Week 07 - Prediction

# Week 07 - Prediction
## Prediction Error, Conditional Statements and Custom Functions
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### Danilo Freire
### 4th March 2019

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# Today's Agenda

* Classification

* General conditional statements

* How to write your own R functions
]
---

# Prediction Error

* .orange[Prediction Error]: actual outcome - predicted outcome

* Mean prediction error: mean(error)

* Root mean square error (RMSE): `$\sqrt{mean(error^2)}$`
]
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# Mean Predictor Error or RMSE?

* They are similar, but RMSE has interesting properties:
  - Since the errors are squared before they are averaged, RMSE gives high weight to large errors
  - Thus, RMSE is more useful when large errors are particularly undesirable
]

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# Prediction Error

```r
# Same code we saw last week, download data
library(pollstR)
chart_name <- "2016-general-election-trump-vs-clinton"
polls2016 <- pollster_charts_polls(chart_name)[["content"]]
polls2016 <- as.data.frame(polls2016)
polls2016$DaysToElection <- as.Date("2016-11-8") - polls2016$end_date
```
]
---

# Prediction Error

```r
last.weeks.data <- subset(polls2016, subset = DaysToElection < 15) # recent polls
margin <- last.weeks.data$Clinton - last.weeks.data$Trump
margin[1:5]                   # latest 5 polls
```

```
## [1] 3 5 4 3 7
```

```r
true.margin <- 48.59 - 46.47  # election result
pred.error <- true.margin - margin
pred.error
```

```
##  [1] -0.88 -2.88 -1.88 -0.88 -4.88  0.12 -0.88  2.12 -0.88 -2.88  1.12
## [12] -4.88
```

```r
mean(pred.error)
```

```
## [1] -1.463333
```

```r
sqrt(mean(pred.error^2))
```

```
## [1] 2.526737
```
---

# National Polls Weren't Far Off

```r
hist(margin, main = "Poll Prediction", col = "grey",
     xlab = "Predicted Clinton's margin of victory (%)")
abline(v = true.margin, col = "red",
       lwd = 2, lty = "dotted") # line width and line type
```

<img src="week07a_files/figure-html/hist-1.png" style="display: block; margin: auto;" />
---

# National Polls Weren't Far Off

```r
error <- margin - true.margin
hist(error, main = "Poll Prediction Error", col = "blue",
     xlab = "Error in Predicted Clinton’s margin of victory (%)")
```

<img src="week07a_files/figure-html/hist02-1.png" style="display: block; margin: auto;" />
---

# Nate Silver

.font150[
"Trump outperformed his national polls by only 1 to 2 percentage points in losing the popular vote to Clinton, making them slightly closer to the mark than they were in 2012. Meanwhile, he beat his polls by only 2 to 3 percentage points in the average swing state"

Nate Silver - [The Real Story of 2016](https://fivethirtyeight.com/features/the-real-story-of-2016)
]
---

# Classification

* Did Trump win electoral college?

* Did civil war occur?

* Did it rain?

* Prediction of binary outcome variable = .orange[classification problem]
]
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# Classification

.font140[
* Wrong prediction: misclassification
  - True positive: correctly predicting civil war in country X at time T
  - False positive: incorrectly predicting civil war in country X at time T
  - True negative: correctly predicting no civil war in country X at time T
  - False negative: incorrectly predicting no civil war in country X at time T

* .orange[Type I error]: false positive

* .orange[Type II error]: false negative
]
---

# False Positives and False Negatives

# Questions?

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# General Conditional Statements

```r
values <- 1:10
ifelse(values < 5, 0, 1)
```

```
##  [1] 0 0 0 0 1 1 1 1 1 1
```
]
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# General Conditional Statements

```r
if (X) {
    expression1a
    ...
    expressionNa
} else if (Y) {
    expression1b
    ...
    expressionNb
} else {
    expression1c
    ...
    expressionNc
}
```
]
---

# General Conditional Statements

.font150[
* Elements of `if(){}else(){}`
  - `X`: logical statement returning either `TRUE` or `FALSE`
  - `Y`: additional statements also returning either `TRUE` or `FALSE`
  - `expression`: code chunks evaluated depending on the value of `X`
  
* Can be combined with for loops
]
---

# Example

```r
values <- 1:10                     # sequence from 1 to 10
results <- rep(NA, length(values)) # empty vector

# Loop
for (i in values) {
  if (values[i] < 5) {
    results[i] <- 0
} else if (values[i] == 5) {
    results[i] <- 5
} else {
    results[i] <- 1
}
}

# Print results
results
```

```
##  [1] 0 0 0 0 5 1 1 1 1 1
```
]
---

# Custom Functions in R

* R packages are just collection of functions

* Custom functions save time and increase reliability. Basic syntax:

```r
function_name <- function(arg_1, arg_2, ...) {
   Function body 
}
```

* Name: the name you want for your function

* Arguments: a placeholder. When a function is invoked, you pass a value to the argument. A function can have as many arguments as you want to

* Function body: what the function does
]
---

# Example: Fahrenheit to Celsius

```r
# Call the function "temp.converter" and the argument "fahrenheit"
temp.converter <- function(fahrenheit) {
  (fahrenheit - 32) / 1.8   # what the function does
}

# Testing the function
temp.converter(0)   
```

```
## [1] -17.77778
```

```r
temp.converter(50)  
```

```
## [1] 10
```

```r
temp.converter(-40)
```

```
## [1] -40
```
]
---

# A Fancier Function

```r
# Call the function "is.prime" and the argument "num"
is.prime <- function(num) {
   if (num == 2) {
      cat("2 is the first prime number")
   } else if (any(num %% 2:(num-1) == 0)) { 
      cat(num, "is not a prime number", "\n") 
   } else { 
      cat(num, "is a prime number", "\n")
   }
}
```
]
---

# Testing the function

```r
is.prime(2)
```

```
## 2 is the first prime number
```

```r
is.prime(10)
```

```
## 10 is not a prime number
```

```r
is.prime(7919)
```

```
## 7919 is a prime number
```

```r
is.prime(sqrt(81))
```

```
## 9 is not a prime number
```
]
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# Questions?

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# See you on Wednesday!