1. Suppose we conduct a linear regression on outcome variable (y) and explanatory variables (3:1, :32, ---, 31,). We posit the following model yi=13o+513i1+321i2+"'+3p$ip+i (1) where si's are i.i.d. with mean 0 and are normally distributed. Consider the following, slightly different model vi = Go + (113.5] + {1285653 + ' ' ' + 01,173? + 5i (2) where 65's are i.i.d. with mean 0 and are normally distributed. In (2), we scaled the second variable 33,} by e. (For example, when 12;; is the height in cm, we can change it to height in meter by multiplying e = 0.01.) Prove that the test results for Ho:2=0 vs Kym-#0 and Ho:a2=0 vs Him-12960 are identical. (Hint: Show that the Ttest statistics are identical. Use matrix formulation.)