data_dive_week_12

R Markdown

Installing and Importing libraries

library(tidyverse)

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library(ggthemes)
library(ggrepel)
library(readr)
library(stats)
library(dplyr)
library(xts)

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## Loading required package: zoo

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library(tsibble)

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library(ggplot2)
library(forecast)

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Loading Data

data <- read.csv("C:/Users/prase/OneDrive/Documents/STATISTICS/signal_metrics.csv")
head(data)

##   Timestamp       Locality Latitude Longitude SignalStrength DataThroughput
## 1   51:30.7        Danapur 25.42617  85.09443      -76.72446       1.105452
## 2   23:56.4      Bankipore 25.59105  85.25081      -77.52335       2.476287
## 3   24:39.7  Ashok Rajpath 25.48233  85.14868      -78.55790       1.031408
## 4   02:26.4 Rajendra Nagar 25.46116  85.23826      -78.77064       1.461008
## 5   32:12.7  Ashok Rajpath 25.61583  85.10455      -77.27129       1.792531
## 6   58:31.2 Rajendra Nagar 25.56698  85.12149      -75.67285       2.572450
##    Latency NetworkType     BB60C    srsRAN BladeRFxA9
## 1 138.9383         LTE -72.50342 -84.97208  -75.12779
## 2 137.6606         LTE -73.45848 -84.77590  -77.94294
## 3 165.4447         LTE -73.88210 -84.76128  -77.21692
## 4 101.6800         LTE -74.04047 -87.27312  -77.86791
## 5 177.4726         LTE -74.08004 -85.93112  -75.57369
## 6 131.5178         LTE -74.66450 -85.16332  -74.51283

Exploration of Data

str(data)

## 'data.frame':    12621 obs. of  11 variables:
##  $ Timestamp     : chr  "51:30.7" "23:56.4" "24:39.7" "02:26.4" ...
##  $ Locality      : chr  "Danapur" "Bankipore" "Ashok Rajpath" "Rajendra Nagar" ...
##  $ Latitude      : num  25.4 25.6 25.5 25.5 25.6 ...
##  $ Longitude     : num  85.1 85.3 85.1 85.2 85.1 ...
##  $ SignalStrength: num  -76.7 -77.5 -78.6 -78.8 -77.3 ...
##  $ DataThroughput: num  1.11 2.48 1.03 1.46 1.79 ...
##  $ Latency       : num  139 138 165 102 177 ...
##  $ NetworkType   : chr  "LTE" "LTE" "LTE" "LTE" ...
##  $ BB60C         : num  -72.5 -73.5 -73.9 -74 -74.1 ...
##  $ srsRAN        : num  -85 -84.8 -84.8 -87.3 -85.9 ...
##  $ BladeRFxA9    : num  -75.1 -77.9 -77.2 -77.9 -75.6 ...

summary(data)

##   Timestamp           Locality            Latitude       Longitude    
##  Length:12621       Length:12621       Min.   :25.41   Min.   :84.96  
##  Class :character   Class :character   1st Qu.:25.52   1st Qu.:85.07  
##  Mode  :character   Mode  :character   Median :25.59   Median :85.14  
##                                        Mean   :25.59   Mean   :85.14  
##                                        3rd Qu.:25.67   3rd Qu.:85.21  
##                                        Max.   :25.77   Max.   :85.32  
##  SignalStrength    DataThroughput      Latency       NetworkType       
##  Min.   :-116.94   Min.   : 1.001   Min.   : 10.02   Length:12621      
##  1st Qu.: -94.88   1st Qu.: 2.492   1st Qu.: 39.96   Class :character  
##  Median : -91.41   Median : 6.463   Median : 75.21   Mode  :character  
##  Mean   : -91.76   Mean   :20.909   Mean   : 85.28                     
##  3rd Qu.: -88.34   3rd Qu.:31.504   3rd Qu.:125.96                     
##  Max.   : -74.64   Max.   :99.986   Max.   :199.99                     
##      BB60C             srsRAN          BladeRFxA9     
##  Min.   :-115.67   Min.   :-124.65   Min.   :-119.21  
##  1st Qu.: -95.49   1st Qu.:-102.55   1st Qu.: -95.17  
##  Median : -91.60   Median : -98.96   Median : -91.46  
##  Mean   : -91.77   Mean   : -99.26   Mean   : -91.77  
##  3rd Qu.: -87.79   3rd Qu.: -95.67   3rd Qu.: -88.15  
##  Max.   : -72.50   Max.   : -81.32   Max.   : -74.51

Checking for missing values

missing_Timestamp_count <- sum(is.na(data$Timestamp))

missing_SignalStrength_count <- sum(is.na(data$SignalStrength))


cat("Missing values in 'Date' column:", missing_Timestamp_count, "\n")

## Missing values in 'Date' column: 0

cat("Missing values in 'temp_max' column:", missing_SignalStrength_count, "\n")

## Missing values in 'temp_max' column: 0

Checking for duplicates in Timestamp column

data <- data %>% distinct(Timestamp, .keep_all = TRUE)

num_duplicates <- sum(duplicated(data$Timestamp))

cat("Number of duplicates in the 'Timestamp' column:", num_duplicates, "\n")

## Number of duplicates in the 'Timestamp' column: 0

Selecting a column of the data that encodes time

I chose ‘Timestamp’ column from my dataset. And, i chose ‘SignalStrength’ column(response variable) to analyze over time.

# Assuming df is your dataframe
data$Timestamp <- as.POSIXct(paste("2023-01-01", data$Timestamp), format="%Y-%m-%d %M:%S")


head(data)

##             Timestamp       Locality Latitude Longitude SignalStrength
## 1 2023-01-01 00:51:30        Danapur 25.42617  85.09443      -76.72446
## 2 2023-01-01 00:23:56      Bankipore 25.59105  85.25081      -77.52335
## 3 2023-01-01 00:24:39  Ashok Rajpath 25.48233  85.14868      -78.55790
## 4 2023-01-01 00:02:26 Rajendra Nagar 25.46116  85.23826      -78.77064
## 5 2023-01-01 00:32:12  Ashok Rajpath 25.61583  85.10455      -77.27129
## 6 2023-01-01 00:58:31 Rajendra Nagar 25.56698  85.12149      -75.67285
##   DataThroughput  Latency NetworkType     BB60C    srsRAN BladeRFxA9
## 1       1.105452 138.9383         LTE -72.50342 -84.97208  -75.12779
## 2       2.476287 137.6606         LTE -73.45848 -84.77590  -77.94294
## 3       1.031408 165.4447         LTE -73.88210 -84.76128  -77.21692
## 4       1.461008 101.6800         LTE -74.04047 -87.27312  -77.86791
## 5       1.792531 177.4726         LTE -74.08004 -85.93112  -75.57369
## 6       2.572450 131.5178         LTE -74.66450 -85.16332  -74.51283

Creating tsibble object of date and response variable

tsib_data <- tsibble::tibble(
  Timestamp = data$Timestamp,
  SignalStrength = data$SignalStrength
)

ggplot(tsib_data, aes(x = Timestamp, y = SignalStrength)) +
  geom_line() +
  labs(title = "Signal Strength Over Time",
       x = "Timestamp",
       y = "Signal Strength") +
  theme_minimal()

To consider different windows of time, we might want to zoom in on specific time ranges in the plot or perform further analysis on subsets of the data based on specific time periods. Without specific details about the data, it’s challenging to provide more detailed guidance on what stands out immediately. We might observe trends, patterns, or anomalies in the data based on the plotted time series.

Use linear regression to detect any upwards or downwards trends

data$Timestamp_numeric <- as.numeric(data$Timestamp)

model <- lm(SignalStrength ~ Timestamp_numeric, data = data)

summary(model)

## 
## Call:
## lm(formula = SignalStrength ~ Timestamp_numeric, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.7616  -3.0082   0.3745   3.3463  16.6025 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)
## (Intercept)       -4.687e+04  7.633e+04  -0.614    0.539
## Timestamp_numeric  2.797e-05  4.564e-05   0.613    0.540
## 
## Residual standard error: 4.867 on 10580 degrees of freedom
## Multiple R-squared:  3.55e-05,   Adjusted R-squared:  -5.901e-05 
## F-statistic: 0.3756 on 1 and 10580 DF,  p-value: 0.54

coef_value <- coef(model)[2]  
p_value <- summary(model)$coefficients["Timestamp_numeric", "Pr(>|t|)"]

cat("Coefficient:", coef_value, "\n")

## Coefficient: 2.796984e-05

cat("P-value:", p_value, "\n")

## P-value: 0.5399764

ggplot(data, aes(x = Timestamp, y = SignalStrength)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "blue") +
  labs(title = "Linear Regression: Signal Strength Over Time",
       x = "Timestamp",
       y = "Signal Strength") +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'

To assess the strength of trends in linear regression, you can look at the coefficient of the predictor variable (“Timestamp”) and consider its magnitude. A larger absolute value of the coefficient generally indicates a stronger trend. Additionally, the statistical significance of the coefficient, as indicated by the p-value, provides information on whether the trend is likely to be real or if it could have occurred by chance.

Use smoothing to detect at least one season

To detect seasonality in your data, we can use smoothing techniques like moving averages or exponential smoothing. After smoothing, we can analyze the autocorrelation function (ACF) to identify the seasonality pattern. The resulting plot should show the original time series along with the smoothed version, making it easier to detect any seasonality.

ts_data <- ts(data$SignalStrength, frequency = 1, start = 1)
smoothed_data <- forecast::ets(ts_data)

autoplot(ts_data) +
  autolayer(smoothed_data$fitted, series = "Smoothed") +
  labs(title = "Signal Strength with Exponential Smoothing",
       x = "Timestamp",
       y = "Signal Strength") +
  theme_minimal()

par(mfrow = c(1, 2))
acf(ts_data, main = "ACF Plot")

The ACF (Autocorrelation Function) plots will help you identify any repeating patterns or seasonality in the data. Look for significant spikes at regular intervals in the plots, as these indicate potential seasonality. We can observe significant spikes at regular intervals in the ACF i.e., it suggests the presence of seasonality. The lag at which spikes occur corresponds to the length of the season.