(7 points) In lecture, we spent a great deal of time talking about simple linear regression, which you also saw in Data 8. To briefly summarize, the simple linear regression model assumes that given a single observation x, our predicted response for this observation is =00+01. (Note: In this problem we write (0,01) instead of (a, b) to more closely mirror the multiple linear regression model notation.) In Lecture 9 we saw that the 0 = 0 and 0 = that minimize the average L loss for the simple linear regression model are: 0 = - 0 Ty 6 = = T Or, rearranging terms, our predictions are: x-x = y + ro 02 (a) (2 points) As we saw in lecture, a residual e, is defined to be the difference between a true response y, and predicted response . Specifically, e;= y. Note that there are n data points, and each data point is denoted by (xi, Yi). Show, using the equation for y above, that the average prediction is also the average value of the response, i.e. | 1 y =