(a) (3 points) As we saw in the lecture, a residual 63,-, for data point \"i E {1, . . . ,n}, is dened to be the difference between a true response y,- and predicted response 33,. Specically, e, = y, 3),. Note that there are 71, data points, and each data point is denoted by (I,, y,) Prove, using the equation for :9 above, that 2:1 8,- : 0. (b) (2 points) Prove that. g} : 1;. You may use your result from part (a). 1. (10 points) In the lecture, we spent a great deal of time talking about simple linear regression, which you also saw in Data 8. To briey summarize, the simple linear re- gression model assumes that given a single observation :13, our predicted response for this observation is fr} 2 90 + 19111:. In Lecture 10 we saw that the 60 = (90 and 91 = 671 that minimize the average L2 loss for the simple linear regression model are: 90 :gm A 0' 612Ty 0113 Or, rearranging terms, our predictions Q are: 3311? z+r0y 0-11