More detail pleas see the file ,total have 8 questions
; Now consider a multiple linear regression where the average length of stay in a hospital (Y) is anticipated to be related to infection risk (X1), routine chest X-ray ratio (X2), and available facilities and services (X3).
1. (10) Use R to obtain the residual information on the MLR model Y~X1+X2+X3, check assumptions from the residual plot, BF test (you could do a grouping on Y) and Normality test.
2.(5) For the MLR model Y~X1+X2+X3, use R to construct the design matrix X and Y, then compute the variance-covariance matrix of the residuals , what is the dimension of the matrix?
3. (5) For the MLR model Y~X1+X2+X3, use R to construct the matrix X and Y, then compute the variance-covariance matrix of the parameter estimates , what is the dimension of the matrix? What are the standard error of the parameter estimates?
4. (8) Obtain an interval estimate of the mean response when X1=4, X2=81, and X3=43 with 90% confidence level.Specify what are the point estimate, critical value, and the standard error.
5. (4) Now consider the interval estimate of the single responsewhen X1=4, X2=81, and X3=43 with 90% confidence level. Without computation, discuss how the point estimate, critical value, and the standard error different are different from question 4.
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