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Identify which variables are quantitative and which are qualitative.

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Quiz Problem 1.2 (5 points) The following are two observations from hcrabs data:

 

Observation Col Spine Width Sat Wt

7 LM NoneOK 26.5 0 2350

8 DM BothOk 24.7 0 1900

(1) (3 points) Identify which variables are quantitative and which are qualitative.

 

(2) (2 points) Col has four levels, D, DM, LM, and M. If we use LM as the reference level, and use 𝑥1, 𝑥2, and 𝑥3 to denote the dummy variables for D, DM, and M with the treatment coding. Find 𝑥1, 𝑥2, and 𝑥3 for two observations in the table.

Quiz Problem 1.3 (10 points) In a study of foetal size, the mandible length (in mm) and gestational age for 167 foetuses were measured from the 15th week of gestation onwards.

(1) (3 points) Load the data frame mandible from the package GLMsData, then use R function plot() to create a scatter plot of Length (y-axis) against Age (x-axis). The title for y-axis should be “Mandible Length (in mm)” and the title for x-axis should be “Age (in weeks)”. Show the plot in your solution.

(2) (2 points) Determine at least two important features of the data evident from the plots.

(3) (3 points) Is a linear relationship appropriate between Length against Age? Use R function scatter.smooth() to create a scatter plot of Length (y-axis) against Age (x-axis). Use the appropriate tiles for x-axis and y-axis. Show the plot in your solution file.

(4) (2 points) Is a model assuming the constant variation appropriate? Explain based on the plot from (1).

 

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