1. Consider the Vocab.csv data on Canvas (in the data folder), containing the number of years of education and the performance on a vocabulary test for a number of individuals. For this problem we want to perform simple linear regression by modeling the relationship between the response (the test score) and the predictor (the education level). As with the simple linear regression done in class, case we want to model ya a (33.; + b However, we want to do this according to the generic method for regression presented in class in which we solve the normal equations= X tX o: = X g using an appropriate choice of X matrix. (a) In R, read in the data and create the X matrix that would be appropriate for estimating a and l). (b) Solve the normal equations with your choice of X and report the values you get for a. and b. (c) Does it appear that people with more education tend to have larger vocabularies? ) (d It is usually hard to make quantitative statements about the value of a year of education= however, you can do so here in the context of this particulary vocabulary test. Make such a quantitative statement here. A B C D E F 2 19740001 1974 Male 14 3 19740002 1974 Male 16 4 19740003 1974 Female 10 5 19740004 1974 Female 10 6 19740005 1974 Female 12 7 19740006 1974 Male 16 8 19740007 1974 Male 17 9 19740008 1974 Male 10 10 19740009 1974 Female 12 11 19740010 1974 Female 11 12 19740011 1974 Male 6 13 19740012 1974 Male 5 14 19740013 1974 Female 11 15 19740014 1974 Female 12 16 19740015 1974 Female 14 17 19740016 1974 Male 12 18 19740017 1974 Male 8 19 19740018 1974 Male 0 20 19740019 1974 Female 8 21 19740020 1974 Female 10 22 19740021 1974 Male 8 23 19740022 1974 Male 12 24 19740023 1974 Female 3 25 19740024 1974 Female 8 26 19740025 1974 Female 3 27 19740026 1974 Male 9 28 19740027 1974 Male 15 29 19740028 1974 Female 7 30 19740029 1974 Female 12 31 19740030 1974 Female 13 32 19740031 1974 Male 12 33 19740033 1974 Female 12 1 00 00 0 01 A W O JU A 34 19740034 1974 Female 8 35 19740035 1974 Female 12 36 19740036 1974 Male 10 37 19740037 1974 Male 14 38 19740038 1974 Female 12 39 19740039 1974 Female 8 6 40 19740040 1974 Female 16 9 41 19740041 1974 Male 16 8 42 19740042 1974 Male 17 43 19740043 1974 Male 13 CO Vocab +