HERE Is THE CODE AND RESULTS(console using Rstudio) PLOTS HERE IS THE DATA Probl

Question

HERE Is THE CODE AND RESULTS(console using Rstudio)

PLOTS

HERE IS THE DATA

Problem 4 The basic process of making paper has not changed in more than 2000 years. It involves two stages: the breaking up of raw material in water to form a suspensionof individual fibers and the formation of felted sheets by spreading this suspension on a suitable porous surfacem through which excess water can drain. Most paper is made from wood pulp that has been bleached with chlorine. Thos bleaching takes palce for two reasons: to remove the last traces of a material called lignin from the raw pulp in order to make the paper stronger and to create a brilliant white writing surface. Chlorine is an ideal chemical for these tasks, but unfortunately its use in paper mills also results in a wide variety of toxic substances being released into the environment. Studies have been conducted to determine which factors in the paper process are most highly correlated with the brightness of the finished paper. An article contains data on the following variables

Explanation / Answer

See as it was mentioned in the question note, its not required to go by forward or backward model selection for variable reduction! In your code, when you are calling lm function for the full model, you are given a summary of coefficients also. Use those results for variable selction. i.e in the output, all the 4 coefficients are given and their corresponding p values are given. Now in general the hypothesis for each coefficient is Ho:Xi is not significant vs H1: Xi is significant. So for a 5% level of significance test if p-value <0.05, we reject Ho. Now if you look into the first section of your code (Y~X1+X2+X3+X4) , only the p-value corresponding to X3 is 0.26 > .05 i.e Ho is accepted ,means X3 is not significant! For the rest of the variables it is <<.05 , so Ho gets rejected and those variables play significant roles, which is what you get by employing backward method!

So your reduced model is Y~X1+X2+X4

I guess you got confused over there! Even your last model in Backward method is same as above. So just change your paper.red1 model to the reduced one.

Everything else is fine. As all the VIF's < 5 , there is no question of multicollinearity.

For any further query comment!

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