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Results tagged with statistical-significance
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user 151862
Statistical significance is a characteristic of a statistic viewed in light of a null hypothesis and a given significance level. It reflects whether the statistic belongs to the rejection region (is statistically significant) or the acceptance region (is not statistically significant).
2
votes
1
answer
255
views
Do you trust an OLS estimated coefficient when it's not statistically significant?
Suppose you add a feature $x$ to an OLS model. The AIC goes down by 100 but the new feature is not statistically significant. The expanded model should be preferred overall but is the estimated coeffi …
- 2,251
6
votes
2
answers
8k
views
How do you get confidence intervals for interactions of variables?
Suppose I am building an OLS model with the following specification:
$$y = \alpha + \beta_0x_0 + \beta_1x_1 + \beta_2x_0x_1 + \epsilon$$
The variable $x_1$ is continuous and $x_0$ is binary. When $x_0 …
- 2,251
4
votes
1
answer
86
views
When testing multiple hypotheses, what does it mean when there are not enough extremes? [closed]
Suppose you are testing a large number of hypotheses, say a million. Unlike the usual situation where you have a lot of very small p-values, in this case all of your p-values are greater than 5%.
Wh …
- 2,251
5
votes
1
answer
2k
views
Why does R-Squared change with a no-intercept model? [duplicate]
Suppose I have one binary predictor $x$ and I fit an OLS model:
$$y = \alpha + \beta I(x=1) + \epsilon$$
Alternatively I can fit the following model
$$y = \beta I(x=1) + \beta I(x=0) + \epsilon$$
Why …
- 2,251
1
vote
Why are interactions harder to estimate at high values of the modulator?
Thanks to whuber who provided the answer in the comments.
The problem was the expression for the standard error was not correct. It should be
$$\text{se}(\hat\beta_1 + \hat\beta_2x_0)= \sqrt{\text{var …
- 2,251
2
votes
1
answer
34
views
Why are interactions harder to estimate at high values of the modulator?
Suppose you have the following model, where all variables are continuous:
$$y = \alpha + \beta_0x_0 + \beta_1x_1 + \beta_2 x_0 x_1 + \epsilon$$
The standard error for the effect of $x_1$ is
$$\text{se …
- 2,251
2
votes
1
answer
32
views
How do I interpret OLS when taking logs points the opposite way?
I am trying to estimate the effect of a binary variable $B$ on a continuous outcome $y$. The outcome $y$ is non-negative and highly skewed, its max being $92$ times greater than its median.
I tried to …
- 2,251