week3.Rmd

---
title: "Week 3"
author: "Meng"
date: "04/02/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Modelling people 
```{r}
f <- function(c) {sqrt(c)*sqrt(24-c)}

optimise(f, c(0,24),maximum = T)

plot(f(0:24), type="l")

```


```{r max profits}
f <- function(q) {q*(50-q)}

optimise(f, c(0, 50), maximum = T)

plot(f(0:50), type="l")
```

```{r best line of fit}
f <- function(m,b)  21*m**2 + 14*m*b + 3*b**2 -94*m -30*b + 81

m <- seq(-10, 10, length = 200)
b <- seq(-10, 10, length = 200)

z <- outer(m,b,f)

persp(m,b,z, theta = -20, phi = 15, ticktype = "detailed") #theta and phi are for the angles of the graph


f1 <- function()

optimise(f, c(-100,100))


```


```{r exercise 7}
x <- c(2,4,7,3,1)
y <- c(45,80,95,55,30)
y_bar <- mean(y)
f_x <- 20*x

1- sum((y-f_x)**2)/sum((y-y_bar)**2)


```
```{r exercise 8}

x <- c(1,25,46,76,140)
y <- c(5,15,22,32,77)
y_bar <- mean(y)
f_x <- 0.5*x

1- sum((y-f_x)**2)/sum((y-y_bar)**2)

```