1. Say we have a simple linear regression with a single response Y and a single quantitative covariate X. The population model is: Yi = Bot BIXitei An observation of X, say Xi, is considered an outlier if it's value varies greatly from the majority of the X observation values. An observation of Y, say Ya, is considered an outlier if for its value of X it has an extreme value of Y (the value of Y varies greatly than what one would predict given the relationship between X and Y for all the other "usual" observations). a. Say we have a dataset where the i-th observation has a typical/usual value for X but it's Y value given X is much larger than what one would predict/expect using the relationship between X and Y for the other observations. Thus it is an outlier in Y given X, but not an outlier in X. In a couple of sentences, explain how much this observation will attenuate (or influence) the estimate B1 (no influence, small influence, large influence). b. Now say we have a dataset where the i-th observation has a typical/usual value for Y given X but it's X value is much larger than the other X values. Thus it is an outlier in X only (but the Y value is not unusual given the X value). In a couple of sentences, explain how much this observation will attenuate (or influence) the estimate , (no influence, small influence, large influence). c. Now say we have a dataset where the i-th observation is an outlier in both X and Y given X. Thus it's value for X differs greatly from the rest of the X observations, and the value of Y differs greatly than what one would predict or expect given the relationship between X and Y forthe other observations. In a couple of sentences, explain how this much observation will attenuate (or influence) the estimate 81 (no influence, small influence, large influence)