University of Ottawa Regression Analysis and Confidence Interval R Questions 1). Discuss a screening tool that can be used in the primary care setting that

University of Ottawa Regression Analysis and Confidence Interval R Questions 1).
Discuss a screening tool that can be used in the primary care setting that can help with the identification of patients with depression and or substance abuse. What is your responsibility as a primary care provider to this patient once a disorder has been identified?
2).
Discuss the guidelines for prescribing hormonal birth control to women with a known history of depression and/or anxiety. How will you manage a patient who reports feeling depressed after starting hormonal birth control? Use R
for all calculations. Provide copies of your code in the
assignment.
Q. 1) (MP 2.7) The purity of oxygen produced by fractionation is thought
to
be related to the percentage of hydrocarbons in the main condensor of the
processing unit. The data can be found at
??oxygen.table
(a) Fit a simple linear regression model to the data.
(b) Test the hypothesis H0 : ?1 = 0.
(c) Calculate R2 .
(d) Find a 95% confidence interval on the slope.
(e) Find a 95% confidence interval on the mean purity when the hydrocarbon percentage is 1.0.
Q. 2) (MP 2.19) Consider the simple linear regression model
y = ?0 + ?1 x + ?
where the intercept ?0 is known.
(a) Find the least squares estimator of ?1 for this model. Does this
answer seem reasonable?
(b) What is Var(?b1 ) for the least squares estimator found in (a)?
(c) Find a 100(1??)% confidence interval for ?1 . Is this interval narrower
than the estimator for the case where both slope and intercept are
unkown?
1
Q. 3) (MP 3.10) Consider the soft drink delivery time data found in the example
?? multiple.R.html
(a) Compute the residuals and the standardized residuals for this model.
(Hint: try help(rstandard) in R)
(b) Observation 9 has an unusually large residual. Assess the impact
of this observation on the model by plotting the fitted model in R.
On inspection of the covariates in this observation, is there anything
unusual about this observation?
Q. 4) (MP 4.24) The matrix
H = X(X t X)?1 X t
is usually called the hat matrix because it maps Y to Yb the vector of fitted
values. Show that in the multiple linear regression model
Var(Yb ) = ? 2 H.
Q. 5) (MP 4.25) Prove that the matrices H and I ? H are idempotent, that is
H2 = H
(I ? H)2 = (I ? H)
2

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