Final Project: Superstore Sales Analysis
2023-11-26
About Dataset
The “Superstore Sales” dataset is a comprehensive and versatile collection of data that provides valuable insights into sales, customer behavior, and product performance. This dataset offers a rich resource for in-depth analysis.
Containing information from diverse regions and segments, the dataset enables exploration of trends, patterns, and correlations in sales and customer preferences. The dataset encompasses sales transactions, enabling researchers and analysts to understand buying patterns, identify high-demand products, and assess the effectiveness of different shipping modes.
Moreover, the dataset provides an opportunity to examine the impact of various factors such as discounts, geographical locations, and product categories on profitability. By analyzing this dataset, businesses and data enthusiasts can uncover actionable insights for optimizing pricing strategies, supply chain management, and customer engagement.
Whether used for educational purposes, business strategy formulation, or data analysis practice, the “Superstore Sales” dataset offers a comprehensive platform to delve into the dynamics of sales operations, customer interactions, and the factors that drive business success.
Modules Used
library(dplyr) ##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## ✔ ggplot2 3.4.3 ✔ stringr 1.5.0
## ✔ lubridate 1.9.2 ✔ tibble 3.2.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(ggplot2)
library(reshape2)##
## Attaching package: 'reshape2'
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## The following object is masked from 'package:tidyr':
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## smithslibrary(pwr)
library(caret)## Loading required package: lattice
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## Attaching package: 'caret'
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## The following object is masked from 'package:purrr':
##
## liftlibrary(caTools)
library(caret)
library(ROSE)## Loaded ROSE 0.0-4library(caret)
library(ggplot2)
library(reshape2)
library(moments)Reading The Data
df <-read.csv('/Users/fahadmehfooz/Desktop/IUPUI/First Semester/Intro to Statistics/Intro to Stats Dataset/Dataset 1/Superstore.csv')
head(df, 5)## Row.ID Order.ID Order.Date Ship.Date Ship.Mode Customer.ID
## 1 1 CA-2013-152156 09-11-2013 12-11-2013 Second Class CG-12520
## 2 2 CA-2013-152156 09-11-2013 12-11-2013 Second Class CG-12520
## 3 3 CA-2013-138688 13-06-2013 17-06-2013 Second Class DV-13045
## 4 4 US-2012-108966 11-10-2012 18-10-2012 Standard Class SO-20335
## 5 5 US-2012-108966 11-10-2012 18-10-2012 Standard Class SO-20335
## Customer.Name Segment Country City State
## 1 Claire Gute Consumer United States Henderson Kentucky
## 2 Claire Gute Consumer United States Henderson Kentucky
## 3 Darrin Van Huff Corporate United States Los Angeles California
## 4 Sean O'Donnell Consumer United States Fort Lauderdale Florida
## 5 Sean O'Donnell Consumer United States Fort Lauderdale Florida
## Postal.Code Region Product.ID Category Sub.Category
## 1 42420 South FUR-BO-10001798 Furniture Bookcases
## 2 42420 South FUR-CH-10000454 Furniture Chairs
## 3 90036 West OFF-LA-10000240 Office Supplies Labels
## 4 33311 South FUR-TA-10000577 Furniture Tables
## 5 33311 South OFF-ST-10000760 Office Supplies Storage
## Product.Name Sales Quantity
## 1 Bush Somerset Collection Bookcase 261.9600 2
## 2 Hon Deluxe Fabric Upholstered Stacking Chairs, Rounded Back 731.9400 3
## 3 Self-Adhesive Address Labels for Typewriters by Universal 14.6200 2
## 4 Bretford CR4500 Series Slim Rectangular Table 957.5775 5
## 5 Eldon Fold 'N Roll Cart System 22.3680 2
## Discount Profit
## 1 0.00 41.9136
## 2 0.00 219.5820
## 3 0.00 6.8714
## 4 0.45 -383.0310
## 5 0.20 2.5164Descriptive Statistics:
colnames(df)## [1] "Row.ID" "Order.ID" "Order.Date" "Ship.Date"
## [5] "Ship.Mode" "Customer.ID" "Customer.Name" "Segment"
## [9] "Country" "City" "State" "Postal.Code"
## [13] "Region" "Product.ID" "Category" "Sub.Category"
## [17] "Product.Name" "Sales" "Quantity" "Discount"
## [21] "Profit"dim(df)## [1] 9994 21Checking the statistics of the dataset
summary(df[, colnames(df)])## Row.ID Order.ID Order.Date Ship.Date
## Min. : 1 Length:9994 Length:9994 Length:9994
## 1st Qu.:2499 Class :character Class :character Class :character
## Median :4998 Mode :character Mode :character Mode :character
## Mean :4998
## 3rd Qu.:7496
## Max. :9994
## Ship.Mode Customer.ID Customer.Name Segment
## Length:9994 Length:9994 Length:9994 Length:9994
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## Country City State Postal.Code
## Length:9994 Length:9994 Length:9994 Min. : 1040
## Class :character Class :character Class :character 1st Qu.:23223
## Mode :character Mode :character Mode :character Median :56430
## Mean :55190
## 3rd Qu.:90008
## Max. :99301
## Region Product.ID Category Sub.Category
## Length:9994 Length:9994 Length:9994 Length:9994
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## Product.Name Sales Quantity Discount
## Length:9994 Min. : 0.444 Min. : 1.00 Min. :0.0000
## Class :character 1st Qu.: 17.280 1st Qu.: 2.00 1st Qu.:0.0000
## Mode :character Median : 54.490 Median : 3.00 Median :0.2000
## Mean : 229.858 Mean : 3.79 Mean :0.1562
## 3rd Qu.: 209.940 3rd Qu.: 5.00 3rd Qu.:0.2000
## Max. :22638.480 Max. :14.00 Max. :0.8000
## Profit
## Min. :-6599.978
## 1st Qu.: 1.729
## Median : 8.666
## Mean : 28.657
## 3rd Qu.: 29.364
## Max. : 8399.976There are 9994 values in every column.
Central tendency can be observed here for all the numeric columns.
Checking unique values in categorical columns and their counts
columns_to_count <- c("Category", "Region", "Country", "Segment", "State")
# Looping through the categorical columns and printing the counts
for (col in columns_to_count) {
if (col %in% names(df)) {
cat("Counts for", col, ":\n")
print(table(df[[col]]))
cat("\n") # Corrected this line
} else {
cat(col, "is not a column in the dataframe.\n\n")
}
}## Counts for Category :
##
## Furniture Office Supplies Technology
## 2121 6026 1847
##
## Counts for Region :
##
## Central East South West
## 2323 2848 1620 3203
##
## Counts for Country :
##
## United States
## 9994
##
## Counts for Segment :
##
## Consumer Corporate Home Office
## 5191 3020 1783
##
## Counts for State :
##
## Alabama Arizona Arkansas
## 61 224 60
## California Colorado Connecticut
## 2001 182 82
## Delaware District of Columbia Florida
## 96 10 383
## Georgia Idaho Illinois
## 184 21 492
## Indiana Iowa Kansas
## 149 30 24
## Kentucky Louisiana Maine
## 139 42 8
## Maryland Massachusetts Michigan
## 105 135 255
## Minnesota Mississippi Missouri
## 89 53 66
## Montana Nebraska Nevada
## 15 38 39
## New Hampshire New Jersey New Mexico
## 27 130 37
## New York North Carolina North Dakota
## 1128 249 7
## Ohio Oklahoma Oregon
## 469 66 124
## Pennsylvania Rhode Island South Carolina
## 587 56 42
## South Dakota Tennessee Texas
## 12 183 985
## Utah Vermont Virginia
## 53 11 224
## Washington West Virginia Wisconsin
## 506 4 110
## Wyoming
## 1Checking the missing values proportions
# Viewing the missing values proportions
missing_vals <- colSums(is.na(df)) / nrow(df)
missing_vals## Row.ID Order.ID Order.Date Ship.Date Ship.Mode
## 0 0 0 0 0
## Customer.ID Customer.Name Segment Country City
## 0 0 0 0 0
## State Postal.Code Region Product.ID Category
## 0 0 0 0 0
## Sub.Category Product.Name Sales Quantity Discount
## 0 0 0 0 0
## Profit
## 0Checking central tendency:
get_mode <- function(x) {
unique_x <- unique(x)
unique_x[which.max(tabulate(match(x, unique_x)))]
}
summarize_numeric_columns <- function(df) {
numeric_columns <- sapply(df, is.numeric)
stats <- data.frame()
for (col_name in names(df)[numeric_columns]) {
column_data <- df[[col_name]]
stats[col_name, "Mean"] <- mean(column_data, na.rm = TRUE)
stats[col_name, "Median"] <- median(column_data, na.rm = TRUE)
stats[col_name, "Mode"] <- get_mode(column_data)
col_IQR <- IQR(column_data, na.rm = TRUE)
stats[col_name, "IQR"] <- col_IQR
stats[col_name, "Lower Bound"] <- quantile(column_data, 0.25, na.rm = TRUE) - 1.5 * col_IQR
stats[col_name, "Upper Bound"] <- quantile(column_data, 0.75, na.rm = TRUE) + 1.5 * col_IQR
}
return(stats)
}
summary_stats_df <- summarize_numeric_columns(df)
summary_stats_df## Mean Median Mode IQR Lower Bound
## Row.ID 4.997500e+03 4997.5000 1.00 4996.50000 -4995.50000
## Postal.Code 5.519038e+04 56430.5000 10035.00 66785.00000 -76954.50000
## Sales 2.298580e+02 54.4900 12.96 192.66000 -271.71000
## Quantity 3.789574e+00 3.0000 3.00 3.00000 -2.50000
## Discount 1.562027e-01 0.2000 0.00 0.20000 -0.30000
## Profit 2.865690e+01 8.6665 0.00 27.63525 -39.72413
## Upper Bound
## Row.ID 14990.50000
## Postal.Code 190185.50000
## Sales 498.93000
## Quantity 9.50000
## Discount 0.50000
## Profit 70.81687Checking Skewness and Kurtosis for the columns
selected_columns <- df[, c("Sales", "Quantity", "Discount", "Profit")]
# Calculating kurtosis and skewness
kurtosis_values <- sapply(selected_columns, kurtosis)
skewness_values <- sapply(selected_columns, skewness)
# Combining the results into a data frame
skew_kurt_result <- rbind(kurtosis = kurtosis_values, skewness = skewness_values)
print(skew_kurt_result)## Sales Quantity Discount Profit
## kurtosis 308.15843 4.990293 5.407740 399.989229
## skewness 12.97081 1.278353 1.684042 7.560297All of them are more peaked than a normal distribution (kurtosis).
None of the columns are normally distributed (skewness).
Interpretation:
Skewness:
Definition: Skewness measures the degree of asymmetry of a distribution. A distribution can be asymmetrical on either the right (positive skew) or left (negative skew) side.
Interpretation:
Positive Skew (Right-skewed): The tail on the right side of the distribution is longer or fatter than the left side. It indicates that a large number of data points are clustered on the left, with a few exceptionally large values to the right.
Negative Skew (Left-skewed): The tail on the left side of the distribution is longer or fatter than the right side. This suggests that a large number of observations are clustered on the right, with some exceptionally small values to the left.
Zero or Close to Zero: If the skewness is zero or close to zero, the data is considered to be fairly symmetrical.
Kurtosis:
Definition: Kurtosis measures the “tailedness” of the distribution. It’s a descriptor of the shape of the tails and the peak of the distribution, relative to a normal distribution. Interpretation:
High Kurtosis (Leptokurtic): A distribution with a kurtosis greater than 3 (excess kurtosis greater than 0) is said to be leptokurtic. Leptokurtic distributions have heavy tails or outliers. The peak is also higher and sharper than the peak of a normal distribution.
Low Kurtosis (Platykurtic): A distribution with a kurtosis less than 3 (excess kurtosis less than 0) is platykurtic. Platykurtic distributions have lighter tails or fewer outliers. The peak is lower and broader than the peak of a normal distribution.
Normal Kurtosis (Mesokurtic): A kurtosis of exactly 3 (excess kurtosis of 0) indicates a mesokurtic distribution, which has a shape similar to a normal distribution.
Exploratory Data Analysis
Univariate Analysis:
Distribution for Profit Variable
# Creating a histogram
hist(df$Sales,
main = "Distribution of Profit",
xlab = "Profit", # X-axis label
ylab = "Frequency", # Y-axis label
col = "green", # Bar color
border = "black", # Border color
breaks = 20,
freq = FALSE) # Number of bins or breaks
# Displaying density also
lines(density(df$Profit), col = "black", lwd = 2)
qqnorm(df$Profit)
qqline(df$Profit, col = "red") 
Its a right skewed distribution. The profit distribution extends to 9000 which can likely be outliers. We would have to dig deeper into this.
Distribution for Quantity Variable
hist(df$Sales,
main = "Distribution of Quantity",
xlab = "Quantity", # X-axis label
ylab = "Frequency", # Y-axis label
col = "green", # Bar color
border = "black", # Border color
breaks = 20,
freq = FALSE) # Number of bins or breaks
# Displaying density also
lines(density(df$Quantity), col = "black", lwd = 2)
qqnorm(df$Sales)
qqline(df$Sales, col = "red") 
> This is also a right skewed distribution.
The Q-Q plot also shows the same, the line diverges on the upper right side.
Checking the Categories Variable
category_table <- table(df$Category)
category_percentages <- round(100 * category_table / sum(category_table), 1)
labels <- paste(names(category_percentages), "-", category_percentages, "%", sep = "")
pie(category_table,
labels = labels,
main = "Categories - Variable Distribution",
xlab = "Categories",
ylab = "Frequency")
The most sold category is office supplies.
barplot(table(df$Region),
main = "Region Variable Distribution",
xlab = "Region",
ylab = "Frequency")
The heighest sale is from west region.
Boxplots to check outliers in Sales:
ggplot(df, aes(y = Sales)) +
geom_boxplot(coef = 1.5) +
labs(y = "Sales") +
ggtitle("Box Plot of Sales")
> So we can see a number of outliers in Sales that can mean a certain
number of things. The sales were specifically high on these days, could
be the discounts given were high or other factors.
Boxplots to check outliers in Profit:
ggplot(df, aes(y = Profit)) +
geom_boxplot(coef = 1.5) +
labs(y = "Profit") +
ggtitle("Box Plot of Profit")
Segment Wise Division
ggplot(data = df, aes(x = Segment)) +
geom_bar() +
labs(x = "Segment", y = "Count") +
ggtitle("Bar Plot of Segment")
Multivariate Analysis
Checking relationship between Sales and Profit?
plot(df$Profit, df$Sales,
main = "Scatter Plot: Sales vs. Profit",
xlab = "Sales",
ylab = "Profit",
col = "red"
)
Is there a relationship between Quantity and Discount?
ggplot(df, aes(x = Quantity, y = Discount)) +
geom_point() +
labs(x = "Quantity", y = "Discount") +
ggtitle("Scatter Plot of Quantity vs. Discount")
The plot seems pretty uniform that means quantity is not affecting the discount.
df$Category <- as.factor(df$Category)
df$Segment <- as.factor(df$Segment)
# Create a grouped bar plot
ggplot(df, aes(x = Category, fill = Segment)) +
geom_bar(position = "dodge", color = "black", stat = "count") +
labs(title = "Grouped Bar Plot of Category and Segment",
x = "Category",
y = "Count") +
scale_fill_manual(values = c("red", "blue", "green")) 
# df_num is containing only numeric columns of df
df_num <- df[sapply(df, is.numeric)]
# Calculating the correlation matrix
df_corr <- cor(df_num)
# Melting the correlation matrix for ggplot
df_corr_melted <- melt(df_corr)
# Creating the heatmap plot
heatmap_plot <- ggplot(data = df_corr_melted, aes(x = Var1, y = Var2, fill = value)) +
geom_tile() +
geom_text(aes(label = round(value, 2)), vjust = 1) +
scale_fill_gradientn(colors = c("blue", "white", "red")) + # Custom color gradient
labs(title = "Correlation Heatmap for Continuous Variables", x = "Features", y = "Features", fill = "Correlation")
# Printing the heatmap plot
print(heatmap_plot)
> No strong correlations can be seen here.
Inferential Statistics:
Hypothesis Testing:
Choice of test:
ANOVA is used for comparing means of continuous data across multiple groups defined by categorical variables.
Chi-Square Test is used for testing relationships between categorical variables or checking the distribution of categorical variables against expected distributions.
Hypothesis 1:
Test Used: Anova
H0: There is no significant difference in quantity ordered between different states
HA: There is a significant difference in quantity ordered between different states.
Significance level: 0.05, Power level: 0.8, Minimum Effect Size: 0.3.
# Since we are finding a relationship between continuous and categorical column, we need to write an anova test
result_statevsquantity <- aov(Quantity ~ State, data = df)
summary(result_statevsquantity)## Df Sum Sq Mean Sq F value Pr(>F)
## State 48 219 4.556 0.92 0.631
## Residuals 9945 49258 4.953Since the probability or p value is 0.631 i.e greater than 0.05, we fail to reject the null hypothesis. And hence there is no significant difference in quantity between different states.
Hypothesis 2:
Test Used: Chi-Square
Null Hypothesis (H0): There is no significant interaction effect between “State” and “Category”
Alternative Hypothesis (HA): There is a significant interaction effect between “State” and “Category”
Significance level: 0.05, Power level: 0.8, Minimum Effect Size: 0.3.
state_vs_category <- chisq.test(table(df$State, df$Category))## Warning in chisq.test(table(df$State, df$Category)): Chi-squared approximation
## may be incorrectstate_vs_category##
## Pearson's Chi-squared test
##
## data: table(df$State, df$Category)
## X-squared = 102.86, df = 96, p-value = 0.2974Since the probability or p value is 0.2974 i.e greater than 0.05, we fail to reject the null hypothesis.
Hypothesis 3:
Test Used: Anova
H0: There’s no effect of subcategory on sales.
HA: Subcategory does have an effect on sales.
# If there are more than 10 subcategories, consolidating them
if (length(unique(df$Sub.Category)) > 10) {
# Here, we'll group the subcategories with the smallest counts into a "Other" category
subcat_counts <- table(df$Sub.Category)
small_subcats <- names(subcat_counts)[order(subcat_counts)][1:(length(subcat_counts)-10)]
df$Sub.Category[df$Sub.Category %in% small_subcats] <- 'Other'
}
result <- aov(Sales ~ Sub.Category, data = df)
anova_summary <- summary(result)
print(anova_summary)## Df Sum Sq Mean Sq F value Pr(>F)
## Sub.Category 10 3.111e+08 31105056 86.97 <2e-16 ***
## Residuals 9983 3.571e+09 357666
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1significance_level <- 0.05
p_value <- anova_summary[[1]]$'Pr(>F)'[1]
if (p_value < significance_level) {
print("Reject the null hypothesis: Sales differ among the subcategories.")
} else {
print("Do not reject the null hypothesis: There's no significant difference in sales among the subcategories.")
}## [1] "Reject the null hypothesis: Sales differ among the subcategories."A significance level of 0.05 corresponds to a 95% confidence interval. This means that if the same experiment or study were repeated many times, 95% of the calculated confidence intervals would contain the true population parameter.
Feature Engineering
# Converting date strings to Date objects
df$Order.Date <- as.Date(df$Order.Date, format = "%d-%m-%Y")
df$Ship.Date <- as.Date(df$Ship.Date, format = "%d-%m-%Y")
# Calculating the number of days between order date and ship date
df$Days_Between <- as.numeric(df$Ship.Date - df$Order.Date)
head(df["Days_Between"], 5)## Days_Between
## 1 3
## 2 3
## 3 4
## 4 7
## 5 7One hot encoding data for Categorical Variables
cols_to_encode <- c("Ship.Mode", "Segment", "Country", "City", "State", "Region", "Category", "Sub.Category")
# Identify columns with more than one level
cols_with_multiple_levels <- sapply(df[cols_to_encode], function(x) length(unique(x)) > 1)
# Create a formula for one-hot encoding with only columns having multiple levels
formula <- as.formula(paste("~", paste(cols_to_encode[cols_with_multiple_levels], collapse = " + ")))
# Create dummy variables
dummy_vars <- dummyVars(formula, data = df)
encoded_data <- predict(dummy_vars, newdata = df)
# Select the columns from 'df' that you want to keep
continuous_cols <- c("Sales", "Quantity", "Discount", "Profit", "Days_Between")
# Combine the selected columns from 'df' with 'encoded_data'
final_data <- cbind(encoded_data, df[continuous_cols])
# Print the result
head(final_data, 1)## Ship.ModeFirst Class Ship.ModeSame Day Ship.ModeSecond Class
## 1 0 0 1
## Ship.ModeStandard Class Segment.Consumer Segment.Corporate
## 1 0 1 0
## Segment.Home Office CityAberdeen CityAbilene CityAkron CityAlbuquerque
## 1 0 0 0 0 0
## CityAlexandria CityAllen CityAllentown CityAltoona CityAmarillo CityAnaheim
## 1 0 0 0 0 0 0
## CityAndover CityAnn Arbor CityAntioch CityApopka CityApple Valley
## 1 0 0 0 0 0
## CityAppleton CityArlington CityArlington Heights CityArvada CityAsheville
## 1 0 0 0 0 0
## CityAthens CityAtlanta CityAtlantic City CityAuburn CityAurora CityAustin
## 1 0 0 0 0 0 0
## CityAvondale CityBakersfield CityBaltimore CityBangor CityBartlett
## 1 0 0 0 0 0
## CityBayonne CityBaytown CityBeaumont CityBedford CityBelleville CityBellevue
## 1 0 0 0 0 0 0
## CityBellingham CityBethlehem CityBeverly CityBillings CityBloomington
## 1 0 0 0 0 0
## CityBoca Raton CityBoise CityBolingbrook CityBossier City CityBowling Green
## 1 0 0 0 0 0
## CityBoynton Beach CityBozeman CityBrentwood CityBridgeton CityBristol
## 1 0 0 0 0 0
## CityBroken Arrow CityBroomfield CityBrownsville CityBryan CityBuffalo
## 1 0 0 0 0 0
## CityBuffalo Grove CityBullhead City CityBurbank CityBurlington CityCaldwell
## 1 0 0 0 0 0
## CityCamarillo CityCambridge CityCanton CityCarlsbad CityCarol Stream
## 1 0 0 0 0 0
## CityCarrollton CityCary CityCedar Hill CityCedar Rapids CityChampaign
## 1 0 0 0 0 0
## CityChandler CityChapel Hill CityCharlotte CityCharlottesville
## 1 0 0 0 0
## CityChattanooga CityChesapeake CityChester CityCheyenne CityChicago CityChico
## 1 0 0 0 0 0 0
## CityChula Vista CityCincinnati CityCitrus Heights CityClarksville
## 1 0 0 0 0
## CityCleveland CityClifton CityClinton CityClovis CityCoachella
## 1 0 0 0 0 0
## CityCollege Station CityColorado Springs CityColumbia CityColumbus
## 1 0 0 0 0
## CityCommerce City CityConcord CityConroe CityConway CityCoon Rapids
## 1 0 0 0 0 0
## CityCoppell CityCoral Gables CityCoral Springs CityCorpus Christi
## 1 0 0 0 0
## CityCosta Mesa CityCottage Grove CityCovington CityCranston
## 1 0 0 0 0
## CityCuyahoga Falls CityDallas CityDanbury CityDanville CityDavis
## 1 0 0 0 0 0
## CityDaytona Beach CityDearborn CityDearborn Heights CityDecatur CityDeer Park
## 1 0 0 0 0 0
## CityDelray Beach CityDeltona CityDenver CityDes Moines CityDes Plaines
## 1 0 0 0 0 0
## CityDetroit CityDover CityDraper CityDublin CityDubuque CityDurham CityEagan
## 1 0 0 0 0 0 0 0
## CityEast Orange CityEast Point CityEau Claire CityEdinburg CityEdmond
## 1 0 0 0 0 0
## CityEdmonds CityEl Cajon CityEl Paso CityElkhart CityElmhurst CityElyria
## 1 0 0 0 0 0 0
## CityEncinitas CityEnglewood CityEscondido CityEugene CityEvanston CityEverett
## 1 0 0 0 0 0 0
## CityFairfield CityFargo CityFarmington CityFayetteville CityFlorence
## 1 0 0 0 0 0
## CityFort Collins CityFort Lauderdale CityFort Worth CityFrankfort
## 1 0 0 0 0
## CityFranklin CityFreeport CityFremont CityFresno CityFrisco CityGaithersburg
## 1 0 0 0 0 0 0
## CityGarden City CityGarland CityGastonia CityGeorgetown CityGilbert
## 1 0 0 0 0 0
## CityGladstone CityGlendale CityGlenview CityGoldsboro CityGrand Island
## 1 0 0 0 0 0
## CityGrand Prairie CityGrand Rapids CityGrapevine CityGreat Falls CityGreeley
## 1 0 0 0 0 0
## CityGreen Bay CityGreensboro CityGreenville CityGreenwood CityGresham
## 1 0 0 0 0 0
## CityGrove City CityGulfport CityHackensack CityHagerstown CityHaltom City
## 1 0 0 0 0 0
## CityHamilton CityHampton CityHarlingen CityHarrisonburg CityHattiesburg
## 1 0 0 0 0 0
## CityHelena CityHempstead CityHenderson CityHendersonville CityHesperia
## 1 0 0 1 0 0
## CityHialeah CityHickory CityHighland Park CityHillsboro CityHolland
## 1 0 0 0 0 0
## CityHollywood CityHolyoke CityHomestead CityHoover CityHot Springs
## 1 0 0 0 0 0
## CityHouston CityHuntington Beach CityHuntsville CityIndependence
## 1 0 0 0 0
## CityIndianapolis CityInglewood CityIowa City CityIrving CityJackson
## 1 0 0 0 0 0
## CityJacksonville CityJamestown CityJefferson City CityJohnson City
## 1 0 0 0 0
## CityJonesboro CityJupiter CityKeller CityKenner CityKenosha CityKent
## 1 0 0 0 0 0 0
## CityKirkwood CityKissimmee CityKnoxville CityLa Crosse CityLa Mesa
## 1 0 0 0 0 0
## CityLa Porte CityLa Quinta CityLafayette CityLaguna Niguel CityLake Charles
## 1 0 0 0 0 0
## CityLake Elsinore CityLake Forest CityLakeland CityLakeville CityLakewood
## 1 0 0 0 0 0
## CityLancaster CityLansing CityLaredo CityLas Cruces CityLas Vegas CityLaurel
## 1 0 0 0 0 0 0
## CityLawrence CityLawton CityLayton CityLeague City CityLebanon CityLehi
## 1 0 0 0 0 0 0
## CityLeominster CityLewiston CityLincoln Park CityLinden CityLindenhurst
## 1 0 0 0 0 0
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## RegionEast RegionSouth RegionWest Category.Furniture Category.Office Supplies
## 1 0 1 0 1 0
## Category.Technology Sub.CategoryAccessories Sub.CategoryAppliances
## 1 0 0 0
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## Discount Profit Days_Between
## 1 0 41.9136 3Modelling: Linear Regression- Predicting Sales of a store on the basis of demographic factors
# Set a random seed for reproducibility
set.seed(123)
# Splitting the data into training and test sets (e.g., 70% for training and 30% for testing)
split <- sample.split(final_data$Sales, SplitRatio = 0.7)
train_data <- final_data[split, ]
test_data <- final_data[!split, ]
# Creating a linear regression model
lm_model <- lm(Sales ~ ., data = train_data)
# Printing the summary of the linear regression model
summary(lm_model)##
## Call:
## lm(formula = Sales ~ ., data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1181.8 -131.4 -25.2 60.6 8466.5
##
## Coefficients: (53 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.722e+02 3.965e+02 1.695 0.0900 .
## `Ship.ModeFirst Class` -5.309e+00 2.121e+01 -0.250 0.8023
## `Ship.ModeSame Day` -2.328e+01 3.579e+01 -0.650 0.5154
## `Ship.ModeSecond Class` 2.246e+01 1.676e+01 1.340 0.1802
## `Ship.ModeStandard Class` NA NA NA NA
## Segment.Consumer 8.854e+00 1.442e+01 0.614 0.5393
## Segment.Corporate -2.995e+00 1.577e+01 -0.190 0.8493
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## `CityJohnson City` 9.855e+01 3.710e+02 0.266 0.7905
## CityJonesboro 5.996e+01 4.282e+02 0.140 0.8886
## CityJupiter NA NA NA NA
## CityKeller 2.421e+02 5.316e+02 0.455 0.6488
## CityKenner 5.719e+02 5.439e+02 1.052 0.2930
## CityKenosha 3.856e+02 4.269e+02 0.903 0.3664
## CityKent 2.122e+02 3.737e+02 0.568 0.5702
## CityKirkwood 3.159e+02 5.282e+02 0.598 0.5498
## CityKissimmee 4.971e+02 5.465e+02 0.910 0.3631
## CityKnoxville 1.230e+02 3.567e+02 0.345 0.7302
## `CityLa Crosse` 2.710e+02 4.427e+02 0.612 0.5406
## `CityLa Mesa` 2.555e+02 4.419e+02 0.578 0.5632
## `CityLa Porte` 9.274e+01 3.697e+02 0.251 0.8019
## `CityLa Quinta` 1.630e+02 5.273e+02 0.309 0.7572
## CityLafayette 5.374e+02 3.519e+02 1.527 0.1267
## `CityLaguna Niguel` 2.809e+01 4.417e+02 0.064 0.9493
## `CityLake Charles` 2.451e+02 4.617e+02 0.531 0.5956
## `CityLake Elsinore` -3.750e+01 5.275e+02 -0.071 0.9433
## `CityLake Forest` 2.953e+02 4.418e+02 0.668 0.5039
## CityLakeland 7.055e+01 3.865e+02 0.183 0.8552
## CityLakeville 2.294e+02 3.803e+02 0.603 0.5463
## CityLakewood 1.528e+02 3.465e+02 0.441 0.6592
## CityLancaster 1.496e+02 3.401e+02 0.440 0.6601
## CityLansing 4.368e+01 3.918e+02 0.112 0.9112
## CityLaredo 2.005e+02 3.740e+02 0.536 0.5919
## `CityLas Cruces` 4.218e+02 4.875e+02 0.865 0.3870
## `CityLas Vegas` 3.423e+01 4.312e+02 0.079 0.9367
## CityLaurel 1.531e+02 5.434e+02 0.282 0.7781
## CityLawrence 1.284e+02 3.442e+02 0.373 0.7092
## CityLawton 2.895e+02 4.878e+02 0.594 0.5528
## CityLayton NA NA NA NA
## `CityLeague City` 1.566e+02 3.868e+02 0.405 0.6856
## CityLebanon 1.038e+02 5.318e+02 0.195 0.8453
## CityLehi 1.201e+02 5.657e+02 0.212 0.8319
## CityLeominster 2.053e+02 3.874e+02 0.530 0.5961
## CityLewiston 4.362e+02 5.663e+02 0.770 0.4412
## `CityLincoln Park` 9.643e+01 4.614e+02 0.209 0.8344
## CityLinden -2.788e+02 5.424e+02 -0.514 0.6072
## CityLindenhurst 3.918e+02 5.286e+02 0.741 0.4586
## `CityLittle Rock` 5.620e+01 4.000e+02 0.140 0.8883
## CityLittleton -2.963e+02 5.242e+02 -0.565 0.5719
## CityLodi NA NA NA NA
## CityLogan 2.631e+02 4.336e+02 0.607 0.5439
## `CityLong Beach` 2.470e+02 3.398e+02 0.727 0.4674
## CityLongmont 1.818e+02 4.052e+02 0.449 0.6537
## CityLongview 1.663e+02 4.663e+02 0.357 0.7214
## CityLorain 4.038e+02 3.651e+02 1.106 0.2688
## `CityLos Angeles` 2.458e+02 3.357e+02 0.732 0.4642
## CityLouisville 2.542e+02 3.332e+02 0.763 0.4457
## CityLoveland 7.417e+01 3.877e+02 0.191 0.8483
## CityLowell 1.994e+02 3.653e+02 0.546 0.5852
## CityLubbock 1.414e+02 3.969e+02 0.356 0.7217
## CityMacon 1.807e+02 3.819e+02 0.473 0.6360
## CityMadison 6.170e+02 4.191e+02 1.472 0.1410
## CityMalden 2.250e+02 4.472e+02 0.503 0.6149
## CityManchester 2.169e+02 3.842e+02 0.564 0.5724
## CityManhattan 4.464e+02 5.659e+02 0.789 0.4303
## CityMansfield 8.410e+01 4.463e+02 0.188 0.8505
## CityManteca 1.505e+02 4.418e+02 0.341 0.7334
## `CityMaple Grove` 3.407e+02 4.256e+02 0.800 0.4235
## CityMargate NA NA NA NA
## CityMarietta 6.477e+01 3.816e+02 0.170 0.8652
## CityMarion 2.670e+02 3.541e+02 0.754 0.4510
## CityMarlborough 1.674e+02 5.312e+02 0.315 0.7526
## CityMarysville -1.088e+02 5.482e+02 -0.199 0.8427
## CityMason 2.158e+02 4.063e+02 0.531 0.5952
## CityMcallen 1.301e+02 3.557e+02 0.366 0.7145
## CityMedford 2.578e+02 4.118e+02 0.626 0.5313
## CityMedina 1.022e+02 3.653e+02 0.280 0.7796
## CityMelbourne 3.176e+01 5.464e+02 0.058 0.9537
## CityMemphis 2.689e+02 3.526e+02 0.763 0.4458
## CityMentor 2.849e+02 3.888e+02 0.733 0.4638
## CityMeriden 2.556e+02 3.753e+02 0.681 0.4958
## CityMeridian 3.991e+02 7.357e+02 0.542 0.5875
## CityMesa -2.232e+01 2.227e+02 -0.100 0.9202
## CityMesquite 8.958e+01 4.133e+02 0.217 0.8284
## CityMiami 1.387e+02 3.697e+02 0.375 0.7076
## CityMiddletown 3.380e+02 3.895e+02 0.868 0.3855
## CityMidland 1.709e+02 3.855e+02 0.443 0.6576
## CityMilford 1.283e+02 4.067e+02 0.316 0.7523
## CityMilwaukee 3.212e+02 3.997e+02 0.804 0.4216
## CityMinneapolis 5.196e+02 3.676e+02 1.413 0.1576
## CityMiramar -1.745e+01 4.075e+02 -0.043 0.9658
## CityMishawaka 2.112e+02 5.254e+02 0.402 0.6877
## `CityMission Viejo` 1.127e+02 4.096e+02 0.275 0.7831
## CityMissoula 6.365e+02 5.660e+02 1.125 0.2607
## `CityMissouri City` -9.021e+01 5.302e+02 -0.170 0.8649
## CityMobile 4.717e+01 3.687e+02 0.128 0.8982
## CityModesto 4.267e+01 4.419e+02 0.097 0.9231
## CityMonroe 4.493e+02 3.690e+02 1.218 0.2234
## CityMontebello 2.514e+02 5.271e+02 0.477 0.6334
## CityMontgomery 1.402e+02 3.686e+02 0.380 0.7037
## CityMoorhead 1.742e+02 4.566e+02 0.382 0.7028
## `CityMoreno Valley` 2.711e+02 3.689e+02 0.735 0.4625
## `CityMorgan Hill` -1.421e+00 4.420e+02 -0.003 0.9974
## CityMorristown -1.739e+01 3.906e+02 -0.045 0.9645
## `CityMount Pleasant` 1.451e+02 5.434e+02 0.267 0.7895
## `CityMount Vernon` 2.739e+02 3.835e+02 0.714 0.4750
## CityMurfreesboro 1.245e+02 3.705e+02 0.336 0.7369
## CityMurray 2.594e+02 4.582e+02 0.566 0.5714
## CityMurrieta NA NA NA NA
## CityMuskogee 2.891e+02 4.877e+02 0.593 0.5534
## CityNaperville 8.991e+01 3.547e+02 0.253 0.7999
## CityNashua 2.372e+02 5.451e+02 0.435 0.6635
## CityNashville 2.603e+02 3.521e+02 0.739 0.4597
## `CityNew Albany` 1.561e+02 4.394e+02 0.355 0.7224
## `CityNew Bedford` 1.440e+02 4.467e+02 0.322 0.7471
## `CityNew Brunswick` 5.546e+01 5.427e+02 0.102 0.9186
## `CityNew Castle` -3.804e+01 4.394e+02 -0.087 0.9310
## `CityNew Rochelle` 1.282e+02 3.671e+02 0.349 0.7269
## `CityNew York City` 2.587e+02 3.379e+02 0.766 0.4440
## CityNewark 1.975e+02 3.390e+02 0.583 0.5602
## `CityNewport News` 1.923e+02 3.629e+02 0.530 0.5961
## `CityNiagara Falls` 1.343e+02 4.438e+02 0.303 0.7623
## CityNoblesville 2.069e+02 5.256e+02 0.394 0.6938
## CityNorfolk NA NA NA NA
## CityNormal 1.971e+02 5.140e+02 0.383 0.7014
## CityNorman NA NA NA NA
## `CityNorth Charleston` 3.371e+02 5.371e+02 0.628 0.5302
## `CityNorth Las Vegas` 4.122e+02 4.284e+02 0.962 0.3361
## `CityNorth Miami` -8.090e+00 5.468e+02 -0.015 0.9882
## CityNorwich 3.088e+02 4.236e+02 0.729 0.4660
## `CityOak Park` 1.928e+02 4.092e+02 0.471 0.6375
## CityOakland 2.254e+02 3.474e+02 0.649 0.5165
## CityOceanside 1.672e+02 3.455e+02 0.484 0.6285
## CityOdessa 1.211e+02 4.143e+02 0.292 0.7700
## `CityOklahoma City` 4.500e+02 4.066e+02 1.107 0.2684
## CityOlathe 4.639e+02 4.432e+02 1.047 0.2954
## CityOlympia 1.936e+02 4.196e+02 0.461 0.6446
## CityOmaha 3.840e+02 4.038e+02 0.951 0.3417
## CityOntario NA NA NA NA
## CityOrange -7.829e+01 4.126e+02 -0.190 0.8495
## CityOrem 4.805e+02 4.225e+02 1.137 0.2555
## `CityOrland Park` 2.164e+02 5.138e+02 0.421 0.6736
## CityOrlando -7.708e+01 4.004e+02 -0.193 0.8474
## `CityOrmond Beach` NA NA NA NA
## CityOswego 5.322e+02 4.255e+02 1.251 0.2111
## `CityOverland Park` 3.820e+02 4.428e+02 0.863 0.3884
## CityOwensboro 2.615e+02 4.398e+02 0.594 0.5522
## CityOxnard 3.683e+02 3.687e+02 0.999 0.3178
## CityPalatine -2.387e+01 5.138e+02 -0.046 0.9630
## `CityPalm Coast` 3.114e+01 4.335e+02 0.072 0.9427
## `CityPark Ridge` 4.234e+02 4.255e+02 0.995 0.3197
## CityParker 5.155e+01 3.638e+02 0.142 0.8873
## CityParma 3.397e+02 3.712e+02 0.915 0.3601
## CityPasadena 2.134e+02 3.428e+02 0.622 0.5337
## CityPasco 3.768e+02 4.098e+02 0.920 0.3578
## CityPassaic -1.800e+02 4.025e+02 -0.447 0.6548
## CityPaterson -1.700e+02 3.765e+02 -0.452 0.6516
## CityPearland 1.345e+02 4.138e+02 0.325 0.7453
## `CityPembroke Pines` -4.426e+00 3.891e+02 -0.011 0.9909
## CityPensacola -2.965e+01 5.464e+02 -0.054 0.9567
## CityPeoria 2.554e+01 2.380e+02 0.107 0.9145
## `CityPerth Amboy` -3.741e-01 4.600e+02 -0.001 0.9994
## CityPharr 1.341e+02 5.308e+02 0.253 0.8005
## CityPhiladelphia 2.551e+02 3.699e+02 0.690 0.4904
## CityPhoenix 1.265e+02 2.130e+02 0.594 0.5524
## `CityPico Rivera` 2.175e+02 5.274e+02 0.412 0.6801
## `CityPine Bluff` -2.863e+01 5.619e+02 -0.051 0.9594
## CityPlainfield 1.210e+02 3.839e+02 0.315 0.7527
## CityPlano 1.919e+02 3.646e+02 0.526 0.5988
## CityPlantation 2.787e+01 3.955e+02 0.070 0.9438
## `CityPleasant Grove` 3.160e+02 4.337e+02 0.728 0.4664
## CityPocatello 3.616e+02 7.202e+02 0.502 0.6156
## CityPomona 2.546e+02 3.921e+02 0.649 0.5161
## `CityPompano Beach` -5.998e+00 4.335e+02 -0.014 0.9890
## `CityPort Arthur` -1.042e+01 3.972e+02 -0.026 0.9791
## `CityPort Orange` 7.375e+01 5.469e+02 0.135 0.8927
## `CityPort Saint Lucie` -3.538e+02 5.465e+02 -0.647 0.5174
## CityPortage 2.775e+02 5.254e+02 0.528 0.5974
## CityPortland 1.941e+02 3.509e+02 0.553 0.5803
## CityProvidence 3.859e+02 4.026e+02 0.959 0.3378
## CityProvo 4.527e+02 4.224e+02 1.072 0.2839
## CityPueblo 1.898e+02 3.638e+02 0.522 0.6019
## CityQuincy 4.928e+01 3.369e+02 0.146 0.8837
## CityRaleigh 1.608e+02 3.676e+02 0.438 0.6618
## `CityRancho Cucamonga` 2.377e+02 3.923e+02 0.606 0.5447
## `CityRapid City` NA NA NA NA
## CityReading 1.835e+02 4.218e+02 0.435 0.6635
## CityRedding 2.673e+02 5.274e+02 0.507 0.6123
## CityRedlands 2.935e+02 3.571e+02 0.822 0.4112
## CityRedmond 1.493e+02 3.631e+02 0.411 0.6809
## `CityRedondo Beach` 2.153e+02 3.742e+02 0.575 0.5650
## `CityRedwood City` 1.136e+02 5.271e+02 0.215 0.8294
## CityReno NA NA NA NA
## CityRenton NA NA NA NA
## CityRevere 9.943e+01 4.147e+02 0.240 0.8105
## CityRichardson 6.911e+02 5.311e+02 1.301 0.1932
## CityRichmond 1.786e+02 3.321e+02 0.538 0.5907
## `CityRio Rancho` 3.601e+02 4.876e+02 0.738 0.4602
## CityRiverside 2.868e+02 3.689e+02 0.777 0.4369
## CityRochester 2.519e+02 3.439e+02 0.732 0.4639
## `CityRochester Hills` 1.122e+01 5.437e+02 0.021 0.9835
## `CityRock Hill` 2.363e+02 5.370e+02 0.440 0.6599
## CityRockford 3.506e+02 3.414e+02 1.027 0.3045
## CityRockville 6.564e+01 4.302e+02 0.153 0.8787
## CityRogers -1.888e+02 5.621e+02 -0.336 0.7370
## CityRome 1.672e+02 3.838e+02 0.436 0.6631
## CityRomeoville 6.372e+01 5.136e+02 0.124 0.9013
## CityRoseville 1.394e+02 3.489e+02 0.400 0.6895
## CityRoswell 3.126e+02 3.542e+02 0.883 0.3775
## `CityRound Rock` -2.804e+00 4.143e+02 -0.007 0.9946
## `CityRoyal Oak` 1.625e+02 4.614e+02 0.352 0.7247
## CitySacramento 1.955e+02 3.688e+02 0.530 0.5960
## CitySaginaw -1.999e+01 3.973e+02 -0.050 0.9599
## `CitySaint Charles` 9.950e+01 3.529e+02 0.282 0.7780
## `CitySaint Cloud` 3.717e+02 5.395e+02 0.689 0.4908
## `CitySaint Louis` 2.932e+01 4.104e+02 0.071 0.9430
## `CitySaint Paul` 1.064e+02 5.399e+02 0.197 0.8438
## `CitySaint Peters` NA NA NA NA
## `CitySaint Petersburg` 1.035e+02 3.845e+02 0.269 0.7878
## CitySalem 1.693e+02 3.423e+02 0.495 0.6208
## CitySalinas 1.908e+02 3.923e+02 0.486 0.6268
## `CitySalt Lake City` 3.472e+02 4.273e+02 0.812 0.4166
## `CitySan Angelo` -3.135e+01 4.141e+02 -0.076 0.9397
## `CitySan Antonio` 5.945e+02 3.461e+02 1.718 0.0859 .
## `CitySan Bernardino` 2.414e+02 3.691e+02 0.654 0.5131
## `CitySan Clemente` 2.080e+02 5.275e+02 0.394 0.6934
## `CitySan Diego` 2.776e+02 3.376e+02 0.822 0.4109
## `CitySan Francisco` 2.628e+02 3.359e+02 0.782 0.4340
## `CitySan Gabriel` 6.418e+02 4.421e+02 1.452 0.1467
## `CitySan Jose` 1.641e+02 3.430e+02 0.478 0.6325
## `CitySan Luis Obispo` 2.377e+02 5.275e+02 0.451 0.6524
## `CitySan Marcos` 1.213e+02 4.463e+02 0.272 0.7858
## `CitySan Mateo` 1.796e+02 5.279e+02 0.340 0.7336
## `CitySandy Springs` 1.642e+02 3.621e+02 0.453 0.6502
## CitySanford -1.843e+01 5.461e+02 -0.034 0.9731
## `CitySanta Ana` -8.262e+01 3.812e+02 -0.217 0.8284
## `CitySanta Barbara` 2.675e+02 3.923e+02 0.682 0.4954
## `CitySanta Clara` 2.271e+02 3.922e+02 0.579 0.5626
## `CitySanta Fe` 2.132e+02 4.874e+02 0.437 0.6618
## `CitySanta Maria` 1.523e+02 5.277e+02 0.289 0.7728
## CityScottsdale 1.474e+01 2.499e+02 0.059 0.9530
## CitySeattle 2.714e+02 3.675e+02 0.739 0.4601
## CitySheboygan 3.693e+02 4.435e+02 0.833 0.4051
## CityShelton 2.004e+02 5.385e+02 0.372 0.7097
## `CitySierra Vista` 5.484e+01 3.531e+02 0.155 0.8766
## `CitySioux Falls` 3.449e+02 4.187e+02 0.824 0.4102
## CitySkokie 1.740e+02 3.734e+02 0.466 0.6413
## CitySmyrna 1.425e+02 3.464e+02 0.411 0.6809
## `CitySouth Bend` 6.766e+01 3.898e+02 0.174 0.8622
## CitySouthaven 1.068e+02 4.226e+02 0.253 0.8005
## CitySparks 3.103e+02 4.756e+02 0.652 0.5141
## CitySpokane 1.017e+02 4.193e+02 0.243 0.8083
## CitySpringdale 1.470e+02 5.618e+02 0.262 0.7936
## CitySpringfield 2.477e+02 3.323e+02 0.745 0.4561
## `CitySterling Heights` 9.008e+01 4.615e+02 0.195 0.8453
## CityStockton 1.704e+02 3.921e+02 0.434 0.6640
## CitySuffolk 2.587e+02 3.795e+02 0.682 0.4954
## CitySummerville 1.081e+02 4.535e+02 0.238 0.8115
## CitySunnyvale 1.696e+02 3.815e+02 0.445 0.6566
## CitySuperior 3.637e+02 4.273e+02 0.851 0.3948
## CityTallahassee 2.841e+02 3.815e+02 0.745 0.4565
## CityTamarac 4.132e+02 4.174e+02 0.990 0.3223
## CityTampa 1.007e+02 3.741e+02 0.269 0.7878
## CityTaylor 3.734e+01 4.615e+02 0.081 0.9355
## CityTemecula 3.222e+02 4.098e+02 0.786 0.4318
## CityTempe 8.192e+00 2.558e+02 0.032 0.9745
## CityTexarkana -8.434e+01 4.824e+02 -0.175 0.8612
## `CityTexas City` -5.758e+01 4.145e+02 -0.139 0.8895
## `CityThe Colony` NA NA NA NA
## CityThomasville 1.177e+02 5.387e+02 0.218 0.8271
## CityThornton 3.976e+01 3.696e+02 0.108 0.9143
## `CityThousand Oaks` 1.916e+02 3.814e+02 0.502 0.6155
## CityTigard 3.757e+02 3.716e+02 1.011 0.3121
## `CityTinley Park` -8.752e+01 5.134e+02 -0.170 0.8647
## CityToledo 2.406e+02 3.421e+02 0.703 0.4818
## CityTorrance 3.869e+02 4.093e+02 0.945 0.3445
## CityTrenton -8.741e+01 3.808e+02 -0.230 0.8184
## CityTroy 2.770e+02 3.436e+02 0.806 0.4202
## CityTucson 2.191e+01 2.192e+02 0.100 0.9204
## CityTulsa 3.369e+02 4.038e+02 0.834 0.4042
## CityTuscaloosa NA NA NA NA
## `CityTwin Falls` 4.532e+02 7.539e+02 0.601 0.5478
## CityTyler 3.595e+02 4.138e+02 0.869 0.3850
## CityUrbandale 3.576e+02 4.334e+02 0.825 0.4094
## CityUtica 1.866e+02 3.669e+02 0.509 0.6111
## CityVacaville NA NA NA NA
## CityVallejo 2.197e+02 4.097e+02 0.536 0.5919
## CityVancouver 2.702e+02 4.356e+02 0.620 0.5351
## CityVineland -1.367e+02 4.025e+02 -0.340 0.7342
## `CityVirginia Beach` 2.261e+02 3.549e+02 0.637 0.5241
## CityVisalia 1.183e+02 4.095e+02 0.289 0.7727
## CityWaco 2.372e+02 3.791e+02 0.626 0.5316
## `CityWarner Robins` 1.017e+02 4.423e+02 0.230 0.8183
## CityWarwick 3.544e+02 4.874e+02 0.727 0.4673
## CityWashington 2.324e+02 4.227e+02 0.550 0.5825
## CityWaterbury 2.363e+02 3.776e+02 0.626 0.5315
## CityWaterloo 3.891e+02 5.462e+02 0.712 0.4763
## CityWatertown 3.182e+02 3.711e+02 0.858 0.3911
## CityWaukesha 1.484e+02 5.664e+02 0.262 0.7933
## CityWausau 2.865e+02 4.432e+02 0.646 0.5181
## CityWaynesboro 3.256e+02 3.669e+02 0.887 0.3749
## `CityWest Allis` 7.056e+01 5.664e+02 0.125 0.9009
## `CityWest Jordan` 3.284e+02 4.431e+02 0.741 0.4586
## `CityWest Palm Beach` 1.314e+01 4.337e+02 0.030 0.9758
## CityWestfield -5.691e+01 4.127e+02 -0.138 0.8903
## CityWestland 9.996e+01 3.856e+02 0.259 0.7954
## CityWestminster 3.214e+02 3.572e+02 0.900 0.3682
## CityWheeling 1.680e+02 4.255e+02 0.395 0.6930
## CityWhittier NA NA NA NA
## CityWichita 3.299e+02 4.336e+02 0.761 0.4468
## CityWilmington 1.336e+02 3.495e+02 0.382 0.7023
## CityWilson 1.310e+02 4.241e+02 0.309 0.7573
## CityWoodbury 2.843e+02 4.567e+02 0.623 0.5336
## CityWoodland 2.914e+02 4.419e+02 0.660 0.5096
## CityWoodstock 1.530e+02 3.786e+02 0.404 0.6861
## CityWoonsocket 4.065e+02 4.875e+02 0.834 0.4043
## CityYonkers 3.001e+02 3.592e+02 0.835 0.4035
## CityYork 1.767e+02 4.115e+02 0.429 0.6676
## CityYucaipa NA NA NA NA
## CityYuma NA NA NA NA
## StateAlabama 2.247e+02 2.553e+02 0.880 0.3789
## StateArizona 2.870e+02 3.365e+02 0.853 0.3937
## StateArkansas 3.142e+02 3.063e+02 1.026 0.3051
## StateCalifornia 1.224e+02 2.395e+02 0.511 0.6092
## StateColorado 2.603e+02 2.490e+02 1.046 0.2958
## StateConnecticut 1.447e+02 2.559e+02 0.566 0.5717
## StateDelaware 1.884e+02 2.475e+02 0.761 0.4466
## `StateDistrict of Columbia` NA NA NA NA
## StateFlorida 2.634e+02 2.770e+02 0.951 0.3418
## StateGeorgia 1.640e+02 2.359e+02 0.695 0.4869
## StateIdaho -6.915e+00 5.752e+02 -0.012 0.9904
## StateIllinois 1.936e+02 2.386e+02 0.811 0.4172
## StateIndiana 1.986e+02 2.314e+02 0.858 0.3908
## StateIowa -1.342e+01 2.746e+02 -0.049 0.9610
## StateKansas NA NA NA NA
## StateKentucky 1.283e+02 2.406e+02 0.533 0.5938
## StateLouisiana -1.633e+02 2.716e+02 -0.601 0.5477
## StateMaine NA NA NA NA
## StateMaryland 1.979e+02 2.626e+02 0.754 0.4512
## StateMassachusetts 2.035e+02 2.095e+02 0.971 0.3314
## StateMichigan 2.912e+02 2.648e+02 1.100 0.2715
## StateMinnesota 8.582e+01 2.663e+02 0.322 0.7472
## StateMississippi 1.917e+02 2.768e+02 0.693 0.4886
## StateMissouri 2.125e+02 2.396e+02 0.887 0.3751
## StateMontana NA NA NA NA
## StateNebraska NA NA NA NA
## StateNevada 2.730e+02 3.434e+02 0.795 0.4266
## `StateNew Hampshire` 1.089e+02 2.749e+02 0.396 0.6919
## `StateNew Jersey` 4.498e+02 2.700e+02 1.666 0.0957 .
## `StateNew Mexico` NA NA NA NA
## `StateNew York` 1.285e+02 2.450e+02 0.525 0.5999
## `StateNorth Carolina` 1.604e+02 2.623e+02 0.612 0.5408
## `StateNorth Dakota` NA NA NA NA
## StateOhio 1.201e+02 2.319e+02 0.518 0.6045
## StateOklahoma NA NA NA NA
## StateOregon 7.871e+01 2.426e+02 0.324 0.7456
## StatePennsylvania 1.671e+02 2.838e+02 0.589 0.5560
## `StateRhode Island` NA NA NA NA
## `StateSouth Carolina` 1.021e+02 2.510e+02 0.407 0.6840
## `StateSouth Dakota` NA NA NA NA
## StateTennessee 2.128e+02 2.258e+02 0.942 0.3460
## StateTexas 1.493e+02 2.495e+02 0.598 0.5497
## StateUtah NA NA NA NA
## StateVermont -3.329e+02 3.207e+02 -1.038 0.2993
## StateVirginia 1.875e+02 2.357e+02 0.795 0.4266
## StateWashington 1.139e+02 2.759e+02 0.413 0.6797
## `StateWest Virginia` 2.703e+02 4.410e+02 0.613 0.5400
## StateWisconsin NA NA NA NA
## StateWyoming NA NA NA NA
## RegionCentral NA NA NA NA
## RegionEast NA NA NA NA
## RegionSouth NA NA NA NA
## RegionWest NA NA NA NA
## Category.Furniture -5.294e+02 4.343e+01 -12.189 < 2e-16 ***
## `Category.Office Supplies` -1.012e+03 4.355e+01 -23.232 < 2e-16 ***
## Category.Technology NA NA NA NA
## Sub.CategoryAccessories -1.106e+03 5.017e+01 -22.046 < 2e-16 ***
## Sub.CategoryAppliances -6.761e+01 2.973e+01 -2.274 0.0230 *
## Sub.CategoryArt -2.044e+02 2.489e+01 -8.212 2.60e-16 ***
## Sub.CategoryBinders -1.773e+02 2.593e+01 -6.837 8.80e-12 ***
## Sub.CategoryChairs -2.395e+02 4.009e+01 -5.975 2.43e-09 ***
## Sub.CategoryFurnishings -6.457e+02 3.835e+01 -16.837 < 2e-16 ***
## Sub.CategoryLabels -2.089e+02 3.163e+01 -6.604 4.33e-11 ***
## Sub.CategoryOther -1.116e+02 2.650e+01 -4.209 2.60e-05 ***
## Sub.CategoryPaper -2.031e+02 2.204e+01 -9.216 < 2e-16 ***
## Sub.CategoryPhones -9.462e+02 4.908e+01 -19.278 < 2e-16 ***
## Sub.CategoryStorage NA NA NA NA
## Quantity 4.442e+01 2.264e+00 19.615 < 2e-16 ***
## Discount 2.182e+02 4.991e+01 4.373 1.24e-05 ***
## Profit 1.514e+00 2.303e-02 65.737 < 2e-16 ***
## Days_Between -9.531e-01 5.362e+00 -0.178 0.8589
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 406.5 on 6438 degrees of freedom
## Multiple R-squared: 0.5793, Adjusted R-squared: 0.543
## F-statistic: 15.94 on 556 and 6438 DF, p-value: < 2.2e-16# Making predictions on the test set
predictions <- predict(lm_model, newdata = test_data)## Warning in predict.lm(lm_model, newdata = test_data): prediction from
## rank-deficient fit; attr(*, "non-estim") has doubtful cases# Calculating the performance metrics (e.g., RMSE)
rmse <- sqrt(mean((predictions - test_data$Sales)^2))
# Printing the RMSE
print(paste("Root Mean Squared Error (RMSE):", rmse))## [1] "Root Mean Squared Error (RMSE): 652.608684865285"Checking the predictions of the model
head(predictions, 5)## 2 4 5 8 11
## 816.0427 144.5988 169.4996 545.6848 976.0285# Set a random seed for reproducibility
set.seed(123)
# Splitting the data into training and test sets (e.g., 70% for training and 30% for testing)
split <- sample.split(final_data$Sales, SplitRatio = 0.85)
train_data <- final_data[split, ]
test_data <- final_data[!split, ]
# Creating a linear regression model
lm_model2 <- lm(Sales ~ ., data = train_data)
# Printing the summary of the linear regression model
summary(lm_model2)##
## Call:
## lm(formula = Sales ~ ., data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1600.2 -140.7 -24.3 70.1 22745.9
##
## Coefficients: (33 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.160e+03 4.430e+02 2.619 0.00883 **
## `Ship.ModeFirst Class` 7.661e+00 2.362e+01 0.324 0.74565
## `Ship.ModeSame Day` -1.001e+01 4.000e+01 -0.250 0.80232
## `Ship.ModeSecond Class` 1.376e+01 1.862e+01 0.739 0.45989
## `Ship.ModeStandard Class` NA NA NA NA
## Segment.Consumer -8.083e+00 1.609e+01 -0.502 0.61551
## Segment.Corporate -2.062e+01 1.759e+01 -1.172 0.24111
## `Segment.Home Office` NA NA NA NA
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## CityAlexandria 4.555e+02 4.088e+02 1.114 0.26521
## CityAllen 2.749e+02 4.893e+02 0.562 0.57424
## CityAllentown 8.180e+02 4.733e+02 1.728 0.08397 .
## CityAltoona 6.308e+02 5.598e+02 1.127 0.25988
## CityAmarillo 6.654e+02 4.322e+02 1.540 0.12370
## CityAnaheim 5.603e+02 4.044e+02 1.385 0.16597
## CityAndover 1.087e+02 4.679e+02 0.232 0.81633
## `CityAnn Arbor` 1.505e+02 4.679e+02 0.322 0.74776
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## `CityArlington Heights` 1.166e+02 6.210e+02 0.188 0.85105
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## `CityAtlantic City` 2.893e+00 6.514e+02 0.004 0.99646
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## CityBellingham 9.044e+02 5.141e+02 1.759 0.07859 .
## CityBethlehem 1.009e+03 4.880e+02 2.067 0.03878 *
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## CityBillings NA NA NA NA
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## CityConway NA NA NA NA
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## CityJamestown 1.739e+03 5.295e+02 3.285 0.00103 **
## `CityJefferson City` 3.629e+02 6.359e+02 0.571 0.56827
## `CityJohnson City` 2.243e+02 4.263e+02 0.526 0.59879
## CityJonesboro -1.304e+01 4.796e+02 -0.027 0.97831
## CityJupiter NA NA NA NA
## CityKeller 4.625e+02 6.382e+02 0.725 0.46869
## CityKenner 6.766e+02 6.526e+02 1.037 0.29991
## CityKenosha 2.898e+02 4.736e+02 0.612 0.54052
## CityKent 3.250e+02 4.250e+02 0.765 0.44446
## CityKirkwood 4.181e+02 6.360e+02 0.657 0.51101
## CityKissimmee 1.818e+02 6.549e+02 0.278 0.78134
## CityKnoxville 3.992e+02 4.113e+02 0.971 0.33180
## `CityLa Crosse` 1.376e+02 5.055e+02 0.272 0.78542
## `CityLa Mesa` 4.761e+02 5.271e+02 0.903 0.36650
## `CityLa Porte` 1.989e+02 4.188e+02 0.475 0.63483
## `CityLa Quinta` 3.875e+02 6.351e+02 0.610 0.54182
## CityLafayette 6.824e+02 4.088e+02 1.670 0.09505 .
## `CityLaguna Niguel` 2.139e+02 4.855e+02 0.440 0.65960
## `CityLake Charles` 3.522e+02 5.483e+02 0.642 0.52070
## `CityLake Elsinore` 1.878e+02 6.352e+02 0.296 0.76748
## `CityLake Forest` 5.804e+02 4.502e+02 1.289 0.19738
## CityLakeland -2.136e+02 4.408e+02 -0.485 0.62792
## CityLakeville 3.415e+02 4.376e+02 0.780 0.43523
## CityLakewood 2.800e+02 4.016e+02 0.697 0.48573
## CityLancaster 6.864e+02 3.956e+02 1.735 0.08273 .
## CityLansing 1.805e+02 4.522e+02 0.399 0.68973
## CityLaredo 4.186e+02 4.283e+02 0.977 0.32844
## `CityLas Cruces` 2.709e+02 5.261e+02 0.515 0.60660
## `CityLas Vegas` 9.617e+01 5.102e+02 0.188 0.85050
## CityLaurel 2.221e+02 6.503e+02 0.341 0.73275
## CityLawrence 1.264e+02 3.963e+02 0.319 0.74981
## CityLawton 1.718e+02 5.647e+02 0.304 0.76096
## CityLayton NA NA NA NA
## `CityLeague City` 3.274e+02 4.446e+02 0.736 0.46154
## CityLebanon 2.045e+02 6.388e+02 0.320 0.74887
## CityLehi -1.864e+02 5.643e+02 -0.330 0.74112
## CityLeominster 1.938e+02 4.445e+02 0.436 0.66285
## CityLewiston 2.746e+02 6.667e+02 0.412 0.68048
## `CityLincoln Park` 7.423e+01 5.026e+02 0.148 0.88259
## CityLinden -2.233e+02 6.511e+02 -0.343 0.73166
## CityLindenhurst 5.714e+02 6.369e+02 0.897 0.36964
## `CityLittle Rock` 7.674e+01 4.633e+02 0.166 0.86844
## CityLittleton -1.450e+02 6.311e+02 -0.230 0.81828
## CityLodi 2.823e+02 6.355e+02 0.444 0.65691
## CityLogan 1.213e+02 4.933e+02 0.246 0.80573
## `CityLong Beach` 4.165e+02 3.951e+02 1.054 0.29187
## CityLongmont 3.021e+02 4.806e+02 0.629 0.52962
## CityLongview 2.838e+02 5.532e+02 0.513 0.60799
## CityLorain 4.745e+02 4.297e+02 1.104 0.26948
## `CityLos Angeles` 4.737e+02 3.907e+02 1.212 0.22540
## CityLouisville 3.049e+02 3.874e+02 0.787 0.43127
## CityLoveland 2.165e+02 4.581e+02 0.473 0.63651
## CityLowell 2.613e+02 4.167e+02 0.627 0.53057
## CityLubbock 3.371e+02 4.671e+02 0.722 0.47049
## CityMacon 2.252e+02 4.405e+02 0.511 0.60925
## CityMadison 4.916e+02 4.701e+02 1.046 0.29568
## CityMalden 9.332e+01 4.894e+02 0.191 0.84879
## CityManchester 3.493e+02 4.398e+02 0.794 0.42710
## CityManhattan 2.892e+02 6.664e+02 0.434 0.66432
## CityMansfield 2.529e+02 5.302e+02 0.477 0.63341
## CityManteca 3.928e+02 5.271e+02 0.745 0.45609
## `CityMaple Grove` 5.178e+02 4.829e+02 1.072 0.28359
## CityMargate -2.131e+02 6.548e+02 -0.325 0.74486
## CityMarietta 2.872e+02 4.403e+02 0.652 0.51433
## CityMarion 4.261e+02 4.072e+02 1.046 0.29537
## CityMarlborough 1.919e+02 6.375e+02 0.301 0.76336
## CityMarysville -4.978e+01 6.573e+02 -0.076 0.93964
## CityMason 3.405e+02 4.823e+02 0.706 0.48021
## CityMcallen 3.441e+02 4.107e+02 0.838 0.40204
## CityMedford 4.451e+02 4.672e+02 0.953 0.34072
## CityMedina 2.784e+02 4.245e+02 0.656 0.51200
## CityMelbourne -2.902e+02 6.548e+02 -0.443 0.65761
## CityMemphis 3.687e+02 4.077e+02 0.904 0.36582
## CityMentor 3.285e+02 4.369e+02 0.752 0.45212
## CityMeriden 4.319e+02 4.375e+02 0.987 0.32362
## CityMeridian 2.142e+02 8.825e+02 0.243 0.80824
## CityMesa 8.584e+01 2.712e+02 0.316 0.75165
## CityMesquite 3.490e+02 4.529e+02 0.771 0.44097
## CityMiami -2.099e+02 4.272e+02 -0.491 0.62324
## CityMiddletown 4.623e+02 4.470e+02 1.034 0.30107
## CityMidland 3.464e+02 4.382e+02 0.791 0.42923
## CityMilford 3.027e+02 4.675e+02 0.647 0.51733
## CityMilwaukee 2.068e+02 4.469e+02 0.463 0.64360
## CityMinneapolis 7.164e+02 4.262e+02 1.681 0.09285 .
## CityMiramar -3.649e+02 4.774e+02 -0.764 0.44463
## CityMishawaka 2.137e+02 5.242e+02 0.408 0.68352
## `CityMission Viejo` 4.004e+02 4.639e+02 0.863 0.38810
## CityMissoula 5.582e+02 6.662e+02 0.838 0.40209
## `CityMissouri City` 1.049e+02 6.369e+02 0.165 0.86913
## CityMobile 1.495e+02 4.233e+02 0.353 0.72385
## CityModesto 2.642e+02 5.271e+02 0.501 0.61621
## CityMonroe 4.584e+02 4.245e+02 1.080 0.28021
## CityMontebello 4.886e+02 6.349e+02 0.770 0.44161
## CityMontgomery 2.491e+02 4.230e+02 0.589 0.55595
## CityMoorhead 3.397e+02 5.436e+02 0.625 0.53207
## `CityMoreno Valley` 4.998e+02 4.287e+02 1.166 0.24371
## `CityMorgan Hill` 2.437e+02 4.639e+02 0.525 0.59941
## CityMorristown 6.870e+01 4.574e+02 0.150 0.88060
## `CityMount Pleasant` 2.579e+02 5.313e+02 0.485 0.62745
## `CityMount Vernon` 4.229e+02 4.314e+02 0.980 0.32697
## CityMurfreesboro 2.117e+02 4.232e+02 0.500 0.61691
## CityMurray 1.140e+02 5.260e+02 0.217 0.82844
## CityMurrieta NA NA NA NA
## CityMuskogee 1.600e+02 5.646e+02 0.283 0.77694
## CityNaperville 1.589e+02 4.125e+02 0.385 0.70001
## CityNashua 4.877e+02 5.488e+02 0.889 0.37424
## CityNashville 3.487e+02 4.072e+02 0.856 0.39182
## `CityNew Albany` 1.343e+02 4.826e+02 0.278 0.78078
## `CityNew Bedford` 1.049e+02 4.537e+02 0.231 0.81715
## `CityNew Brunswick` 1.203e+02 6.516e+02 0.185 0.85358
## `CityNew Castle` -8.239e+00 5.241e+02 -0.016 0.98746
## `CityNew Rochelle` 2.582e+02 4.276e+02 0.604 0.54587
## `CityNew York City` 4.270e+02 3.938e+02 1.084 0.27832
## CityNewark 4.398e+02 3.945e+02 1.115 0.26494
## `CityNewport News` 2.057e+02 4.189e+02 0.491 0.62333
## `CityNiagara Falls` 2.987e+02 4.886e+02 0.611 0.54101
## CityNoblesville 7.526e+02 4.825e+02 1.560 0.11886
## CityNorfolk NA NA NA NA
## CityNormal 2.232e+02 6.211e+02 0.359 0.71930
## CityNorman 1.075e+03 6.663e+02 1.613 0.10678
## `CityNorth Charleston` 4.447e+02 6.432e+02 0.691 0.48931
## `CityNorth Las Vegas` 4.781e+02 5.050e+02 0.947 0.34380
## `CityNorth Miami` -2.681e+02 5.507e+02 -0.487 0.62638
## CityNorwich 4.730e+02 5.023e+02 0.942 0.34639
## `CityOak Park` 3.201e+02 4.830e+02 0.663 0.50757
## CityOakland 4.683e+02 4.046e+02 1.158 0.24707
## CityOceanside 3.348e+02 4.025e+02 0.832 0.40552
## CityOdessa 3.187e+02 4.535e+02 0.703 0.48220
## `CityOklahoma City` 3.104e+02 4.536e+02 0.684 0.49375
## CityOlathe 3.329e+02 4.936e+02 0.674 0.50010
## CityOlympia 3.479e+02 4.805e+02 0.724 0.46909
## CityOmaha 2.750e+02 4.506e+02 0.610 0.54169
## CityOntario NA NA NA NA
## CityOrange 8.103e+00 4.638e+02 0.017 0.98606
## CityOrem 3.595e+02 4.738e+02 0.759 0.44807
## `CityOrland Park` 2.806e+02 6.209e+02 0.452 0.65135
## CityOrlando -4.107e+02 4.501e+02 -0.912 0.36165
## `CityOrmond Beach` NA NA NA NA
## CityOswego 5.373e+02 5.098e+02 1.054 0.29189
## `CityOverland Park` 2.346e+02 4.930e+02 0.476 0.63416
## CityOwensboro 3.597e+02 5.244e+02 0.686 0.49281
## CityOxnard 5.582e+02 4.242e+02 1.316 0.18829
## CityPalatine 3.586e+01 6.209e+02 0.058 0.95395
## `CityPalm Coast` -2.981e+02 5.110e+02 -0.583 0.55966
## `CityPark Ridge` 4.318e+02 5.099e+02 0.847 0.39705
## CityParker 1.800e+02 4.275e+02 0.421 0.67381
## CityParma 4.726e+02 4.209e+02 1.123 0.26158
## CityPasadena 4.038e+02 3.971e+02 1.017 0.30925
## CityPasco 4.592e+02 4.720e+02 0.973 0.33060
## CityPassaic -9.670e+01 4.639e+02 -0.208 0.83490
## CityPaterson -6.006e+01 4.338e+02 -0.138 0.88988
## CityPearland 3.296e+02 4.889e+02 0.674 0.50026
## `CityPembroke Pines` -3.067e+02 4.458e+02 -0.688 0.49152
## CityPensacola -3.436e+02 6.548e+02 -0.525 0.59974
## CityPeoria 1.225e+02 2.896e+02 0.423 0.67238
## `CityPerth Amboy` 1.242e+01 4.728e+02 0.026 0.97904
## CityPharr 3.389e+02 4.890e+02 0.693 0.48839
## CityPhiladelphia 7.616e+02 4.341e+02 1.754 0.07941 .
## CityPhoenix 2.171e+02 2.602e+02 0.834 0.40421
## `CityPico Rivera` 4.303e+02 6.353e+02 0.677 0.49823
## `CityPine Bluff` 7.590e+01 5.723e+02 0.133 0.89449
## CityPlainfield 1.580e+02 4.457e+02 0.355 0.72291
## CityPlano 3.827e+02 4.226e+02 0.905 0.36524
## CityPlantation -3.256e+02 4.532e+02 -0.718 0.47255
## `CityPleasant Grove` 3.028e+02 4.850e+02 0.624 0.53233
## CityPocatello 2.258e+02 8.547e+02 0.264 0.79167
## CityPomona 4.865e+02 4.499e+02 1.081 0.27965
## `CityPompano Beach` -3.501e+02 5.111e+02 -0.685 0.49336
## `CityPort Arthur` 1.668e+02 4.538e+02 0.368 0.71321
## `CityPort Orange` -2.151e+02 6.551e+02 -0.328 0.74271
## `CityPort Saint Lucie` -5.578e+02 5.507e+02 -1.013 0.31116
## CityPortage 3.489e+02 6.327e+02 0.551 0.58134
## CityPortland 3.160e+02 4.085e+02 0.773 0.43928
## CityProvidence 2.675e+02 4.503e+02 0.594 0.55252
## CityProvo 3.165e+02 4.737e+02 0.668 0.50409
## CityPueblo 2.151e+02 4.275e+02 0.503 0.61492
## CityQuincy 1.045e+02 3.919e+02 0.267 0.78974
## CityRaleigh 1.903e+02 4.262e+02 0.447 0.65521
## `CityRancho Cucamonga` 4.721e+02 4.638e+02 1.018 0.30877
## `CityRapid City` 2.984e+02 6.665e+02 0.448 0.65438
## CityReading 7.628e+02 4.880e+02 1.563 0.11802
## CityRedding 4.925e+02 6.351e+02 0.775 0.43807
## CityRedlands 5.128e+02 4.127e+02 1.243 0.21399
## CityRedmond 2.625e+02 4.265e+02 0.615 0.53828
## `CityRedondo Beach` 4.412e+02 4.406e+02 1.002 0.31659
## `CityRedwood City` 3.236e+02 6.348e+02 0.510 0.61023
## CityReno 1.918e+02 5.684e+02 0.337 0.73580
## CityRenton 1.112e+02 5.531e+02 0.201 0.84069
## CityRevere 1.099e+02 4.536e+02 0.242 0.80864
## CityRichardson 7.320e+02 5.299e+02 1.381 0.16725
## CityRichmond 2.564e+02 3.867e+02 0.663 0.50724
## `CityRio Rancho` 2.487e+02 5.645e+02 0.441 0.65958
## CityRiverside 5.939e+02 4.184e+02 1.419 0.15581
## CityRochester 4.060e+02 4.006e+02 1.013 0.31087
## `CityRochester Hills` 1.467e+02 6.480e+02 0.226 0.82091
## `CityRock Hill` 3.467e+02 6.432e+02 0.539 0.58994
## CityRockford 3.829e+02 4.026e+02 0.951 0.34160
## CityRockville 1.625e+02 4.715e+02 0.345 0.73037
## CityRogers -2.275e+02 6.733e+02 -0.338 0.73540
## CityRome 3.144e+02 4.530e+02 0.694 0.48766
## CityRomeoville 1.803e+02 6.206e+02 0.291 0.77140
## CityRoseville 3.583e+02 4.033e+02 0.889 0.37424
## CityRoswell 3.957e+02 4.099e+02 0.965 0.33438
## `CityRound Rock` 1.366e+03 4.535e+02 3.012 0.00260 **
## `CityRoyal Oak` 3.042e+02 5.427e+02 0.560 0.57520
## CitySacramento 7.530e+02 4.183e+02 1.800 0.07190 .
## CitySaginaw 9.405e+01 4.593e+02 0.205 0.83778
## `CitySaint Charles` 1.605e+02 4.126e+02 0.389 0.69738
## `CitySaint Cloud` 4.993e+02 5.434e+02 0.919 0.35826
## `CitySaint Louis` 1.072e+02 4.868e+02 0.220 0.82572
## `CitySaint Paul` 2.300e+02 5.436e+02 0.423 0.67222
## `CitySaint Peters` 1.642e+02 6.363e+02 0.258 0.79641
## `CitySaint Petersburg` -2.404e+02 4.421e+02 -0.544 0.58667
## CitySalem 2.975e+02 3.988e+02 0.746 0.45568
## CitySalinas 4.271e+02 4.500e+02 0.949 0.34254
## `CitySalt Lake City` 1.724e+02 4.738e+02 0.364 0.71601
## `CitySan Angelo` 1.816e+02 4.891e+02 0.371 0.71051
## `CitySan Antonio` 6.551e+02 4.002e+02 1.637 0.10162
## `CitySan Bernardino` 4.763e+02 4.287e+02 1.111 0.26659
## `CitySan Clemente` 4.601e+02 6.352e+02 0.724 0.46894
## `CitySan Diego` 4.938e+02 3.925e+02 1.258 0.20841
## `CitySan Francisco` 4.895e+02 3.909e+02 1.252 0.21046
## `CitySan Gabriel` 7.812e+02 4.859e+02 1.608 0.10796
## `CitySan Jose` 4.044e+02 3.997e+02 1.012 0.31167
## `CitySan Luis Obispo` 4.812e+02 6.353e+02 0.757 0.44880
## `CitySan Marcos` 3.295e+02 4.889e+02 0.674 0.50041
## `CitySan Mateo` 4.075e+02 6.357e+02 0.641 0.52153
## `CitySandy Springs` 2.054e+02 4.185e+02 0.491 0.62353
## CitySanford -2.729e+02 5.504e+02 -0.496 0.62000
## `CitySanta Ana` 3.506e+02 4.183e+02 0.838 0.40191
## `CitySanta Barbara` 7.887e+02 4.337e+02 1.818 0.06906 .
## `CitySanta Clara` 4.386e+02 4.500e+02 0.975 0.32975
## `CitySanta Fe` 4.963e+01 5.644e+02 0.088 0.92992
## `CitySanta Maria` 3.857e+02 6.355e+02 0.607 0.54395
## CityScottsdale 9.728e+01 2.901e+02 0.335 0.73733
## CitySeattle 3.787e+02 4.257e+02 0.890 0.37364
## CitySheboygan 2.211e+02 5.064e+02 0.437 0.66245
## CityShelton 4.005e+02 5.425e+02 0.738 0.46045
## `CitySierra Vista` 1.354e+02 3.833e+02 0.353 0.72401
## `CitySioux Falls` 2.107e+02 4.698e+02 0.448 0.65386
## CitySkokie 1.956e+02 4.068e+02 0.481 0.63055
## CitySmyrna 2.388e+02 4.029e+02 0.593 0.55336
## `CitySouth Bend` 1.313e+02 4.606e+02 0.285 0.77561
## CitySouthaven 2.704e+02 4.766e+02 0.567 0.57048
## CitySparks 2.599e+02 5.684e+02 0.457 0.64754
## CitySpokane 1.070e+02 4.802e+02 0.223 0.82371
## CitySpringdale 1.539e+02 6.730e+02 0.229 0.81916
## CitySpringfield 3.413e+02 3.871e+02 0.882 0.37795
## `CitySterling Heights` 2.060e+02 5.428e+02 0.379 0.70436
## CityStockton 3.958e+02 4.636e+02 0.854 0.39324
## CitySuffolk 3.816e+02 4.385e+02 0.870 0.38427
## CitySummerville 2.241e+02 5.367e+02 0.418 0.67631
## CitySunnyvale 4.319e+02 4.405e+02 0.980 0.32688
## CitySuperior 2.392e+02 4.787e+02 0.500 0.61736
## CityTallahassee -1.343e+02 4.396e+02 -0.306 0.75998
## CityTamarac 7.514e+01 4.901e+02 0.153 0.87816
## CityTampa -2.412e+02 4.309e+02 -0.560 0.57565
## CityTaylor 1.930e+02 5.026e+02 0.384 0.70103
## CityTemecula 5.550e+02 4.861e+02 1.142 0.25363
## CityTempe 1.266e+02 2.933e+02 0.432 0.66609
## CityTexarkana -7.687e+01 5.721e+02 -0.134 0.89311
## `CityTexas City` 1.411e+02 4.895e+02 0.288 0.77312
## `CityThe Colony` 2.752e+02 5.307e+02 0.518 0.60414
## CityThomasville 2.012e+02 5.415e+02 0.372 0.71019
## CityThornton 1.454e+02 4.279e+02 0.340 0.73410
## `CityThousand Oaks` 4.215e+02 4.499e+02 0.937 0.34876
## CityTigard 5.012e+02 4.374e+02 1.146 0.25193
## `CityTinley Park` -9.046e+00 6.205e+02 -0.015 0.98837
## CityToledo 3.288e+02 3.974e+02 0.827 0.40801
## CityTorrance 8.018e+02 4.636e+02 1.729 0.08378 .
## CityTrenton 1.525e+01 4.356e+02 0.035 0.97207
## CityTroy 3.650e+02 4.007e+02 0.911 0.36227
## CityTucson 1.341e+02 2.673e+02 0.502 0.61588
## CityTulsa 2.396e+02 4.516e+02 0.530 0.59580
## CityTuscaloosa 2.367e+01 6.367e+02 0.037 0.97035
## `CityTwin Falls` 3.123e+02 9.055e+02 0.345 0.73023
## CityTyler 4.251e+02 4.533e+02 0.938 0.34839
## CityUrbandale 4.148e+02 5.126e+02 0.809 0.41845
## CityUtica 3.446e+02 4.314e+02 0.799 0.42443
## CityVacaville 1.819e+02 6.355e+02 0.286 0.77463
## CityVallejo 6.084e+02 4.638e+02 1.312 0.18966
## CityVancouver 4.134e+02 4.803e+02 0.861 0.38946
## CityVineland -9.540e+01 4.637e+02 -0.206 0.83702
## `CityVirginia Beach` 3.727e+02 4.088e+02 0.912 0.36191
## CityVisalia 3.824e+02 4.639e+02 0.824 0.40981
## CityWaco 4.243e+02 4.441e+02 0.955 0.33940
## `CityWarner Robins` 1.587e+02 5.272e+02 0.301 0.76337
## CityWarwick 2.927e+02 5.260e+02 0.556 0.57796
## CityWashington 1.671e+02 4.673e+02 0.358 0.72062
## CityWaterbury 3.908e+02 4.432e+02 0.882 0.37799
## CityWaterloo 4.514e+02 6.559e+02 0.688 0.49133
## CityWatertown 4.761e+02 4.316e+02 1.103 0.26998
## CityWaukesha -6.911e+00 6.668e+02 -0.010 0.99173
## CityWausau 1.464e+02 5.061e+02 0.289 0.77232
## CityWaynesboro 4.268e+02 4.265e+02 1.001 0.31693
## `CityWest Allis` -4.904e+01 6.666e+02 -0.074 0.94135
## `CityWest Jordan` 2.145e+02 4.933e+02 0.435 0.66371
## `CityWest Palm Beach` -3.271e+02 5.112e+02 -0.640 0.52229
## CityWestfield 9.824e+00 4.729e+02 0.021 0.98342
## CityWestland 2.396e+02 4.342e+02 0.552 0.58109
## CityWestminster 5.813e+02 4.127e+02 1.409 0.15898
## CityWheeling 3.658e+02 4.669e+02 0.783 0.43338
## CityWhittier NA NA NA NA
## CityWichita 2.067e+02 4.847e+02 0.426 0.66983
## CityWilmington 3.075e+02 4.061e+02 0.757 0.44899
## CityWilson 1.769e+02 4.801e+02 0.369 0.71244
## CityWoodbury 5.053e+02 5.038e+02 1.003 0.31586
## CityWoodland 5.017e+02 4.856e+02 1.033 0.30157
## CityWoodstock 2.013e+02 4.492e+02 0.448 0.65401
## CityWoonsocket 2.216e+02 5.259e+02 0.421 0.67348
## CityYonkers 4.766e+02 4.172e+02 1.142 0.25337
## CityYork 7.131e+02 4.877e+02 1.462 0.14373
## CityYucaipa 4.588e+02 6.353e+02 0.722 0.47022
## CityYuma NA NA NA NA
## StateAlabama 5.669e+00 2.593e+02 0.022 0.98256
## StateArizona 3.670e+01 3.608e+02 0.102 0.91898
## StateArkansas 1.732e+02 3.280e+02 0.528 0.59757
## StateCalifornia -2.407e+02 2.427e+02 -0.992 0.32128
## StateColorado 1.517e+01 2.551e+02 0.059 0.95258
## StateConnecticut -1.430e+02 2.673e+02 -0.535 0.59268
## StateDelaware -1.704e+02 2.537e+02 -0.672 0.50177
## `StateDistrict of Columbia` NA NA NA NA
## StateFlorida 4.736e+02 2.888e+02 1.640 0.10113
## StateGeorgia -2.641e+01 2.388e+02 -0.111 0.91192
## StateIdaho 3.315e+01 7.082e+02 0.047 0.96266
## StateIllinois -4.970e+00 2.434e+02 -0.020 0.98371
## StateIndiana 1.520e+01 2.327e+02 0.065 0.94792
## StateIowa -2.108e+02 2.894e+02 -0.728 0.46634
## StateKansas NA NA NA NA
## StateKentucky -8.211e+01 2.444e+02 -0.336 0.73691
## StateLouisiana -3.876e+02 2.836e+02 -1.367 0.17176
## StateMaine NA NA NA NA
## StateMaryland -4.977e+00 2.663e+02 -0.019 0.98509
## StateMassachusetts 4.542e+01 2.120e+02 0.214 0.83039
## StateMichigan 2.762e+01 2.624e+02 0.105 0.91617
## StateMinnesota -2.167e+02 2.771e+02 -0.782 0.43417
## StateMississippi -5.833e+01 2.754e+02 -0.212 0.83225
## StateMissouri -1.080e+01 2.434e+02 -0.044 0.96461
## StateMontana NA NA NA NA
## StateNebraska NA NA NA NA
## StateNevada 7.503e+01 3.863e+02 0.194 0.84603
## `StateNew Hampshire` -3.693e+02 2.857e+02 -1.293 0.19619
## `StateNew Jersey` 2.467e+02 2.813e+02 0.877 0.38054
## `StateNew Mexico` NA NA NA NA
## `StateNew York` -1.605e+02 2.505e+02 -0.641 0.52158
## `StateNorth Carolina` -2.693e+00 2.714e+02 -0.010 0.99209
## `StateNorth Dakota` NA NA NA NA
## StateOhio -1.100e+02 2.342e+02 -0.470 0.63867
## StateOklahoma NA NA NA NA
## StateOregon -1.895e+02 2.488e+02 -0.761 0.44647
## StatePennsylvania -4.921e+02 3.065e+02 -1.606 0.10838
## `StateRhode Island` NA NA NA NA
## `StateSouth Carolina` -1.253e+02 2.515e+02 -0.498 0.61827
## `StateSouth Dakota` NA NA NA NA
## StateTennessee -4.918e+01 2.247e+02 -0.219 0.82677
## StateTexas -1.655e+02 2.527e+02 -0.655 0.51245
## StateUtah NA NA NA NA
## StateVermont -3.550e+02 3.419e+02 -1.038 0.29915
## StateVirginia -4.155e+01 2.390e+02 -0.174 0.86200
## StateWashington -1.231e+02 2.905e+02 -0.424 0.67184
## `StateWest Virginia` -6.242e+01 4.753e+02 -0.131 0.89552
## StateWisconsin NA NA NA NA
## StateWyoming NA NA NA NA
## RegionCentral NA NA NA NA
## RegionEast NA NA NA NA
## RegionSouth NA NA NA NA
## RegionWest NA NA NA NA
## Category.Furniture -8.857e+02 4.804e+01 -18.436 < 2e-16 ***
## `Category.Office Supplies` -1.384e+03 4.829e+01 -28.668 < 2e-16 ***
## Category.Technology NA NA NA NA
## Sub.CategoryAccessories -1.479e+03 5.571e+01 -26.550 < 2e-16 ***
## Sub.CategoryAppliances -5.642e+01 3.298e+01 -1.711 0.08713 .
## Sub.CategoryArt -2.149e+02 2.775e+01 -7.746 1.07e-14 ***
## Sub.CategoryBinders -1.681e+02 2.886e+01 -5.823 6.01e-09 ***
## Sub.CategoryChairs -2.553e+02 4.442e+01 -5.747 9.44e-09 ***
## Sub.CategoryFurnishings -6.652e+02 4.259e+01 -15.621 < 2e-16 ***
## Sub.CategoryLabels -2.205e+02 3.510e+01 -6.283 3.49e-10 ***
## Sub.CategoryOther -1.240e+02 2.950e+01 -4.204 2.65e-05 ***
## Sub.CategoryPaper -2.068e+02 2.444e+01 -8.463 < 2e-16 ***
## Sub.CategoryPhones -1.303e+03 5.446e+01 -23.936 < 2e-16 ***
## Sub.CategoryStorage NA NA NA NA
## Quantity 5.067e+01 2.517e+00 20.128 < 2e-16 ***
## Discount 1.542e+02 5.528e+01 2.790 0.00529 **
## Profit 1.210e+00 2.398e-02 50.463 < 2e-16 ***
## Days_Between 3.285e+00 5.974e+00 0.550 0.58238
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 500.6 on 7917 degrees of freedom
## Multiple R-squared: 0.4514, Adjusted R-squared: 0.4115
## F-statistic: 11.31 on 576 and 7917 DF, p-value: < 2.2e-16# Making predictions on the test set
predictions <- predict(lm_model2, newdata = test_data)## Warning in predict.lm(lm_model2, newdata = test_data): prediction from
## rank-deficient fit; attr(*, "non-estim") has doubtful cases# Calculating the performance metrics (e.g., RMSE)
rmse <- sqrt(mean((predictions - test_data$Sales)^2))
# Printing the RMSE
print(paste("Root Mean Squared Error (RMSE):", rmse))## [1] "Root Mean Squared Error (RMSE): 404.803076422241"AIC-BIC to compare models:
# Compare models using AIC
aic_model1 <- AIC(lm_model)
aic_model2 <- AIC(lm_model2)
# Compare models using BIC
bic_model1 <- BIC(lm_model)
bic_model2 <- BIC(lm_model2)
# Printing the AIC and BIC values
print(paste("AIC for lm_model:", aic_model1))## [1] "AIC for lm_model: 104433.670401841"print(paste("AIC for lm_model2:", aic_model2))## [1] "AIC for lm_model2: 130256.169483449"print(paste("BIC for lm_model:", bic_model1))## [1] "BIC for lm_model: 108257.616996843"print(paste("BIC for lm_model2:", bic_model2))## [1] "BIC for lm_model2: 134329.402133133"AIC_BIC is better for lm_model as it is lower. Therefore, AIC-BIC suggest model 1 is better.
Key Takeaways:
There are no missing values in the columns.
All of them are more peaked than a normal distribution (kurtosis). None of the columns are normally distributed (skewness). Except for days_between, all of them are right skewed.
So we can see a number of outliers in Sales that can mean a certain number of things. The sales were specifically high on these days, could be the discounts given were high or other fa
The plot seems pretty uniform that means quantity is not affecting the discount.
No strong linear correlations can be seen here.
Hypothesis testing suggests there is no significant difference in quantity ordered between different states.
Hypothesis testing also suggests there is no significant interaction effect between “State” and “Category”
Hypothesis testing also suggests sales differ among the subcategories.
Did feature engineering to create new feature days_between. Encoded categorical columns so they can be accepted by the model.
Data split into train and test sets.
Trained 2 different regression models which predicts on the basis of all the factors, what would be the Sale for a partcular superstore.
Finally compared and chose the right model on the basis of AIC-BIC score.