Marketing-Analytics-Hw1-Khachatryan-Ela.Rmd

---
title: "Marketing Analytics Homework 1 Khachatryan Ela"
output: pdf_document
date: "2023-09-27"
---

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

## R Markdown

#importing necessary libraries
```{r}
libs <- c('ggplot2', 'knitr', 'diffusion', 'ggpubr')

load_libraries <- function(libs) {
  new_libs <- libs[!(libs %in% installed.packages()[,"Package"])]
  if (length(new_libs) > 0) {
    install.packages(new_libs)
  }
  lapply(libs, library, character.only = TRUE)
}

load_libraries(libs)

```



## Getting data for the look-alike innovation
```{r}
tesla <- read.csv("Tesla sales by year.csv", fileEncoding="UTF-8-BOM", sep = ";")
tesla
```

## Visualizing Tesla sales 

```{r}
tesla$year <- factor(tesla$year)

plot_tesla = ggplot(data = tesla, aes(x = year, y = sales)) +
  geom_bar(stat = 'identity') +
  ggtitle('Tesla sales in thousand units')

plot_tesla
```

## 4. Estimating Bass model parameters for the look-alike innovation.
```{r}

sales_tesla = tesla$sales

t = 1:length(sales_tesla)

bass_m = nls(sales_tesla ~ m*(((p+q)**2/p)*exp(-(p+q)*t))/
               (1+(q/p)*exp(-(p+q)*t))**2,
              start=c(list(m=sum(sales_tesla),p=0.02,q=0.4)))

options(scipen = 999, digits = 4) ## to avoid scientific notations
summary(bass_m)
```

## 5. Make predictions of the diffusion of the innovation you chose at stage 1.

```{r}
diff_m = diffusion(sales_tesla)
p=round(diff_m$w,4)[1]
q=round(diff_m$w,4)[2]
m=round(diff_m$w,4)[3]
diff_m
```

```{r}
## Period when the sales will reach to the peak.

data.frame(Predicted=log(q/p)/(p+q),
                 Actual=which.max(tesla$sales))
```
``` {r}
## Defining bass function
bass.f <- function(t,p,q){ ((p+q)**2/p)*exp(-(p+q)*t)/
    (1+(q/p)*exp(-(p+q)*t))**2
  }
```



## 6. Estimate the number of adopters by time period. Thus, you will need to estimate the potential market share. You can use Fermi’s logic here.

```{r}
## Modeling f(t) and visualizing it
time_ad = ggplot(data.frame(t = c(1:9)), aes(t)) +
  stat_function(fun = bass.f, args = c(p=0.0298, q=0.073)) +
  labs(title = 'f(t)')
ggarrange(time_ad, plot_tesla)

```


```{r}
## Predicting sales
tesla$pred_sales = bass.f(1:9, p = 0.000847, q = 0.540172)*17339.9
ggplot(data = tesla, aes(x = year, y = sales)) +
  geom_bar(stat = 'identity') +
  geom_point(mapping = aes(x=year, y=pred_sales), color = 'red')
```