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mine-cetinkaya-rundel committed Sep 24, 2023
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Expand Up @@ -321,7 +321,8 @@ m_lot_r_sq_adj <- update(m_full, . ~ . - lot, data = duke_forest) |> glance() |>
```

::: {.workedexample data-latex=""}
Results corresponding to the full model for the housing data are shown in @tbl-price-mlr. How should we proceed under the backward elimination strategy?
Results corresponding to the full model for the housing data are shown in @tbl-price-mlr.
How should we proceed under the backward elimination strategy?

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Because eliminating `bed` leads to a model with a higher adjusted $R^2$ than the full model, we drop `bed` from the model.

It might seem counter-intuitive to exclude information on number of bedrooms from the model.
After all, we would expect homes with more bedrooms to cost more, and we can see a clear relationship between number of bedrooms and sale price in @fig-single-scatter. However, note that `area` is still in the model, and it's quite likely that the area of the home and the number of bedrooms are highly associated.
After all, we would expect homes with more bedrooms to cost more, and we can see a clear relationship between number of bedrooms and sale price in @fig-single-scatter.
However, note that `area` is still in the model, and it's quite likely that the area of the home and the number of bedrooms are highly associated.
Therefore, the model already has information on "how much space is available in the house" with the inclusion of `area`.

Since we eliminated a predictor from the model in the first step, we see whether we should eliminate any additional predictors.
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$$

::: {.workedexample data-latex=""}
The residual plot for the model with all of the predictor variables except `bed` is given in @fig-price-resid-mlr-nobed. How do the residuals in @fig-price-resid-mlr-nobed compare to the residuals in @fig-price-resid-slr?
The residual plot for the model with all of the predictor variables except `bed` is given in @fig-price-resid-mlr-nobed.
How do the residuals in @fig-price-resid-mlr-nobed compare to the residuals in @fig-price-resid-slr?

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::: {.alltutorials data-latex=""}
[Tutorial 3: Regression modeling](https://openintrostat.github.io/ims-tutorials/03-model/)

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<https://openintrostat.github.io/ims-tutorials/03-model>
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:::

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[Tutorial 3 - Lesson 1: Visualizing two variables](https://openintro.shinyapps.io/ims-03-model-01/)

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<https://openintro.shinyapps.io/ims-03-model-01>
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[Tutorial 3 - Lesson 2: Correlation](https://openintro.shinyapps.io/ims-03-model-02/)

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<https://openintro.shinyapps.io/ims-03-model-02>
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:::

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[Tutorial 3 - Lesson 3: Simple linear regression](https://openintro.shinyapps.io/ims-03-model-03/)

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<https://openintro.shinyapps.io/ims-03-model-03>
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[Tutorial 3 - Lesson 4: Interpreting regression models](https://openintro.shinyapps.io/ims-03-model-04/)

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<https://openintro.shinyapps.io/ims-03-model-04>
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[Tutorial 3 - Lesson 5: Model fit](https://openintro.shinyapps.io/ims-03-model-05/)

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<https://openintro.shinyapps.io/ims-03-model-05>
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:::

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[Tutorial 3 - Lesson 6: Parallel slopes](https://openintro.shinyapps.io/ims-03-model-06/)

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<https://openintro.shinyapps.io/ims-03-model-06>
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:::

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[Tutorial 3 - Lesson 7: Evaluating and extending parallel slopes model](https://openintro.shinyapps.io/ims-03-model-07/)

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<https://openintro.shinyapps.io/ims-03-model-07>
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::: {.singletutorial data-latex=""}
[Tutorial 3 - Lesson 8: Multiple regression](https://openintro.shinyapps.io/ims-03-model-08/)

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<https://openintro.shinyapps.io/ims-03-model-08>
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[Tutorial 3 - Lesson 9: Logistic regression](https://openintro.shinyapps.io/ims-03-model-09/)

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<https://openintro.shinyapps.io/ims-03-model-09>
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::: {.singletutorial data-latex=""}
[Tutorial 3 - Lesson 10: Case study: Italian restaurants in NYC](https://openintro.shinyapps.io/ims-03-model-10/)

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<https://openintro.shinyapps.io/ims-03-model-10>
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You can also access the full list of tutorials supporting this book at
<https://openintrostat.github.io/ims-tutorials>.
You can also access the full list of tutorials supporting this book at <https://openintrostat.github.io/ims-tutorials>.
:::

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::: {.singlelab data-latex=""}
[Introduction to linear regression - Human Freedom Index](https://www.openintro.org/go?id=ims-r-lab-model)

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<https://www.openintro.org/go?id=ims-r-lab-model>
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:::

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You can also access the full list of labs supporting this book at
<https://www.openintro.org/go?id=ims-r-labs>.
You can also access the full list of labs supporting this book at <https://www.openintro.org/go?id=ims-r-labs>.
:::

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