Forecasting with Two-way ANOVA in R - With replication and no interaction.Rmd

---
title: "Forecasting with Two-Way ANOVA in R - With Replication and No Interaction"
author: "Anita Owens"
output:
  html_document:
    df_print: paged
    toc: true
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---

Question: Do coupons and advertising affects peanut butter sales?

## 1. Set up environment

```{r Load packages}
# Install pacman if needed
if (!require("pacman")) install.packages("pacman")

# load packages
pacman::p_load(pacman,
  tidyverse, openxlsx, ggpubr)
```

## 2. Load data

```{r Import peanutbutter dataset}
#Dataset is in datasets subfolder
(peanutbutter <- read.xlsx("datasets/Coupondata.xlsx"))
```

```{r Lowercase column names}
#Lowercase column names
(peanutbutter<- rename_with(peanutbutter, tolower))
```

```{r Pivot data from wide to long dataset}
#Pivot data from wide to long dataset
(peanutbutter_long <- peanutbutter %>% 
  pivot_longer(!advertising, names_to = "coupon", values_to = "sales"))
```

## 3. Data Visualization

```{r Plot sales vs advertising colored by coupon}
#Plot using ggpubr
ggline(peanutbutter_long, x = "advertising", y = "sales", 
       add = c("mean_se", "jitter"),
       color = "coupon", palette = "startrek",
       title = "Sales increase when ad spending increases",
       subtitle = "(Advertising and coupon do not interact) ",
       legend.title = "coupon status"
       )
```

## 4. Two-way ANOVA

```{r Two-way ANOVA table}
two_way_aov <- aov(sales ~ advertising*coupon, data = peanutbutter_long)

#The anova table
summary(two_way_aov)
```

Since the p-values for the main effects advertising and then coupon are small and the interaction (advertising\*coupon) is very large. Advertising and coupon factors (separately) increases sales.

## 5. AOV Model Diagnostics

```{r Plot the model diagnostics}
#Diagnostic plots
#plot(two_way_aov)

hist(two_way_aov$residuals, prob = TRUE)
lines(density(two_way_aov$residuals))

qqnorm(two_way_aov$residuals)
qqline(two_way_aov$residuals)
```

## 6. Forecast

```{r What we can expect in sales?}
#What we can expect in sales when there is advertising vs. no advertising
peanutbutter_long %>% 
  group_by(advertising) %>% 
  summarize(sales_forecast = round(mean(sales),2),
            std_dev = round(sd(sales),2))
#What we can expect in sales when there is a coupon vs no coupon
peanutbutter_long %>% 
  group_by(coupon) %>% 
  summarize(sales_forecast = round(mean(sales),2),
            std_dev = round(sd(sales),2))
```

+---------------------------------+----------------------------------+
| Sales with:                     | Forecast                         |
+:================================+:=================================+
| No advertising                  | 80.67                            |
+---------------------------------+----------------------------------+
| With advertising                | 158.33                           |
+---------------------------------+----------------------------------+
| No coupon                       | 109                              |
+---------------------------------+----------------------------------+
| With coupon                     | 130                              |
+---------------------------------+----------------------------------+

[***Ads tends to increase sales by 78 (158.33 - 80.67) over no ad and coupon tends to increase sales by 21 (130 - 109) over no coupon.***]{.ul}

So in the case of peanut butter sales, if we wanted to predict peanut butter sales with both coupon and advertising we can use the following equation:

> predicted sales = overall average + factor A effect (if significant) + factor B effect (if significant)

```{r Forecast when there is both advertising and a coupon}
#Calculate the overall average
overall_avg <- mean(peanutbutter_long$sales)
paste("The overall sales average is", overall_avg, sep=" ")

#Calculate advertising effect
adv_effect <- (158.33 - 80.67)

#Calculate coupon effect
coupon_effect <- (130-109)

#Calculate Forecast:
#predicted value = overall average + factor A effect (if significant) + factor B effect (if significant)
predicted_sales <- overall_avg + adv_effect + coupon_effect

paste("Forecast when there is both advertising and a coupon is:", predicted_sales, sep = " ")
```

## 7. Final Summary

The forecast equation we can use to predict with two-way ANOVA (with or without replication) is the:

> predicted value = overall average + factor A effect (if significant) + factor B effect (if significant)

If a factor is **not significant** than the factor effect is assumed to be 0.

Two-way ANOVA (with replication), if interaction effect **is significant**, then the predicted value is the value of the response variable (y) is equal to the mean of all observations having that combination of factor levels. If interaction effect, **is not significant**, you can proceed with your analysis as if it were two-way ANOVA without replication scenario.