Question: 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, X₁ is weight of the object, X₂ is the distance the object fell, X₃ record if a hard hat, bump hat, or no hat worn at the time of the accident.

a. Write the no-interaction linear regression model.

b. Interpret all the \(\beta \) ’s in the context of this question.

c. State the null hypothesis and the alternative hypothesis in terms of 3s for the following two situations

I. Does wearing a bump hat reduce the expected severity of injury as compared with wearing no protection? (Assuming X1 and X2 are held constant.)

II. 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).