Consider a set of data ...

. Consider a set of data (Ti, yi ), 1 = 1, ..., 7, provided in Table S. If we believe that I, and y; has a linear relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try to find o and ? such that the straight line y = o + I minimizes the sum of squared errors for all the data points: min Ely - (a + Bz.)]. i=1 X Y 38 137 58 201 50 152 52 107 37 150 173 37 194 54 168 59 154 43 137 30 38 53 193 59 154 40 175 85 247 Table S: Data for Problem 2 While almost all statistical software and packages provide tools for one to solve the above linear regression problem, we may also consider it as a nonlinear program and solve it with an optimization solver (e.g, MS Excel solver). For the data provided in the following table, solve the linear regression problem. Write down the optimal / you find by rounding it to the first digit after the decimal point (e.g., 9.011, 1.229, and 3.245 should be rounded to 9.01, 1.23, and 3.25 to be written down)