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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?

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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

附件oxygen.table

(a) Fit a simple linear regression model to the data.

(b) Test the hypothesis H0 : β1 = 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 = β0 + β1 x + ε

where the intercept β0 is known.

(a) Find the least squares estimator of β1 for this model. Does this

answer seem reasonable?

(b) What is Var(βb1 ) for the least squares estimator found in (a)?

(c) Find a 100(1−α)% confidence interval for β1 . 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

附件 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 ) = σ 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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