Multiple Linear Regression to Determine If a Price Cut Increases Sales.Rmd

---
title: "Do price cuts increase sales?"
author: "Anita Owens"
output:
  html_document:
    df_print: paged
    toc: true
    toc_float:
      collapsed: false
      smooth_scroll: false
    toc_depth: 2
---

## 1. Background


Which factors influence grocery sales?

Page 210.

For 12 straight weeks, you have observed sales (in number of cases) of canned tomatoes at Mr. D's Supermarket.
1. Was a promotional notice for canned tomatoes placed in all shopping carts?
2. Was a coupon for canned tomotoes given to each customer?
3. Was a price reduction (none, 1, or 2 cents off) given?

Use this data to determine how these factors influence sales.

Predict sales of canned tomatoes during a week in which you use a shopping cart notice, a coupon, and reduce price by 1 cent.


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

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


```{r Load Data}

grocery <- read.xlsx("datasets/Grocery.xlsx")
```


```{r Inspect Data}
str(grocery)
```



```{r Data Transformation}
#Convert all character variables into factor in one line:
grocery <- grocery %>% mutate_if(is.character, as.factor)

#factor Price Reduction variable
grocery$Price.Reduction <- as.factor(grocery$Price.Reduction)
```



```{r Grocery model}
# All variables with the exception of Week as an independent variable
grocery_model_lm <- lm(Sales ~ Coupon + Cart.Notice + Price.Reduction, data = grocery)

summary(grocery_model_lm)
```


We have 2 significant and 2 insignificant variables. 

Forecast equation:

Predicted Sales = 14.500 - 1.16*CouponYes + 20.16*Cart.NoticeYes + 5*Price.Reduction1 + 12.75*Price.Reduction2.




```{r Create New Price.Reduction variable}
#Create new price reduction variable
grocery <- grocery %>% 
    mutate(Price.Reduction_new =
      case_when(
        Price.Reduction == 2 ~ 2,
        Price.Reduction == 1 ~ 0,
        Price.Reduction == 0 ~ 0))


#We need to factor Price.Reduction_new
grocery$Price.Reduction_new <- as.factor(grocery$Price.Reduction_new)

#Check levels
levels(grocery$Price.Reduction_new)

#Inspect results
str(grocery)
```

```{r Re-run model}

#Model sales as explained by Cart.Notice and Price.Reduction_new
grocery_model_lm_signifvars <- lm(Sales ~ Cart.Notice + Price.Reduction_new, data = grocery)

#Print model output
summary(grocery_model_lm_signifvars)

```
Forecast equation for significant variables only:

Predicted Sales = 16.417 + 20.167*Cart.NoticeYes + 10.250*Price.Reduction_new2


## Making predictions

Predict sales of canned tomatoes during a week in which you use a shopping cart notice, a coupon, and reduce price by 1 cent.


§ Out-of-sample data
	□ we use the estimated model on a new dataset
	® predict function
		◊ we can apply this model to a new dataset



```{r Create new data frame for predictions}
# Create new data frame and print output
(new_data <- data.frame(Cart.Notice = "Yes", Coupon = "Yes", Price.Reduction = "1"))

```




```{r Create predictions using original model - all variables}
library(broom)

# make predictions - response returns the fitted values
augment(grocery_model_lm, newdata = new_data)
```

Using all variables our predicted sales are 38.5.


```{r Create new dataframe for predictions for 2nd model}

# Create new data frame
(new_data_02 <- data.frame(Cart.Notice = "Yes", Price.Reduction_new="0"))

```



```{r Create predictions using 2nd model}
#Using broom package
augment(grocery_model_lm_signifvars, newdata = new_data_02)

#Manual equation for making the predictions
16.417 + (20.167*1) + (0)
```

Using significant variables gives us 36.58 predicted sales.


```{r Use contrasts function to view factor type variable details, eval=FALSE, include=FALSE}

contrasts(grocery$Price.Reduction)
```