I think the \(\alpha\) parameter needs to be set better in the model:
knitr::include_graphics("RStudio/r-rstudio-1-3-console.png")
\[ \begin{eqnarray} Y_{i} &=& \alpha + \beta x_{i} + \varepsilon_{i} \\ Z_{i} &=& \gamma + \beta x_{i} + \varepsilon_{i} \end{eqnarray} \]
I think the paper by Eloyan and Ghosh (2013) is awesome! I like to cite it by (Eloyan and Ghosh 2013).
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summary(cars)
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
The mean distance of each car is 42.98 miles.
The equation was
model = lm( mpg ~ cyl + carb, data = mtcars)
tab = broom::tidy(model, conf_int = TRUE)
knitr::kable(tab)
term | estimate | std.error | statistic | p.value |
---|---|---|---|---|
(Intercept) | 37.812739 | 2.0540223 | 18.409118 | 0.0000000 |
cyl | -2.625023 | 0.3755924 | -6.989020 | 0.0000001 |
carb | -0.526146 | 0.4152914 | -1.266932 | 0.2152603 |
# DT::datatable(tab)
pander::pander(tab)
term | estimate | std.error | statistic | p.value |
---|---|---|---|---|
(Intercept) | 37.81 | 2.054 | 18.41 | 1.532e-17 |
cyl | -2.625 | 0.3756 | -6.989 | 1.102e-07 |
carb | -0.5261 | 0.4153 | -1.267 | 0.2153 |
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Eloyan, Ani, and Sujit K Ghosh. 2013. “A Semiparametric Approach to Source Separation Using Independent Component Analysis.” Computational Statistics & Data Analysis 58. Elsevier: 383–96.