Econo

Problemas propuestos de regresión lineal múltiple.


Problema 1. “Se realiza un experimento para determinar la duración de vida de ciertos circuitos electrónicos [pic] en función de dos variables de fabricación [pic] y [pic], con los siguientes resultados:
|Y |11 |8 |73 |21 |46 |30 |
|[pic] |-10 |0 |10 |-10 |0 |10 |
|[pic] |0|-5 |5 |0 |5 |-5 |


1) Ajustar un modelo de regresión lineal.
2) Calcular el coeficiente de determinación y la varianza residual. ¿Es el ajuste adecuado?
3) Construir un intervalo de confianza al 90% para la predicción en el punto (0,0).


Problema 2. “Los datos indican la gravedad específica [pic], contenido de humedad [pic] y fuerza [pic] de diez vigas demadera. Encontrar el modelo de regresión que mejor se ajusta a estos datos”.
|Y |11,14 |12,74 |13,13 |11,5 |12,38 |
|194 |7,75 |21,67857 |1,285714 |2,46429 |0,55782313 |
|203 |20,97222 |38,5 |1,194444 |2,22222 |0,63071298 |
|192 |24,16667 |39,6 |2,1|2,3 |0,43619048 |
|186 |2,33333 |7,75 |0,833333 |1,25 |0,43478261 |
|205 |23,27778 |37,58333 |1,083333 |3,33333 |0,55268022 |
|201 |2,63636 |9,54545 |0,545455 |2,36364 |0,34328358 |
|205 |21,77778 |36,61111 |3,555556 |3,61111 |0,54873646 |
|194|12,28571 |30,45714 |0,971429 |2,42857 |0,48484848 |
|206 |15,22222 |30,94444 |1,277778 |3,38889 |0,57756563 |
|204 |6,87879 |18,0303 |1,30303 |2,54545 |0,58823529 |
|178 |7,41935 |24,90323 |1,483871 |2,70968 |0,4611399 |
|203 |6,2381 |15,95238 |1,095238|2,33333 |0,42975207 |
|201 |3,73333 |16,96667 |0,933333 |2,26667 |0,41121495 |
|186 |18,35714 |35,25 |1,785714 |2,96429 |0,55685131 |
|187 |3,1 |10,5 |0,55 |1,6 |0,5 |
|211 |4,73529 |17,79412 |0,676471 |2,5 |0,68085106 |
|197|3,30556 |23,47222 |0,861111 |2,66667 |0,3826087 |
|181 |9,125 |30,625 |2,375 |3,125 |0,41025641 |
|203 |2,55 |10,5 |0,7 |1,6 |0,53658537 |
|205 |6,38235 |15,79412 |1,235294 |2,26471 |0,51533742 |
|205 |5,64706 |23,02941 |1|2,58824 |0,45882353 |
|205 |14,77778 |33,75 |2,055556 |2,75 |0,58938547 |
|190 |11,87097 |33,80645 |2,096774 |2,12903 |0,43003413 |
|200 |10,80556 |26,19444 |1,527778 |3,11111 |0,46745562 |
|195 |10,17143 |25,94286 |1,942857 |2,17143 |0,50553506 |
|203|22,22857 |38 |2,514286 |3,57143 |0,58640777 |
|200 |8,44444 |16,74074 |0,555556 |1,92593 |0,59235669 |
|200 |5,78788 |19,39394 |0,848485 |1,42424 |0,576 |
|192 |6,16129 |28,41935 |1,064516 |2 |0,44370861 |
|203 |6,25 |14,1875 |0,5625|2,15625 |0,49655172 |
|204 |4,27273 |16,60606 |0,818182 |2,48485 |0,43283582 |
|207 |21,80556 |37,77778 |3,472222 |2,72222 |0,54173765 |
|204 |2,45455 |7 |0,818182 |1,90909 |0,57142857 |
|195 |9,32353 |25,41176 |1,176471 |1,73529 |0,40357143 |
|183...