regression coefficients between two different states substantially different? Note: a permutation test is a fairly advanced statistical technique, but not much statistical knowledge is required to answer this question. For a bit more (optional) discussion on the permutation test, see the end of this part. 1. (3 points) From the census data frame, extract all rows that correspond to tracts in Virginia or West Virginia, and call the resulting data frame census. vw. Verify that this has 2321 rows. 2. (6 points) Now perform two separate linear regressions using census . vw. The first is a linear regression of Mail_Return_Rate_CEN_2010 (as the response) on pct_NH_White_alone_ACS_09_13 and pct_Renter_Occp_HU_ACS_09_13 (as the predictors), using only the tracts in Virginia; the second is again a linear regression of Mail_Return_Rate_CEN_2010 (as the response) on pct_NH_White_alone_ACS_09_13 and pct_Renter_Occp_HU_ACS_09_13 (as the predictors), but now using only the tracts in West Virginia. Ignoring the intercept terms, each linear regression model here gives you two coefficients (one for pct_NH_White_alone_ACS_09_13 and one for pct_Renter_Occp_HU_ACS_09_13). Compare the two sets of coefficients. Are they the same? 3. (6 points) Even though the two coefficients for Virginia and West Virginia may be different, it is hard to tell just how different they are. To help answer this question, we will look at the linear regression coefficients if we were to randomly scramble census tracts between Virginia and West Virginia, then refit the linear regression models. This is the idea behind a permutation test. Vaguely speaking, if the two sets of coefficients were truly the same, then shuffling the labels should have no real effect on our estimated coefficients. First, make a copy of census . vw called census . vw. perm. Then, randomly permute the entries in census . vw. perm$State_name. (Hint: recall the function sample( ).) Once this is done, rerun the two regression models from Part 4 Question 2 using census . vw. perm, and report the coefficients for Virginia, and for West Virginia