Consider a situation in which the regression data set is divided into two parts as shown in Table 2.10. The regression model is given by yi =    β (1) 0 + β1xi + εi , i = 1, 2, · · · , n1; β (2) 0 + β1xi + εi , i = n1 + 1, · · · , n1 + n2. In other words, there are two regression lines with common slope. Using the centered regression model yi =    β (1∗) 0 + β1(xi − x¯1) + εi , i = 1, 2, · · · , n1; β (2∗) 0 + β1(xi − x¯2) + εi , i = n1 + 1, · · · , n1 + n2, where ¯x1 = Pn1 i=1 xi/n1 and ¯x2 = Pn1+n2 i=n1+1 xi/n2. Show that the least squares estimate of β1 is given by b1 = Pn1 i=1(xi − x¯1)yi + Pn1+n2 i=n1+1(xi − x¯2)yi Pn1 i=1(xi − x¯1) 2 + Pn1+n2 i=n1+1(xi − x¯2) 2