Use data3.dat. Recall that Distraction and LD are response variables.

(a) Fit a log linear model including the main effects of Distraction and LD and the interaction terms between Level, Male, Night, and Wet. Could we drop the interaction term?

(b) Start with the model in Part (a) and carry out a forward selection.

(c) Draw the association graph for the model selected in Part (b).

(d) Test whether Distraction and LD are conditionally independent given other variables in the model from Part (b)?

(e) Whether the model from Part (b) is equivalent to the main effects logit model or the model with two-way interactions if treating LD as the binary response variable? Justify your answer

(f) Is the model from Part (b) lack of fit? Justify your answer.

Data3 has variables Level, Male, Night, Wed, LD, Distraction and Count.

• Distraction: the response of participant to the question whether RDAS-HC system distracts the driver. It has values from -3 to 3. -3 denotes no distraction at all, 0 notes neutral, and 3 denotes significant distraction.
• LD: lane occurrence (0: no; 1: yes)
• Level: the level of RDAS-HC system (0: control; 1: level 1 of RDAS-HC; 2: level 2 of RDAS-HC)
• Male: the gender of participant (0: female; 1: male)
• Night: the illumination condition (0: daylight; 1: night)
• Wet: the pavement condition (0:dry; 1: wet)

A sample is given below. Please provide R code.

Level	Male	Night	Wet	LD	Distraction	Count
1	0	0	0	0	-3	2
2	0	0	0	0	-3	1
1	0	1	0	0	-3	4
2	0	1	0	0	-3	1
0	1	1	0	0	-3	2
1	0	0	1	0	-3	1
2	0	0	1	0	-3	1
0	1	0	1	0	-3	1
1	0	1	1	0	-3	1