Question: Refer to the data in the file "asm2Q1.xls" on the annual number of fatalities (FATALS, y ) from gas and dust explosion in coal mines for the years 1915 to 1978 and the number of labour hours (HOURS, x , in millions) of production work.

1. Fit a simple linear regression model to the data and construct a 95% prediction interval for y when x = 60.
2. Use Szroeter’s test to investigate the constant variance assumption of the simple linear regression model in a). What conclusion can you draw at 5% level?
3. Suppose instead, a new regression model is fitted using the transformed y value y ^* =sqrt(y) , ie, the model
   y ^* = sqrt(y) =  ₀ +  ₁ x + e
   is fitted. Construct again a 95% prediction interval for y (not y* ) when x = 60 based on this transformed model.
4. Use Szroeter’s test to investigate the constant variance assumption for the model in c). What conclusion can you draw at 5% level?
5. Compare the two intervals in a) and in c). Which one would you recommend? Explain.

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