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Small changes to reg inference lecture #30

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33 changes: 20 additions & 13 deletions chapter_reginference/reg_inference.Rmd
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Expand Up @@ -60,9 +60,9 @@ layout: true

# Recap from last week

* ***Confidence interval***: a plausible range of value for the population parameter
* ***Confidence interval***: a plausible range of values for the population parameter.

* ***Hypothesis testing***: null hypothesis $(H_0)$ vs alternative hypothesis $(H_A)$, (observed) test statistic, null distribution
* ***Hypothesis testing***: null hypothesis $(H_0)$ vs alternative hypothesis $(H_A)$, (observed) test statistic, null distribution.

* ***p-value***: probability of observing a test statistic as or more extreme than the observed test statistic assuming the null hypothesis is true.

Expand All @@ -89,7 +89,7 @@ layout: true

# Back to class size and student performance

* Let's go back the ***STAR*** experiment data, and focus on:
* Let's go back to the ***STAR*** experiment data, and focus on:

* *small* and *regular* classes,
* *Kindergarten* grade.
Expand Down Expand Up @@ -202,7 +202,7 @@ Entry | Meaning

Let's imagine we could redo the experiment 1000 times on 1000 different samples:

* We'd run 1000 regression and would get 1000 estimates of $\beta_k$, $b_k$.
* We'd run 1000 regressions and would get 1000 estimates of $\beta_k$, $b_k$.

--

Expand All @@ -218,21 +218,28 @@ Let's imagine we could redo the experiment 1000 times on 1000 different samples:

--

* Let's simulate the sampling distribution of $b_\textrm{small}$ to see where it comes from.
* `R` obtains this estimated standard error from ***theory*** which we will see in a few slides.

--

* Let's simulate the bootstrap distribution of $b_\textrm{small}$ to see how close the simulated value is to the theoretical value.

---

class:inverse

# Task 1 (10 min)

As we did for the sampling distribution of the proportion of *green pasta*, we want to generate the bootstrap distribution of $b_\textrm{small}$.
As we did for the bootstrap distribution of the proportion of *green pasta*, we want to generate the bootstrap distribution of $b_\textrm{small}$.

1. Copy the loading and cleaning code from slide 3 and run it.

1. Generate the bootstrap distribution of $b_\textrm{small}$ based on 1000 samples drawn from `star_df`. *Hint*: use the appropriate functions and arguments from the `infer` package so use the help pages.
1. Generate the bootstrap distribution of $b_\textrm{small}$ based on 1000 samples drawn from `star_df`. *Hints:*
* `specify()`: use the `explanatory` and `response` arguments and set them equal to the relevant variable.
* `generate()`: 1000 replicates of type bootstrap.
* `calculate()`: set the `stat` argument to `slope` and add the following argument: `order = c("TRUE", "FALSE")`.

1. Plot this simulated sampling distribution and compute mean and the standard error of $b_\textrm{small}$.
1. Plot this bootstrap distribution and compute the mean and the standard error of $b_\textrm{small}$.

---

Expand Down Expand Up @@ -399,7 +406,7 @@ plot_null_distrib +

--

Very unlikely to obtain $b_\textrm{small}$ = `r coeff_star[2]` when $H_0$ is true.
Very unlikely to obtain $b_\textrm{small}$ = `r reg_summary_star_df[2,1]` when $H_0$ is true.

---

Expand Down Expand Up @@ -521,7 +528,7 @@ layout: true

---

# Standard Normal Distribution: A Refresher
# Normal Distributions: A Refresher

.center[
```{r, echo = FALSE, out.width = "850px"}
Expand Down Expand Up @@ -578,7 +585,7 @@ class:inverse

# Task 2 (5 min)

1. Using the bootstrap distributed you generated in Task 1, compute the 95% confidence interval using the *percentile method*.
1. Using the bootstrap distribution you generated in Task 1, compute the 95% confidence interval using the *percentile method*.

1. How similar is it to the confidence intervals obtained in the previous slide?

Expand Down Expand Up @@ -746,9 +753,9 @@ class:inverse

# Task 3.2 (10 min)

1. Produce a scatterplot of the relationship between the log wage and the level of education.
1. Produce a scatterplot of the relationship between the log wage and the level of education, by gender (`color`).

1. Add the *regression line* with `geom_smooth`. What does this line represents?
1. Add a *linear regression line* to the plot using the `geom_smooth` layer. What does this line represents?

1. Let's illustrate what the shaded area stands for.

Expand Down
33 changes: 20 additions & 13 deletions chapter_reginference/reg_inference.html
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Expand Up @@ -16,7 +16,7 @@
# ScPoEconometrics
## Regression Inference
### Florian Oswald, Gustave Kenedi and Pierre Villedieu
### SciencesPo Paris </br> 2020-04-14
### SciencesPo Paris </br> 2020-04-15

---

Expand All @@ -37,9 +37,9 @@

# Recap from last week

* ***Confidence interval***: a plausible range of value for the population parameter
* ***Confidence interval***: a plausible range of values for the population parameter.

* ***Hypothesis testing***: null hypothesis `\((H_0)\)` vs alternative hypothesis `\((H_A)\)`, (observed) test statistic, null distribution
* ***Hypothesis testing***: null hypothesis `\((H_0)\)` vs alternative hypothesis `\((H_A)\)`, (observed) test statistic, null distribution.

* ***p-value***: probability of observing a test statistic as or more extreme than the observed test statistic assuming the null hypothesis is true.

Expand All @@ -66,7 +66,7 @@

# Back to class size and student performance

* Let's go back the ***STAR*** experiment data, and focus on:
* Let's go back to the ***STAR*** experiment data, and focus on:

* *small* and *regular* classes,
* *Kindergarten* grade.
Expand Down Expand Up @@ -198,7 +198,7 @@

Let's imagine we could redo the experiment 1000 times on 1000 different samples:

* We'd run 1000 regression and would get 1000 estimates of `\(\beta_k\)`, `\(b_k\)`.
* We'd run 1000 regressions and would get 1000 estimates of `\(\beta_k\)`, `\(b_k\)`.

--

Expand All @@ -214,21 +214,28 @@

--

* Let's simulate the sampling distribution of `\(b_\textrm{small}\)` to see where it comes from.
* `R` obtains this estimated standard error from ***theory*** which we will see in a few slides.

--

* Let's simulate the bootstrap distribution of `\(b_\textrm{small}\)` to see how close the simulated value is to the theoretical value.

---

class:inverse

# Task 1 (10 min)

As we did for the sampling distribution of the proportion of *green pasta*, we want to generate the bootstrap distribution of `\(b_\textrm{small}\)`.
As we did for the bootstrap distribution of the proportion of *green pasta*, we want to generate the bootstrap distribution of `\(b_\textrm{small}\)`.

1. Copy the loading and cleaning code from slide 3 and run it.

1. Generate the bootstrap distribution of `\(b_\textrm{small}\)` based on 1000 samples drawn from `star_df`. *Hint*: use the appropriate functions and arguments from the `infer` package so use the help pages.
1. Generate the bootstrap distribution of `\(b_\textrm{small}\)` based on 1000 samples drawn from `star_df`. *Hints:*
* `specify()`: use the `explanatory` and `response` arguments and set them equal to the relevant variable.
* `generate()`: 1000 replicates of type bootstrap.
* `calculate()`: set the `stat` argument to `slope` and add the following argument: `order = c("TRUE", "FALSE")`.

1. Plot this simulated sampling distribution and compute mean and the standard error of `\(b_\textrm{small}\)`.
1. Plot this bootstrap distribution and compute the mean and the standard error of `\(b_\textrm{small}\)`.

---

Expand Down Expand Up @@ -500,7 +507,7 @@

---

# Standard Normal Distribution: A Refresher
# Normal Distributions: A Refresher

.center[
&lt;img src="../img/photos/standard_normal_distrib.png" width="850px" style="display: block; margin: auto;" /&gt;
Expand Down Expand Up @@ -571,7 +578,7 @@

# Task 2 (5 min)

1. Using the bootstrap distributed you generated in Task 1, compute the 95% confidence interval using the *percentile method*.
1. Using the bootstrap distribution you generated in Task 1, compute the 95% confidence interval using the *percentile method*.

1. How similar is it to the confidence intervals obtained in the previous slide?

Expand Down Expand Up @@ -739,9 +746,9 @@

# Task 3.2 (10 min)

1. Produce a scatterplot of the relationship between the log wage and the level of education.
1. Produce a scatterplot of the relationship between the log wage and the level of education, by gender (`color`).

1. Add the *regression line* with `geom_smooth`. What does this line represents?
1. Add a *linear regression line* to the plot using the `geom_smooth` layer. What does this line represents?

1. Let's illustrate what the shaded area stands for.

Expand Down
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