(a) 在估计模型中观察大的方差因子（即 > 10）。

(b) 与解释变量的估计斜率的符号相反的符号

(c) 观察解释变量之间的强相关性（即 jrj > 0:7）。

1. Facebook: In this example we investigate the performance metrics for posts published on Facebook
pages. Di erent posts’ performance metrics extracted from a cosmetic company’s page were used
to model the number of Likes on a post. See Figures (1) for output helpful for this problem. All
variables are listed in detail below.
 Response Variable (y): Likes ! Number of \Likes” on the publication.
 Explanatory Variable (x1): Lifetime post total impressions (1000s) ! Impressions are the
number of times a post from a page is displayed, whether the post is clicked or not. People may
see multiple impressions of the same post. For example, someone might see a Page update in
News Feed once and then a second time if a friend shares it. Units are in 1000s.
 Explanatory Variable (x2): Lifetime post total reach (1000s) ! The number of people who
saw a page post (unique users). Units are in 1000s.
 Explanatory Variable (x3): Lifetime Engaged Users ! The number of engaged users.
 Explanatory Variable (x4): Lifetime Post Consumers ! The number of people who clicked
anywhere in a post.
 Explanatory Variable (x5): Lifetime Post Consumptions !The number of clicks anywhere
in a post.
We discussed several tools (procedures) that are used to detect indicators of multicollinearity. For
parts (1a, 1b, 1c) read each description below. Circle all variables (if any) which suggest a problem
with multicollinearity in the estimated model that is consistent with the provided description.

(a) Observing large Variance In ation Factors (i.e. > 10) in an estimated model.

(b) An opposite sign of the estimated slope for an explanatory variable compared to the sign of the
correlation between this explanatory variable and the response variable. Here the concern is
related to inconsistencies when the original correlation is moderate or strong (i.e. jrj > 0:3).