In a regression analysis of on-the job head injuries of warehouse laborers cause

Question

In a regression analysis of on-the job head injuries of warehouse laborers caused by falling objects, y is a measure of severity of the injury, x_1 is an index reflecting both the weight of the object and the distance from which it fell, and x_2 and x_3 are indicator variables for the nature of head protection worn at the time of the accident, coded as follows: The regression function used in the study is y = beta_0 + beta_1x_1 + beta_2x_2 + beta_3 x_3 + epsilon For each of the following questions, specify the null hypothesis H_0 for the appropriate test in terms of the model parameter(s). (a) For the same object (x_1 fixed), does wearing a bump cap reduce the expected severity of the injury as compared to wearing no protection? (b) For the same object (x_1 fixed), is the expected severity of injury the same when wearing a hard hat, as when wearing a bump cap?

Explanation / Answer

a) Null Hypothesis E(y) (when x3 is one and x2 is zero) is less than E(y) (when x2 and x3are zero).

b) Null Hypothesis isE(y) (when x3 is one and x2 is one) is equal to E(y) (when x2 is zero and x3is one).

such that beta2 = beta 3

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