Applied Statistical Methods - Notebook 1

Problem 1: Regression Analysis

The following dataset on body weight and on futher observations on a number of animals is given.

Animal	Breast Circumference	Body Weight	BCS	HEI
1	176	471	5.0	161
2	177	463	4.2	121
3	178	481	4.9	157
4	179	470	3.0	165
5	179	496	6.8	136
6	180	491	4.9	123
7	181	518	4.4	163
8	182	511	4.4	149
9	183	510	3.5	143
10	184	541	4.7	130

The data can be read from https://charlotte-ngs.github.io/asmss2023/data/asm_bw_mult_reg.csv. The additional columns contain data on body condition score (BCS) and height (HEI).

Tasks

• Build a regression model of body weight on the other observations using the dataset given above.
• Set up the matrix \(\mathbf{X}\) and the vectors \(\mathbf{y}\), \(\mathbf{b}\) and \(\mathbf{e}\).
• Compute estimate for the regression coefficients in the model defined above.

Your Solution

• Start by building the model which includes the decision of what type of components go into the vector \(\mathbf{b}\). Then write down the model in matrix-vector notation.
• Determine all the components of \(\mathbf{X}\), \(\mathbf{y}\), \(\mathbf{b}\) and \(\mathbf{e}\).
• Compute the solution for $

Problem 2

Use the same dataset as in Problem 1 and verify your results using the function lm() in R.

Your Solution

• Read the data into a dataframe
• Use the lm() function which takes a formula to define the model and a dataframe
• Use the function summary() on the result of lm() to show the results

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Latest Changes: 2023-02-27 09:09:37 (pvr)