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