Statistics 512: Homework 1Solutions1. A regression analysis relating test scores (Y) to training hours (X) produced the followingfitted question: ˆy= 25-0.5x.(a) What is the fitted value of the response variable corresponding tox= 7?
(b) What is the residual corresponding to the data point withx= 3 andy= 30?
(c) Ifxincreases 3 units, how does ˆychange?
(d) An additional test score is to obtained for a new observation atx= 6. Would the testscore for the new observation necessarily be 22? Explain.
(e) The error sums of squares (SSE) for this model was found to be 7. If there weren= 16observations, provide the best estimate forσ2.
2. Explain the different between the following two equations:ˆY=b0+b1XY=β0+β1X+.