- Quick Review
- Regression Basics
- Single redux
- Logistic Regression
April 6th, 2021
We started with the notion that a given \(\alpha\), (pvalue cutoffs) can lead to a big FDR: \(\alpha \rightarrow q(\alpha)\).
BH reverse that. They fix FDR, and find the relevant \(\alpha\). The algorithm is the key to doing that. \(q \rightarrow \alpha^*(q)\)
What is driving sales? Brand differences? Price changes? Ads?
Blue points are based on ongoing promotional activity.
It looks like ads are important.
Fit a line for sales by brand controlling for promotional activity.
\[ log(Sales) \approx \alpha + \gamma Brand + \beta Ads \]
\(\alpha+\gamma_b\) are like our baseline sales. But we can bring in \(\beta\) more sales with some promotional activity.
This should be mostly review, but perhaps with a different emphasis.
Many problems involve a response or outcome (
And a bunch of covariates or predictors (
x) to be used for regression.
A general tactic is to deal in averages and lines.
\[E[y|x] = f(x'\beta)\]
\(x = [1,x_1,x_2,x_3,...,x_p]\) is our vector of covariates.
(Our number of covariates is \(p\) again)
\(\beta = [\beta_0,\beta_1,\beta_2,...,\beta_p]\) are the corresponding coefficients.
The product \(x'\beta = \beta_0+\beta_1 x_1 + \beta_2 x_2+\cdots+\beta_p x_p\).
For simplicity we denote \(x_0 = 1\) to estimate intercepts