Applied Statistical Methods - Notebook 5

Problem 1: Interactions

Use the following dataset on Breed, Breast Circumference and Body Weight and fit a fixed linear effects model with Body Weight as response and Breed and Breast Circumference as predictors and include an interaction term between the two predictors. Compute the expected difference in Body Weight for two animals which differ in Breast Circumference by $1cm$ for everyBreed`.

The dataset is available under

[1] "https://charlotte-ngs.github.io/asmss2023/data/asm_bw_flem.csv"

https://charlotte-ngs.github.io/asmss2023/data/asm_bw_flem.csv

Your Solution

• Read the data
• Fit fixed linear effects model for Body Weight using Breed and Breast Circumference and the interaction with function lm()
• From the solution of the summary() of the lm() result get the regression coefficient and the interaction effects and compute the expected difference in Body Weight for all three breeds.

Problem 2: Simulation

Use the following values for intercept and regression slope for Body Weight on Breast Circumference to simulate a dataset of size \(N\). What is the number for \(N\) that has to be chosen such that the regression analysis of the simulated data gives the same result as the true regression slope.

The true values are:

• Intercept: \(-1070\)
• Regression slope: \(8.7\)
• Residual standard error: \(12\)

Hints

• Start with \(N=10\), simulate a dataset and analyse the data with lm()
• If the result (rounded to 1 digits after decimal point) is not the same then double the size of the dataset, hence use, \(N=20\)
• Continue until you get close to the true value.
• Assume that the random resiudals follow a normal distribution with mean zero and standard devation equal to \(12\)
• Take breast circumference to be normally distributed with a mean of \(180\) and a standard deviation of \(2.6\)
• Use a linear regression model with an intercept to model expected body weight based on breast circumference.

Your Solution

• Start with \(N=10\), simulate a dataset and analyse the data with lm()
• If the result (rounded to 1 digits after decimal point) is not the same then double the size of the dataset, hence use, \(N=20\)
• Continue until you get close to the true value.

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Latest Changes: 2023-05-07 13:49:44 (pvr)