Please answer all parts with detailed solutions data: > y=c(0.000450, 0.000450,

Question

Please answer all parts with detailed solutions

data:

> y=c(0.000450, 0.000450, 0.000473, 0.000507, 0.000457, 0.000452, 0.000453, 0.000426, 0.001215, 0.001256, 0.001145, 0.001085, 0.001066, 0.001111, 0.001364, 0.001254, 0.001396, 0.001575, 0.001615, 0.001733, 0.002753, 0.003186, 0.003227, 0.003469, 0.001911, 0.002588, 0.002635, 0.002725)
> x1=c(0.0105, 0.0110, 0.0106, 0.0116, 0.0121, 0.0123, 0.0122, 0.0122, 0.0123, 0.0122, 0.0094, 0.0100, 0.0101, 0.0099, 0.0110, 0.0117, 0.0110, 0.0104, 0.0067, 0.0066, 0.0044, 0.0073, 0.0078, 0.0067, 0.0091, 0.0079, 0.0068, 0.0065)
> x2=c(90.9, 84.6, 88.9, 488.7, 454.4, 439.2, 447.1, 451.6, 487.8, 467.6, 95.4, 87.1, 82.7, 87.0, 516.4, 488.0, 534.5, 542.3, 98.8, 84.8, 69.6, 436.9, 406.3, 447.9, 58.5, 394.3, 461, 469.2)
> x3=c(0.0164,0.0165, 0.0164,0.0187,0.0187,0.0187,0.0186,0.0187,0.0192,0.0192,0.0163,0.0162,0.0162,0.0163,0.0190,0.0189,0.0189,0.0189,0.0163,0.0162,0.0163,0.0189,0.0192,0.0192,0.0164,0.0177,0.0173,0.0173)
>x4=c(0.0177,0.0172,0.0157,0.0082,0.0070,0.0065,0.0071,0.0062,0.0153,0.0129,0.0354,0.0342,0.0323,0.0337,0.0161,0.0149,0.0163,0.0164,0.0379,0.0360,0.0327,0.0263,0.0200,0.0197,0.0331,0.0674,0.0770,0.0780)

f. Using t test, determine the contribution of x1 and x4 to the model. Are both regressors Ti and T4 necessary? g. Is multicollinearity a potential concern in this model? h. Obtain the ANOVA table that decomposes the regression sum of squares into extra sum of squares associated with X1, with X4given X1. i. Test whether r4 can be dropped from the regression model given that X1 is remained. j) List the diagonal elements of the hat matrix. k) Plot the standard residual plot and studentized plots and offer your comments 1) Compute the PRESS residuals and plot m) Plot the residuals against the predictors and offer your comments n) Use added variable plots to decide the need for adding T4 in the simple linear regression model with 1 o) Check the assumption of constant error variability p) Check the normality assumption of model error. Problem 2:

Explanation / Answer

Soution: All solution are performed in R and Rstudio

#input the data

y = c(0.000450, 0.000450, 0.000473, 0.000507, 0.000457, 0.000452, 0.000453, 0.000426, 0.001215, 0.001256, 0.001145, 0.001085, 0.001066, 0.001111, 0.001364, 0.001254, 0.001396, 0.001575, 0.001615, 0.001733, 0.002753, 0.003186, 0.003227, 0.003469, 0.001911, 0.002588, 0.002635, 0.002725)
x1=c(0.0105, 0.0110, 0.0106, 0.0116, 0.0121, 0.0123, 0.0122, 0.0122, 0.0123, 0.0122, 0.0094, 0.0100, 0.0101, 0.0099, 0.0110, 0.0117, 0.0110, 0.0104, 0.0067, 0.0066, 0.0044, 0.0073, 0.0078, 0.0067, 0.0091, 0.0079, 0.0068, 0.0065)
x2=c(90.9, 84.6, 88.9, 488.7, 454.4, 439.2, 447.1, 451.6, 487.8, 467.6, 95.4, 87.1, 82.7, 87.0, 516.4, 488.0, 534.5, 542.3, 98.8, 84.8, 69.6, 436.9, 406.3, 447.9, 58.5, 394.3, 461, 469.2)
x3=c(0.0164,0.0165, 0.0164,0.0187,0.0187,0.0187,0.0186,0.0187,0.0192,0.0192,0.0163,0.0162,0.0162,0.0163,0.0190,0.0189,0.0189,0.0189,0.0163,0.0162,0.0163,0.0189,0.0192,0.0192,0.0164,0.0177,0.0173,0.0173)
x4=c(0.0177,0.0172,0.0157,0.0082,0.0070,0.0065,0.0071,0.0062,0.0153,0.0129,0.0354,0.0342,0.0323,0.0337,0.0161,0.0149,0.0163,0.0164,0.0379,0.0360,0.0327,0.0263,0.0200,0.0197,0.0331,0.0674,0.0770,0.0780)

z.lin = lm(y ~., data=z) # running a linear regression model on the data

f)

t.test(x1,x4)

Both the Regressor is not required in the model

g) Checking for Multicollinearity in the data

z = data.frame(y,x1,x2,x3,x4)

round(cor(z),2)

After looking into the data. Most of the predicter variable are Multi correlated.

h) anova(z.lin)

I) Since x1 and X4 are highly correleated with each other, Thus any one variable can be dropped.

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