Combining relationships. Suppose that x1 =2x2- 4 so that x1 and x2 are positively correlated. Let y =3x2 + 4 so that y and x2 are positively correlated.
(a) Use the relationship between x1 and x2 to find the linear relationship between y and x1. Are y and x1 positively correlated?
(b) Add the equations x1= 2x2- 4 and y =3x2 + 4 together and solve for y to obtain an equation relating y to both x1 and x2. Are the coefficients of both x's positive? Combining explanatory variables that are correlated can produce surprising results.