c) (10 points) You estimate 3;,- = [31 + [32 ln 3;,- + s,- by OLS. Your estimate for [32 is statistically signicant at 1%. Then, you realized you had forgotten to include a variable, 10,-, that you think should be in your model. So, you add it and estimate 3},- = ,81 + [32 In x, + 3311),- + 6,. The estimate for ,82 does not change, but it is now statistically signicant at 5%. Given this observation, answer the following questions. 1. Does this observation say anything about what happened to the stan- dard errors of b2 (the estimator for 32)? Why? 2. Does this observation say anything about the strength of the linear relationship between In x, and 10,? Why? 3. Does this observation say anything about the expectation of ()2 in the model without 11),? Why? 4. Does this observation say anything about what would be the value of the 3;; estimate if you were to regress y, = 31 + B310, + 77,? Why? Explain each of your answers based on what we have seen in this course