295
2805
3103
825
3373
68
3210
3203
2698
1553
3633
1025
2413
2701
3818
125
3420
0
3215
375
2623
1920
2643
1408
3353
1995
3558
1600
2828
1243
3148
1988
3773
0
3405
375
3278
1051
2868
1733
3900
363
2508
1230
3555
1816
3630
625
3215
0
3180
0
3938
588
3466
1050
2678
800
3223
900
3428
638
3967
1751
3525
900
3143
900
3700
388
3245
305
2010
808
3055
875
3458
613
4235
1183
3890
1050
4005
520
3773
353
3465
2700
3460
0
3360
0
3863
0
3105
0
3715
2443
3450
995
3735
1975
4095
1313
2770
4000
2760
3518
4100
188
2800
0
2865
3438
3430
1150
4266
2880
2911
2100
2746
2740
2663
0
2940
2475
2640
3180
2930
1950
2955
2225
3595
2478
2905
3648
2533
1565
2820
3615
2755
2705
2806
2476
4200
0
2448
3325
4095
1413
2355
2726
4050
0
3990
1725
3975
0
2738
2475
2848
638
2818
2505
2470
2026
3855
360
3803
2446
2940
1725
3791
2808
3785
800
3755
1138
3745
900
3743
3118
2113
2488
4350
480
3860
1334
2053
2276
3705
940
3703
2948
2381
2760
3670
2175
3655
460
3650
1773
3643
3085
3638
1375
3733
2288
3725
2616
3630
875
3628
0
3628
1013
3800
1925
3615
2443
3600
2163
3598
2376
1740
2909
3583
2508
3580
3166
2700
2206
3565
2150
3550
2455
3548
113
3543
1088
3538
2388
3530
4805
3525
1933
3525
1950
3523
1971
3950
500
4420
2450
3871
2050
3503
950
3498
1015
3488
1715
3480
1113
3478
1200
3468
2871
3460
2250
3455
2828
1546
3316
3435
0
3433
745
755
2663
3423
3338
3423
1588
3420
830
2793
1273
3405
2145
3405
1875
3395
1988
3391
2895
3390
583
3935
163
3375
2905
3360
3135
3360
3075
3355
0
2655
2688
3338
2263
3338
2588
3330
3148
3326
2468
3315
1525
3315
2948
3310
0
3310
2826
3308
2326
3308
2820
3295
2513
3295
3171
3285
1325
3285
2493
3271
3441
3268
1238
3261
2588
3260
3590
3255
1548
3248
3190
3236
2350
3235
0
3230
2150
3225
2535
3225
638
3225
2260
3218
3275
3218
1013
3210
2433
3203
2450
3201
2298
3200
2363
3195
1578
3190
2500
3188
2526
3188
2538
3181
2393
3176
2163
3175
3481
3165
2163
3390
3421
3630
2300
3150
1188
3140
2666
3135
1538
3615
1888
3110
0
3095
2293
3090
538
3073
2351
3068
2373
3065
2148
3573
2013
3060
2603
3040
1510
3028
2513
3023
2418
3023
2281
3015
1183
3008
2275
2993
2725
2985
2388
2985
2026
3520
675
3510
1851
2970
1961
2970 3266.35552
2363 2122.92068
s
iversidad en Estados Unidos, ACT (American College Test), y en el GPA a pendiente y para el intercepto. Comente la dirección de la relación ¿tiene, en dicho si ACT aumenta cinco puntos? lique.
GPA gorro
u
u^2
y gorro ^2
2.71428571
0.08571429
0.00734694
0.17015625
3.02087912
0.37912088
0.14373264
0.03515625
3.22527473 -0.22527473
0.0507487
0.04515625
3.32747253
0.17252747
0.02976573
0.08265625
3.53186813
0.06813187
0.00464195
0.15015625
3.12307692 -0.12307692
0.01514793
0.04515625
3.12307692 -0.42307692
0.17899408
0.26265625
0.0043473
0.23765625
0.43472527
1.02875
3.63406593
0.06593407
2.61208791 -2.61208791
0.57742379
para la pendiente y para el intercepto. Comente la dirección de la relación ¿tiene, en PA predicho si ACT aumenta cinco puntos?
tación útil porque ACT no está cerca de cero para la población de interés.
? .Explique.
stra de estudiantes.
o por semana y las horas de trabajo pagado por semana. Cualquiera de las eno por semana durante la noche y totwrk corresponde al total de
no trabaja es 3,586.4 minutos, o alrededor de 59,77 horas. Esto viene a
fecto sea grande? wrk se mide en minutos), y así = - 0.151 (120) = -18,12 minutos. Esto es no de los cinco días hábiles.
sleep gorro
u
u^2
y gorro ^2
3068.11281
44.8871918
2014.85999
23517.9168
2829.63291
90.3670856
8166.21015
119962.149
3162.02746 -492.027457
242091.018
355639.911
3015.65326
67.3467386
4535.5832
33619.2482
3197.45273
250.547275
62773.9369
32994.7156
3404.72823
658.271767
433321.719
634642.421
3267.85103 -87.8510251
7717.80262
7457.27654
3042.48602 -114.486018
13107.0483
114484.461
3231.67203
136.327973
18585.3161
10331.5995
3156.60061 -138.600607
19210.1282
61680.4663
2619.34249 -1044.34249
1090651.24
2860683.51
3530.601 -235.600997
55507.8296
820.506001
335404.724
282645.849
3218.85863
579.141368
3180.41845 -172.418447
29728.1209
66747.5768
3205.593
42.4070002
1798.35367
336.925264
3141.67677
541.32323
293030.839
173592.619
3133.68724
67.3127583
4531.00743
4271.34453
2981.73545 -401.735451
161391.373
471083.905
3239.66156
180.338444
32521.9544
23606.625
3353.77614 -263.776145
69577.8546
31101.2709
3062.8367 -302.836704
91710.0695
256395.917
3092.53363 -212.533632
45170.5446
149270.591
3208.60792
261.392084
68325.8214
41471.0726
3186.74977 -513.749772
263938.828
352070.778
2895.96108
-75.961077
5770.08523
199233.254
3045.50093 -172.500935
29756.5724
154728.568
3071.12772 -1166.12772
1359853.87
1853288.86
3247.19885 -321.198847
103168.699
115841.883
3188.70947 -585.709467
343055.58
440040.551
3108.06045
129.939548
16884.2862
804.035746
3066.90684
821.093158
674193.975
386441.854
3045.50093 -329.500935
108570.866
302891.203
3140.01857
104.981434
11021.1014
456.058409
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