Aresearcher wants to conduct a multiple regression analysis, where y is the dependent variable and {x1, x2, x3, x4} are the explanatory variables. first, he estimates the following model: y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + , and finds that r2 = 0.85 and r2 adj = 0.82. 2 then, he decides to drop x4 from the model. after estimating this new regression y = β0 + β1x1 + β2x2 + β3x3 + , he finds that r2 = 0.42 and r2 adj = 0.40. you can assume that all the usual conditions for linear regression are satisfied. which of the following statements is false? a) it must be the case that b4, the estimate of the unknown slope parameter β4 in the first regression, is significantly smaller than 0. b) dropping the variable x4 from the model seems like a bad idea, since x4 clearly predict the dependent variable y . c) about 42% of the variance of y can be explained by the variance in x1, x2 and x3. d) about 15% of the variance of y cannot be explained by the variance in x1, x2, x3 and x4. e) since the adjusted r-squared decreases a lot after dropping x4, the first model seems preferable to the second one.