Reference no: EM132228338

Biostatistics Assignment Problems -

The data for this problem set are from Chapter 8, problem number 4. The variables are:

Y = homicide rate per 100,000 population.

X₁ = city's population in thousands.

X₂ = percentage of families with yearly income less than $5,000.

X₃ = unemployment rate.

This dataset is listed on page 154 of KKMN and is on the class blackboard site as file ch08q04. For this problem set, we will examine the potential influences of city population (X1), poverty (X2), and unemployment (X3) on the homicide rate (Y).

Answer to most of the assigned problems can be obtained directly from SAS output. Some problems require you to perform additional hand calculation to obtain the answer.

• Write the formula.
• Show intermediate steps.
• Calculate plausible answer. For example, sums of squares SS cannot be negative, correlation coefficient is a bounded by -1 and 1 etc.

1. Obtain the fitted regression equations for the following models:

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + E

Y = β₀ + β₁X₁ + β₂X₂ + E

Y = β₀ + β₂X₂ + β₃X₃ + E

Y = β₀ + β₁X₁ + E

Y = β₀ + β₂X₂ + E

Y = β₀ + β₃X₃ + E

2. What is the numerical value for each of the following sums of squares?

Note, SSR = regression SS and SSE = residual (error) SS.

SSR(X₁, X₂, X₃)

SSE(X₁, X₂, X₃)

SSR(X₁)

SSR(X₂)

SSR(X₃)

SS(X₂|X₃)

SS(X₃|X₁, X₂)

3. For each of the following F statistics, state the model being used and the null hypothesis (in terms of regression parameters) that is tested by the F statistic. Then compute the F statistic and state the conclusion about the null hypothesis.

F(X₁, X₂, X₃)

F(X₁)

F(X₂)

F(X₂, X₃|X₁)

F(X₂|X₃)

F(X₃|X₁, X₂)

4. Test the following:

H₀ : ρYX₂|X₃ = 0

H₀ : ρYX₃|X₁,X₂ = 0

H₀ : ρY|X₂ = 0

5. Obtain point estimates for the parameters ρYX₂, ρYX₃, and ρYX₂|X₃.

Note - Follow all the instructions. Write the formula and Show intermediate steps before writing the final answer.

Textbook - Applied Regression Analysis and Other Multivariate Methods (4th/5th edition) Authors: Kleinbaum, Kupper, Nizam, & Muller.

Attachment:- Assignment Files.rar