Question 1 : In a regression analysis of on-the-job head injuries to warehouse laborers caused by failing objects. Y is measured of severity of the injury, X ₁ is weight of the object, X ₂ is the distance the object fell, X ₃ record if a hard hat, bump hat, or no hat worn at the time of the accident.

1. Write the no-interaction linear regression model.
2. Interpret all the \(\beta \) ’s in the context of this question.
3. State the null hypothesis and the alternative hypothesis in terms of 3s for the following two situations

1. Does wearing a bump hat reduce the expected severity of injury as compared with wearing no protection? (Assuming X1 and X2 are held constant.)
2. Wearing a hat or not has no influence on the expected severity of injury when X1 and X2 are held constant.

d. Write the interaction linear regression model and then re-do part (b).

Question 2 : Consider the following data set

1. Obtain the scatterplot and comment on the plot.
2. Define the necessary dummy variables and write down the interaction linear regression model for this problem.
3. Obtain the best fitted model.
4. Test if interaction is significant or not (use 5% significance level for the test).
5. Regardless of your result in part (d), at 1% level of significance, is sex an important variable? How about age?

Question 3 : The board directors of a professional association conducted a random sample survey of 13 members to assess the effects of several possible amounts of dues increase. The sample results follow. X denotes the dollar increase in annual dues posited in the survey interview and Y = 1 if the interviewee indicated that the membership will not be renewed at that amount of dues increase and 0 if the membership will be renewed.

1. Obtain the best simple linear regression model and interpret the estimated coefficients.
2. Obtain the best fitted linear probability model and interpret the estimated coefficients.

c. Obtain the best logit model and interpret the estimated coefficients.

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