1. ThefileAutoAccident.datcontainsdataonseverityofdrivers'injuriesinautoac- cidents (Injury: 1=Not Severe, 2=Severe), along with the type of accident (Type: 1=Collision, 2=Rollover), the type ofautomobile (Car: 1=Small, 2=Standard), and whether or not the driver wasejected from the vehicle during the accident (Ejected: 1=No, 2=Yes). The data are also availablewith qualitative descriptors atAutoAccident.csv.

	Type	Collision	Rollover
Car	Ejected	Injury
Small	No	Not Severe		350	60
		Severe		150	112
	Yes	Not Severe		26	19
		Severe		23	80
Standard	No	Not Severe		1878	148
		Severe		1022	404
	Yes	Not Severe		111	22
		Severe		161	265

Analyze the data treating severity of injury as the response variable. Include the following pieces in your analysis:

1. Fit a model with main effects and a model with all two wayinteractions. [10 pts]
2. Report the goodness-of-fit test for both models.[10 pts]
3. Use both the likelihood ratio test and Waldtest to compare the model with just main effects against the model with all two-wayinteractions. What do you conclude? [10pts]
4. Report the estimates, standard errors, and Waldtests associated with each parameter in the main effects model. Give a table with the conditional odds ratiosforeachvariable,alongwith95%confidenceintervals(besuretoclearly state what the baseline group is for each odds ratio). [Hint: the connection between conditional odds ratio and the value of parameter] [20pts]