1.) The RMSE (also known as \sigma" is 10.0) and R 2 = 0 . 32 . The number of cases was over 12,000. The autism i score represents a child's placement on the 100 point autism spectrum disorder scale and iron i is the number of iron molecules per million in the child's blood. If the autism i score is greater than 20, the child is deemed to be in the \moderate autism" range, and if it is greater than 50, the child is deemed to be in the \severe autism" range. The iron i variable ranges from 1 to 4 in this sample (so the lowest observed score represents 1 iron molecule per million).
a) Conduct a null hypothesis test" for the effect of iron. Define your terms. Write out your steps.
b)We just learned of a family that lived in houses with lead paint and measured iron value for their children at 10.0. What would the model lead us to predict about their prospects for autism (moderate or severe)?
c) Suppose you just found out that your research assistant does not understand numbers. You told him to calculate iron parts per million, but he actually calculated a model after calculating iron parts per billion. How are your hypothesis tests likely to change if the iron variable is recalculated by dividing iron molecules by 1,000,000 instead of 1,000,000,000?
d) How will the estimated coecient for iron change after the iron variable is re-scaled. What effect would that have on our conclusions about the model.