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# NUMBER 1: Climate change dataset analysis using z-scores, z-tests, independent t-tests, dependent t-tests, nonparametric tests, and one way ANOVA with post-hoc comparisons
# Climate change dataset from online:
climate <- read.csv("/Users/yahavmanor/Desktop/ENP164/Exam2/climate_metrics.csv")
climate
## State Leaning Rainfall_in.year Snowfall_in.year Avg_Temp_F AQI
## 1 Texas Red 32.5 1.2 70.5 55
## 2 California Blue 22.1 4.5 65.3 42
## 3 Florida Red 54.1 0.1 74.2 50
## 4 New York Blue 41.2 25.3 54.8 38
## 5 Alabama Red 56.8 0.7 69.8 60
## 6 Illinois Blue 39.7 22.4 55.2 45
## 7 Ohio Red 40.0 20.1 53.1 50
## 8 Massachusetts Blue 43.3 36.7 51.9 35
## 9 Georgia Red 50.5 0.8 68.9 53
## 10 Colorado Blue 16.9 60.5 45.7 40
## 11 Arizona Red 13.5 5.4 72.5 57
## 12 Washington Blue 38.2 14.7 53.5 39
## 13 Missouri Red 42.0 18.5 60.2 52
## 14 Vermont Blue 36.1 86.5 45.2 34
## 15 Mississippi Red 59.7 0.4 70.0 61
## 16 New Jersey Blue 45.5 23.0 54.1 37
## 17 North Carolina Red 47.8 4.1 66.3 51
## 18 Pennsylvania Blue 42.6 28.7 52.9 43
## 19 Louisiana Red 60.2 0.1 71.0 58
## 20 Michigan Blue 32.4 64.7 49.6 44
## 21 Oklahoma Red 36.7 6.1 68.5 56
## 22 Maryland Blue 44.2 21.2 55.5 41
## 23 Kansas Red 34.8 18.3 62.1 54
## Climate_Spending_Per_Capita
## 1 120
## 2 310
## 3 90
## 4 280
## 5 85
## 6 240
## 7 130
## 8 300
## 9 100
## 10 260
## 11 110
## 12 270
## 13 120
## 14 290
## 15 75
## 16 250
## 17 95
## 18 265
## 19 80
## 20 230
## 21 90
## 22 245
## 23 100
# Data explanation + variable classification:
# Leaning indicates whether the state is Red or Blue (as of the most recent polls) - NOMINAL
# Average temp shows the average temperature in F that year - INTERVAL
# Rainfall and snowfall shows total in year - RATIO
# AQI is the air quality index (for reference, good air quality is between 0-50) - RATIO
# Climate spending per capita indicates how much the state dedicated finances to climate change initiatives in the past year - RATIO
# Before getting started on analyzing the data, let's clean it up a little
#Checking all data is numeric
is.numeric(climate$Rainfall_in.year)
## [1] TRUE
is.numeric(climate$Snowfall_in.year)
## [1] TRUE
is.numeric(climate$Avg_Temp_F)
## [1] TRUE
is.numeric(climate$AQI)
## [1] TRUE
is.numeric(climate$Climate_Spending_Per_Capita)
## [1] TRUE
# All results came back as TRUE, indicating that all data entries in these columns are numeric
#Checking all data does not have missing values
is.na(climate$Rainfall_in.year)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
is.na(climate$Snowfall_in.year)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
is.na(climate$Avg_Temp_F)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
is.na(climate$AQI)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
is.na(climate$Climate_Spending_Per_Capita)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# All results came back as FALSE, indicating that there is available data in each of these columns (nothing is "na")
# Now that we have checked that all of the data is clean, let's plot distributions of each column and take a look at their summary statistics
summary(climate$Rainfall_in.year)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 13.50 35.45 41.20 40.47 46.65 60.20
summary(climate$Snowfall_in.year)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.10 2.65 18.30 20.17 24.15 86.50
summary(climate$Avg_Temp_F)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 45.20 53.30 60.20 60.47 69.35 74.20
summary(climate$AQI)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 34.00 40.50 50.00 47.61 54.50 61.00
summary(climate$Climate_Spending_Per_Capita)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 75.0 97.5 130.0 179.8 262.5 310.0
hist(climate$Rainfall_in.year, breaks = 2, main = "Rainfall per year across the states in this dataset", xlab = "Rainfall (inches)", ylab = "Frequency", freq=FALSE)
hist(climate$Snowfall_in.year, breaks = 2, main = "Snowfall per year across the states in this dataset", xlab = "Snowfall (inches)", ylab = "Frequency", freq=FALSE)
hist(climate$Avg_Temp_F, breaks = 2, main = "Average temp across the states in this dataset", xlab = "Average Temp (F)", ylab = "Frequency", freq=FALSE)
hist(climate$AQI, breaks = 2, main = "Average AQI across the states in this dataset", xlab = "AQI", ylab = "Frequency", freq=FALSE)
hist(climate$Climate_Spending_Per_Capita, breaks = 2, main = "Average climate spending per capita across the states in this dataset", xlab = "Climate spending per capita ($ per person per year)", ylab = "Frequency", freq=FALSE)
# To make comparisons on various climate metrics between Red and Blue leaning states, let's find some z-scores for a couple of the metrics! I randomly chose AQI, rainfall lper year, and spending as the metrics for z-score analysis in this code
# Calculate overall means and standard deviations
mean_AQI <- mean(climate$AQI)
sd_AQI <- sd(climate$AQI)
mean_Rainfall <- mean(climate$Rainfall_in.year)
sd_Rainfall <- sd(climate$Rainfall_in.year)
mean_Spending <- mean(climate$Climate_Spending_Per_Capita)
sd_Spending <- sd(climate$Climate_Spending_Per_Capita)
# Manually compute z-scores using the z-score formula for each metric
AQI_z <- (climate$AQI - mean_AQI) / sd_AQI
Rainfall_z <- (climate$Rainfall_in.year - mean_Rainfall) / sd_Rainfall
Spending_z <- (climate$Climate_Spending_Per_Capita - mean_Spending) / sd_Spending
AQI_z
## [1] 0.8767717 -0.6653150 0.2836614 -1.1398032 1.4698819 -0.3094488
## [7] 0.2836614 -1.4956693 0.6395276 -0.9025591 1.1140158 -1.0211811
## [13] 0.5209055 -1.6142913 1.5885039 -1.2584252 0.4022835 -0.5466929
## [19] 1.2326378 -0.4280709 0.9953937 -0.7839370 0.7581496
#The z-scores of AQI demonstrate a lot of variation, some values being relatively close to 0 (indicating that they match the average of all of the states' AQI's) with others being much further away, like 1.58 (indicating that the AQI is above the mean) or -1.49 Indicating that the AQI is below the mean). In order to better understand the z-scores of each state without having to constantly cross reference with the original table, I am coding to add another column in my dataset for easier analysis:
climate$AQI_z <- (climate$AQI - mean_AQI) / sd_AQI
climate$Rainfall_z <- (climate$Rainfall_in.year - mean_Rainfall) / sd_Rainfall
climate$Spending_z <- (climate$Climate_Spending_Per_Capita - mean_Spending) / sd_Spending
head(climate)
## State Leaning Rainfall_in.year Snowfall_in.year Avg_Temp_F AQI
## 1 Texas Red 32.5 1.2 70.5 55
## 2 California Blue 22.1 4.5 65.3 42
## 3 Florida Red 54.1 0.1 74.2 50
## 4 New York Blue 41.2 25.3 54.8 38
## 5 Alabama Red 56.8 0.7 69.8 60
## 6 Illinois Blue 39.7 22.4 55.2 45
## Climate_Spending_Per_Capita AQI_z Rainfall_z Spending_z
## 1 120 0.8767717 -0.65661565 -0.6776477
## 2 310 -0.6653150 -1.51347579 1.4760400
## 3 90 0.2836614 1.12301695 -1.0177037
## 4 280 -1.1398032 0.06018081 1.1359840
## 5 85 1.4698819 1.34547103 -1.0743797
## 6 240 -0.3094488 -0.06340478 0.6825761
# Now, it is much easier to see which states have extreme z-scores that indicate a deviation from the mean. For example, Colorado's z-score for rainfall per year is -1.94, indicating that it is much lower than the mean. New York's AQI is -1.13, indicating that its air quality is much lower than the mean. Vermont's climate spending per capita z-score is 1.24, indicating that Vermont spends more on climate change initiatives in comparison to the mean. Using just my background knowledge having lived in the United States for the greater portion of my life, much of this data does make sense to me. Colorado gets less rainfall, as the west coast typically does, but much more snow. New York's air quality is poorer as there is more pollution from factories, public transportation, and such a condensed population on just a few islands in New York City. I also know that Vermont tends to vote blue and that there is a great focus on wilderness preservation there, which contributes to the fact that they spend more on climate change initiatives than the other states in this dataset. While these z-scores do validate what I know about each state in the dataset, let's conduct a two sample z-test to draw comparisons between the Blue and Red states.
# To make comparisons on climate metrics between Red and Blue leaning states, we can create two different samples, red_spending and blue_spending, then conduct a two sample z-test to better understand whether there exists a statistically significant difference between the Red and Blue states in terms of how much they spend on climate change initiatives per capita
red_spending <- climate$Climate_Spending_Per_Capita[climate$Leaning == "Red"] # variable for spending in Red States
blue_spending <- climate$Climate_Spending_Per_Capita[climate$Leaning == "Blue"] # variable for spending in Blue States
# Next, I conduct a two sample z-test on these two samples
sd_red <- sd(red_spending)
sd_blue <- sd(blue_spending)
z.test(red_spending, blue_spending, mu = 0, sigma.x = sd_red, sigma.y = sd_blue, conf.level = 0.95)
##
## Two-sample z-Test
##
## data: red_spending and blue_spending
## z = -18.242, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -185.7067 -149.6721
## sample estimates:
## mean of x mean of y
## 99.58333 267.27273
#The p-value for this test is less than 0.05, indicating that there exists a statistically significant difference between the climate spending in Red and Blue states
# Next, let's conduct an independent groups t-test to see if there exists a statistical difference between the means of two independent groups. In this test, I want to see if there is a statistically significant difference in the AQI of red and blue leaning states. These two samples are independent from each other, as the AQI of one state does not impact the AQI of another. There does exist a chance that some influence exists, as a state's air quality may be reduced if it is next to a state with very bad pollution, but for the purposes of analyzing this data, we assume that each sample is independent.
# Independent t-test: Avg_Temp between Red and Blue states
# Null hypothesis: there exists no statistically significant difference between the AQI's of red and blue leaning states
# Alternative hypothesis: there exists a statistically significant difference between the AQI's of red and blue leaning states
t_test_AQI <- t.test(Avg_Temp_F ~ Leaning, data = climate, var.equal = TRUE)
print(t_test_AQI)
##
## Two Sample t-test
##
## data: Avg_Temp_F by Leaning
## t = -5.9319, df = 21, p-value = 6.898e-06
## alternative hypothesis: true difference in means between group Blue and group Red is not equal to 0
## 95 percent confidence interval:
## -19.171116 -9.218278
## sample estimates:
## mean in group Blue mean in group Red
## 53.06364 67.25833
# The resulting p-value, 6.898e-06, is less than 0.05. indicating that we can reject the null hypothesis in favor of the alternative, meaning that there does exist a statistically significant difference between the AQI's of red and blue leaning states. This difference may be attributed to the fact that there exists a statistically significant difference between red and blue leaning states in terms of climate spending per capita. Let's take a look at this too:
t_test_spending <- t.test(Climate_Spending_Per_Capita ~ Leaning, data = climate, var.equal = TRUE)
print(t_test_spending)
##
## Two Sample t-test
##
## data: Climate_Spending_Per_Capita by Leaning
## t = 18.557, df = 21, p-value = 1.667e-14
## alternative hypothesis: true difference in means between group Blue and group Red is not equal to 0
## 95 percent confidence interval:
## 148.8974 186.4813
## sample estimates:
## mean in group Blue mean in group Red
## 267.27273 99.58333
# The p-value here is also less than 0.05, indicating that there does exist a statistically significant difference between red and blue leaning states in terms of climate spending per capita. These two findings may indicate that spending less on climate change initiatives could somehow link to AQI
# Next, I chose to conduct a dependent groups t-test on two variables that may be dependent on each other, rainfall and snowfall per year
# For this t-test, the following hypotheses were made:
# Null hypothesis: there is no statistically significant difference between the groups being compared (mean difference between the paired scores is 0)
# Alternative hypothesis: there is a statistically significant difference between the groups being compared (mean difference between the paired scores is not 0)
# Dependent t-test: Compare Rainfall vs. Snowfall within states
t_test_dep <- t.test(climate$Rainfall_in.year, climate$Snowfall_in.year, paired=TRUE)
print(t_test_dep)
##
## Paired t-test
##
## data: climate$Rainfall_in.year and climate$Snowfall_in.year
## t = 3.2718, df = 22, p-value = 0.003487
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 7.431179 33.160125
## sample estimates:
## mean difference
## 20.29565
# The p-value here is 0.003, which is less than the threshold value of 0.05. This indicaates that there does exist a statistically significant difference between the groups being compared. To understand why this difference exists, I took a look at the means of each:
mean(climate$Rainfall_in.year - climate$Snowfall_in.year)
## [1] 20.29565
# Since the mean is positive, rainfall per year in each state in this dataset is higher. This result may be an indication of climate change, as global warming causes less rain and more snow, for higher temperatures mean that rain freezes less (and therefore does not turn into snow). This finding may indicate climate change activity across the states in this dataset.
# Next, I want to conduct a nonparametric test to see if whether a state is red or blue leaning has an impact on their climate change spending per capita, as assumed in the prompt of this question. First, I want to take a look at the normality of the data between red and blue states in terms of their spending. This is because nonparametric tests are typically conducted on data that is non-normal, as it focuses on non-parametric measures, like median and ranks.
shapiro.test(red_spending)
##
## Shapiro-Wilk normality test
##
## data: red_spending
## W = 0.95386, p-value = 0.6939
shapiro.test(blue_spending)
##
## Shapiro-Wilk normality test
##
## data: blue_spending
## W = 0.97096, p-value = 0.896
# Even though both p-values are above the threshold value of 0.05, indicating that the data is normally distributed, I still chose to conduct a nonparametric test, as this is a more robust choice for such a small sample size (n = 23)
# Nonparametric test: Wilcoxon rank-sum test for Climate Spending by Leaning
# Null hypothesis: There exists no statistically significant difference between groups being compared
# Alternative hypothesis: There exists a statistically significant difference between groups being compared
wilcox_test <- wilcox.test(Climate_Spending_Per_Capita ~ Leaning, data = climate)
## Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
## compute exact p-value with ties
print(wilcox_test)
##
## Wilcoxon rank sum test with continuity correction
##
## data: Climate_Spending_Per_Capita by Leaning
## W = 132, p-value = 5.478e-05
## alternative hypothesis: true location shift is not equal to 0
# The p-value is 5.478e-05, which is less than the p-value threshold of 0.05, indicating that we reject the null hypothesis in favor of the alternative. In the case of this data, we accept that there exists a difference between the groups, meaning that between Red and Blue leaning states, there is a statistically significant difference between their climate change spending per capita. This results supports the idea that was presented in the prompt of this question, which is that "more conservative states tending to avoid enacting climate sensitive legislation and more liberal leaning states having greater willingness to enact climate preserving measures".
# Finally, I want to conduct a one-way ANOVA test as well as post-hoc comparisons to determine whether average per capita climate spending differs across different levels of climate-related variables — specifically AQI (air quality), average temperature, rainfall, and snowfall.
anova_result <- aov(Climate_Spending_Per_Capita ~ Leaning + AQI + Avg_Temp_F + Rainfall_in.year + Snowfall_in.year, data=climate)
summary(anova_result)
## Df Sum Sq Mean Sq F value Pr(>F)
## Leaning 1 161383 161383 565.406 1.74e-14 ***
## AQI 1 2993 2993 10.484 0.00484 **
## Avg_Temp_F 1 131 131 0.458 0.50767
## Rainfall_in.year 1 1543 1543 5.405 0.03272 *
## Snowfall_in.year 1 323 323 1.131 0.30236
## Residuals 17 4852 285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# P-value for AQI is less than 0.05, indicating that there is a statistically significant relationship between Air Quality Index (AQI) and per capita climate spending. In other words: as AQI levels differ across states, per capita spending on climate issues also tends to differ in a statistically significant way. The same goes for rainfall per year. The other environmental factors (temperature and snowfall), all with p-values above 0.05, do not have a statistically significant relationship with climate spending per capita based on this model. The categorical variable Leaning seems to have a very strong relationship with climate spending per capita, something that has been established previously in the nonparametric test.
# To take a look at these values more, I chose to conduct a post-hoc comparison, a pairwise t test using the bonferroni method,
pairwise.t.test(climate$Climate_Spending_Per_Capita, climate$Leaning, p.adjust.method = "bonferroni")
##
## Pairwise comparisons using t tests with pooled SD
##
## data: climate$Climate_Spending_Per_Capita and climate$Leaning
##
## Blue
## Red 1.7e-14
##
## P value adjustment method: bonferroni
# A pairwise t-test comparing per capita climate spending between Red and Blue-leaning states revealed a statistically significant difference (p < 0.001). This result indicates that the mean per capita spending on climate issues differs substantially between states based on political leaning.
# ------------------------------------------------------------------------------------------------------------
# NUMBER 2: Unemployment rates
# The following dataset was created by me and is a culmination of information I found online from various sources, including which states have right to work laws (https://mosey.com/blog/right-to-work-states/), as well as each state's population, GDP, and unemployment rate as of 2024.
unemployment <- read.csv("/Users/yahavmanor/Desktop/ENP164/Exam2/unemployment.csv")
unemployment
## State UnemploymentRate RightToWork StateGDP Population
## 1 Alabama 3.2 1 250 5.1
## 2 Alaska 4.8 0 55 0.7
## 3 Arizona 4.0 1 430 7.4
## 4 Arkansas 3.5 1 170 3.0
## 5 California 5.4 0 3500 39.0
## 6 Colorado 3.9 0 480 5.8
## 7 Connecticut 4.2 0 310 3.6
## 8 Delaware 4.0 0 95 1.0
## 9 Florida 3.1 1 1200 22.6
## 10 Georgia 3.4 1 750 11.0
## 11 Hawaii 5.0 0 95 1.4
## 12 Idaho 3.0 1 120 1.9
## 13 Illinois 4.5 0 950 12.6
## 14 Indiana 3.6 1 450 6.8
## 15 Iowa 3.1 1 210 3.2
## 16 Kansas 3.2 1 200 2.9
## 17 Kentucky 4.0 1 230 4.5
## 18 Louisiana 4.3 1 270 4.6
## 19 Maine 3.4 0 80 1.4
## 20 Maryland 4.1 0 450 6.2
## 21 Massachusetts 3.8 0 700 7.0
## 22 Michigan 4.5 0 610 10.0
## 23 Minnesota 3.2 0 450 5.7
## 24 Mississippi 3.5 1 140 3.0
## 25 Missouri 3.6 1 330 6.1
## 26 Montana 3.1 1 80 1.1
## 27 Nebraska 2.8 1 150 2.0
## 28 Nevada 5.5 1 210 3.3
## 29 New Hampshire 2.9 0 95 1.4
## 30 New Jersey 4.3 0 780 9.3
## 31 New Mexico 4.9 1 110 2.1
## 32 New York 4.7 0 2100 19.6
## 33 North Carolina 3.5 1 740 10.8
## 34 North Dakota 2.7 1 90 0.8
## 35 Ohio 4.1 0 750 11.8
## 36 Oklahoma 3.2 1 250 4.0
## 37 Oregon 4.2 0 330 4.3
## 38 Pennsylvania 4.3 0 860 12.9
## 39 Rhode Island 4.1 0 70 1.1
## 40 South Carolina 3.2 1 300 5.3
## 41 South Dakota 2.9 1 80 0.9
## 42 Tennessee 3.2 1 420 7.0
## 43 Texas 3.6 1 2300 30.0
## 44 Utah 2.8 1 300 3.4
## 45 Vermont 3.0 0 50 0.6
## 46 Virginia 3.4 1 650 8.7
## 47 Washington 4.3 0 750 7.9
## 48 West Virginia 4.5 1 100 1.8
## 49 Wisconsin 3.2 0 410 5.9
## 50 Wyoming 3.4 1 50 0.6
# Data explanation and variable classification:
# RightToWork: 1 = Right-to-Work state, 0 = Not (NOMINAL)
# StateGDP: State GDP in billions USD (RATIO)
# Population: State population in millions (RATIO)
# Unemployment Rate: percentage unemployed in that state (RATIO)
# Before getting started on analyzing the data, let's clean it up a little
#Checking all data is numeric
is.numeric(unemployment$UnemploymentRate)
## [1] TRUE
is.numeric(unemployment$RightToWork)
## [1] TRUE
is.numeric(unemployment$StateGDP)
## [1] TRUE
is.numeric(unemployment$Population)
## [1] TRUE
# All results came back as TRUE, indicating that all data entries in these columns are numeric
#Checking all data does not have missing values
is.na(unemployment$UnemploymentRate)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE
is.na(unemployment$RightToWork)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE
is.na(unemployment$StateGDP)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE
is.na(unemployment$Population)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE
# All results came back as FALSE, indicating that there is available data in each of these columns (nothing is "na")
# Now that we have checked that all of the data is clean, let's plot distributions of each column and take a look at their summary statistics
summary(unemployment$UnemploymentRate)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.700 3.200 3.600 3.762 4.275 5.500
summary(unemployment$RightToWork)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 1.00 0.56 1.00 1.00
summary(unemployment$StateGDP)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 50.0 112.5 300.0 491.0 640.0 3500.0
summary(unemployment$Population)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.600 1.925 4.550 6.662 7.775 39.000
hist(unemployment$UnemploymentRate, breaks = 2, main = "Unemployment rate across all 50 states", xlab = "Unemployment rate", ylab = "Frequency", freq=FALSE)
hist(unemployment$RightToWork, breaks = 2, main = "Right to work across all 50 states", xlab = "Right to work (0 = no, 1 = yes)", ylab = "Frequency", freq=FALSE)
hist(unemployment$StateGDP, breaks = 2, main = "GDP across all 50 states", xlab = "GDP (billions in USD)", ylab = "Frequency", freq=FALSE)
hist(unemployment$Population, breaks = 2, main = "Population across all 50 states", xlab = "Population (in millions)", ylab = "Frequency", freq=FALSE)
# To start analyzing correlations between the data, let's take a look at unemployment rate against the state's GDP, right to work, and its population. For a pearson correlation, 1 indicates a strong correlation between the two variables, while -1 indicates a very negative correlation (as one increases, the other decreases or vice versa), and 0 indicates no correlation
# Pearson correlation between UnemploymentRate and StateGDP
cor(unemployment$UnemploymentRate, unemployment$StateGDP, method = "pearson")
## [1] 0.3500356
# The correlation of these two variables is 0.35. As this number is closer to 0 than it is to 1, it can be concluded that there is some positive correlation between these two variables but that it is not very strong. This is actually a very interesting finding, as typically higher GDP does indicate lower unemployment, as a higher GDP means higher economic growth, which means higher demand for jobs. However, other factors certainly can impact this relationship, like the types of jobs available and the population of that state.
# Pearson correlation between UnemploymentRate and Population
cor(unemployment$UnemploymentRate, unemployment$Population, method = "pearson")
## [1] 0.2978144
# The correlation of these two variables is 0.29. As this number is closer to 0 than it is to 1, it can be concluded that there is some positive correlation between these two variables but that it is not very strong. This does make some intuitive sense, as a higher population may indicate less jobs, which leads to higher unemployment.
# Pearson correlation between UnemploymentRate and Right to Work
cor(unemployment$UnemploymentRate, unemployment$RightToWork, method = "pearson")
## [1] -0.4136383
# The correlation of these two variables is -0.41. As this number is closer to 0 than it is to -1, it can be concluded that there is some negative correlation between these two variables but that it is not very strong. This does make some intuitive sense, as right to work increases (or is set to "1", meaning that it exists), unemployment decreases.
# Next, let's do the same correlation testing but with the spearman test
# Spearman correlation between UnemploymentRate and StateGDP
cor(unemployment$UnemploymentRate, unemployment$StateGDP, method = "spearman")
## [1] 0.2996755
# Spearman correlation between UnemploymentRate and Population
cor(unemployment$UnemploymentRate, unemployment$Population, method = "spearman")
## [1] 0.3081042
# Spearman correlation between UnemploymentRate and right to work
cor(unemployment$UnemploymentRate, unemployment$RightToWork, method = "spearman")
## [1] -0.4282484
# All of these models printed very similar correlationss to the pearson tests. The difference between the pearson and spearman tests is that pearson is used to measure linear data in a continuous relationship, while spearman takes a look at ordinal, or monotonic, data. The fact that the correlations stayed about the same indicates that there are not any significant outliers in the data and that the data is both linear and monotonic.
# To better understand the relationship between StateGDP and unemployment rates, I chose to create a simple linear regression of GDP as a predictor for unemployment
# Fitting the model
model_gdp <- lm(UnemploymentRate ~ StateGDP, data = unemployment)
# Determine the correlation coefficient and R-squared
summary(model_gdp)
##
## Call:
## lm(formula = UnemploymentRate ~ StateGDP, data = unemployment)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9381 -0.5233 -0.1312 0.4342 1.8474
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.5708080 0.1195256 29.875 <2e-16 ***
## StateGDP 0.0003894 0.0001504 2.589 0.0127 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6645 on 48 degrees of freedom
## Multiple R-squared: 0.1225, Adjusted R-squared: 0.1042
## F-statistic: 6.702 on 1 and 48 DF, p-value: 0.01271
# Correlation coefficient: 0.2996755 (from previous analysis)
# Multiple R-squared: 0.1225; this value is relatively low (close to 0), indicating that the model does not predict the dependent variable well
# Adjusted R-squared: 0.1042; this low value demonstrates the same insight as the multiple R-squared
# Scatterplot + plot of best fitting line
plot(unemployment$StateGDP, unemployment$UnemploymentRate,
main="Unemployment Rate vs State GDP",
xlab="State GDP (in billions USD)", ylab="Unemployment Rate (%)",
pch=19, col="blue")
abline(model_gdp, col="red", lwd=2)
# GDP clearly demonstrates some correlation with unemployment rates, though the correlation is not very strong. The two seem to have somewhat of a positive correlation, meaning as GDP increases, unemployment increases. Therefore, it can be concluded that GDP is a possible predictor of unemployment in the United States across all of the states.
# To better understand the relationship between population and unemployment rates, I chose to create a simple linear regression of Population as a predictor for unemployment
# Fitting the model
model_pop <- lm(UnemploymentRate ~ Population, data = unemployment)
# Determine the correlation coefficient and R-squared
summary(model_pop)
##
## Call:
## lm(formula = UnemploymentRate ~ Population, data = unemployment)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1086 -0.5322 -0.1594 0.5010 1.8322
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.57531 0.12897 27.721 <2e-16 ***
## Population 0.02802 0.01297 2.161 0.0357 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6772 on 48 degrees of freedom
## Multiple R-squared: 0.08869, Adjusted R-squared: 0.06971
## F-statistic: 4.672 on 1 and 48 DF, p-value: 0.03568
# Correlation coefficient: 0.3081042 (from previous analysis)
# Multiple R-squared: 0.08869; this value is relatively low (close to 0), indicating that the model does not predict the dependent variable well
# Adjusted R-squared: 0.06971; this low value demonstrates the same insight as the multiple R-squared
# Scatterplot + plot of best fitting line
plot(unemployment$Population, unemployment$UnemploymentRate,
main="Unemployment Rate vs Population",
xlab="Population (in millions)", ylab="Unemployment Rate (%)",
pch=19, col="blue")
abline(model_pop, col="red", lwd=2)
# Population also clearly demonstrates some correlation with unemployment rates, though the correlation is also not very strong. The two seem to have somewhat of a positive correlation, meaning as population increases, unemployment increases. This does make some sense, as I mentioned before, as a higher number of people means a higher demand for jobs, which could lead to higher unemployment. Therefore, it can be concluded that population is a possible predictor of unemployment in the United States across all of the states.
# ------------------------------------------------------------------------------------------------------------
# NUMBER 3: Mental health and social media use
# The following dataset was found online. Some of it was already cleaned up before importing into this code interface. This was a study conducted on 18-25 year olds.
anxiety <- read.csv("/Users/yahavmanor/Desktop/ENP164/Exam2/mentalhealth.csv")
anxiety
## participant anxiety_score hours_social_media number_of_platforms age
## 1 1 14 6.5 4 19
## 2 2 7 3.0 2 21
## 3 3 18 9.0 5 20
## 4 4 12 5.5 3 18
## 5 5 5 1.5 1 22
## 6 6 16 8.0 4 20
## 7 7 9 4.0 2 23
## 8 8 13 6.0 3 19
## 9 9 6 2.0 1 21
## 10 10 19 9.5 5 18
## 11 11 8 3.5 2 20
## 12 12 11 5.0 3 22
## 13 13 15 7.5 4 21
## 14 14 10 4.5 2 19
## 15 15 6 2.5 1 23
## 16 16 17 8.5 4 18
## 17 17 13 6.0 3 20
## 18 18 7 3.0 2 22
## 19 19 12 5.5 3 21
## 20 20 9 4.0 2 19
## 21 21 5 1.0 1 22
## 22 22 16 8.0 4 20
## 23 23 18 9.5 5 19
## 24 24 11 5.0 3 21
## 25 25 14 6.5 4 23
## 26 26 7 3.0 2 20
## 27 27 15 7.5 4 18
## 28 28 9 4.0 2 22
## 29 29 12 5.5 3 21
## 30 30 6 2.0 1 23
## 31 31 17 8.5 5 19
## 32 32 13 6.0 3 20
## 33 33 8 3.5 2 21
## 34 34 10 4.5 2 22
## 35 35 5 1.5 1 23
## 36 36 16 8.0 4 18
## 37 37 14 6.5 4 20
## 38 38 7 3.0 2 21
## 39 39 12 5.5 3 22
## 40 40 9 4.0 2 19
## 41 41 6 2.0 1 23
## 42 42 18 9.5 5 18
# Data explanation:
# Anxiety score on a scale of 1-21 rated by the participant (21 being very anxious) (ORDINAL)
# Number of platforms means number of social media platforms used on a frequent (once a week at minimum) basis (RATIO)
# Hours_social_media is hours spent per day, reported by the particiapnt (RATIO)
# Prediction:
# All of the variables used in this analysis are ratio variables, as they all have a true 0 and are continuous with equal intervals. Based on my knowledge and own personal use of social media as well as what I know about anxiety, I expect hours spent on social media and platforms used to have a statistically significant impact on a model that predicts anxiety scores. Age, however, may impact anxiety, but I do not think that this will be as strong of an impact since anxiety impacts people at different ages differently.
# Before getting started on analyzing the data, let's clean it up a little
#Checking all data is numeric
is.numeric(anxiety$participant)
## [1] TRUE
is.numeric(anxiety$anxiety_score)
## [1] TRUE
is.numeric(anxiety$hours_social_media)
## [1] TRUE
is.numeric(anxiety$number_of_platforms)
## [1] TRUE
is.numeric(anxiety$age)
## [1] TRUE
# All results came back as TRUE, indicating that all data entries in these columns are numeric
#Checking all data does not have missing values
is.na(anxiety$participant)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE
is.na(anxiety$anxiety_score)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE
is.na(anxiety$hours_social_media)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE
is.na(anxiety$number_of_platforms)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE
is.na(anxiety$age)
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE
# All results came back as FALSE, indicating that there is available data in each of these columns (nothing is "na")
# Now that we have checked that all of the data is clean, let's plot distributions of each column and take a look at their summary statistics
summary(anxiety$anxiety_score)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 7.25 11.50 11.31 14.75 19.00
summary(anxiety$hours_social_media)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 3.125 5.250 5.226 7.250 9.500
summary(anxiety$number_of_platforms)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 2.833 4.000 5.000
summary(anxiety$age)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 18.0 19.0 20.5 20.5 22.0 23.0
hist(anxiety$anxiety_score, breaks = 2, main = "Anxiety scores across participants", xlab = "Anxiety Score (out of 21)", ylab = "Frequency", freq=FALSE)
hist(anxiety$hours_social_media, breaks = 2, main = "Hours spent on social media across participants", xlab = "Hours (per day)", ylab = "Frequency", freq=FALSE)
hist(anxiety$number_of_platforms, breaks = 2, main = "Number of social media platforms used across participants", xlab = "Number of Platforms", ylab = "Frequency", freq=FALSE)
hist(anxiety$age, breaks = 2, main = "Age across participants", xlab = "Age", ylab = "Frequency", freq=FALSE)
# Next, we want to see which variables in this model are accurate predictors of a participant's anxiety score. To do so, I will compare two models: one with two predictors and one with three predictors
anxiety.full = lm(anxiety$anxiety_score ~ anxiety$hours_social_media + anxiety$number_of_platforms + anxiety$age)
summary(anxiety.full) # model with three predictors
##
## Call:
## lm(formula = anxiety$anxiety_score ~ anxiety$hours_social_media +
## anxiety$number_of_platforms + anxiety$age)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6549 -0.1964 0.0151 0.2490 0.8826
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.76649 1.07781 1.639 0.109
## anxiety$hours_social_media 1.61033 0.11141 14.455 <2e-16 ***
## anxiety$number_of_platforms 0.22984 0.20458 1.123 0.268
## anxiety$age 0.02322 0.04702 0.494 0.624
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3659 on 38 degrees of freedom
## Multiple R-squared: 0.9931, Adjusted R-squared: 0.9926
## F-statistic: 1822 on 3 and 38 DF, p-value: < 2.2e-16
# In the model with all three predictors, anxiety.full, the multiple R-squared is 0.9931, and the adjusted R-squared is 0.9926
anxiety.noage = lm(anxiety$anxiety_score ~ anxiety$hours_social_media + anxiety$number_of_platforms)
summary(anxiety.noage) # model with two predictors
##
## Call:
## lm(formula = anxiety$anxiety_score ~ anxiety$hours_social_media +
## anxiety$number_of_platforms)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.64550 -0.20028 0.03013 0.26054 0.86978
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.2942 0.1368 16.773 <2e-16 ***
## anxiety$hours_social_media 1.5936 0.1051 15.161 <2e-16 ***
## anxiety$number_of_platforms 0.2423 0.2010 1.206 0.235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3624 on 39 degrees of freedom
## Multiple R-squared: 0.9931, Adjusted R-squared: 0.9927
## F-statistic: 2787 on 2 and 39 DF, p-value: < 2.2e-16
# In the model with two predictors, anxiety.noage, the multiple R-squared is 0.9931, and the adjusted R-squared is 0.9927
anova (anxiety.full, anxiety.noage)
## Analysis of Variance Table
##
## Model 1: anxiety$anxiety_score ~ anxiety$hours_social_media + anxiety$number_of_platforms +
## anxiety$age
## Model 2: anxiety$anxiety_score ~ anxiety$hours_social_media + anxiety$number_of_platforms
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 38 5.0887
## 2 39 5.1213 -1 -0.032642 0.2438 0.6243
# p-value = 0.6243
# The almost equal adjusted R-squared values (0.9926 and 0.9927) between the model with age and without age as a predictor of anxiety scores demonstrates that adding the third predictor (age) didn’t really improve the model’s explanatory power in a meaningful way. Additionally, the p-value of the ANOVA test is above the threshold value of 0.05, indicating that we accept the null hypothesis which states that there exists no statistically significant difference between the models. This suggests that social media use has a much bigger impact on anxiety than age does. Therefore, the both of these models are just as good at predicting as the other. I am curious to see, though, how much the other variables predict the model since age clearly has such an insignificant impact. I conducted the following analysis just as a bonus (out of curiosity):
anxiety.nohours = lm(anxiety$anxiety_score ~ anxiety$age + anxiety$number_of_platforms)
summary(anxiety.nohours)
##
## Call:
## lm(formula = anxiety$anxiety_score ~ anxiety$age + anxiety$number_of_platforms)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.84351 -0.51786 -0.02662 0.75767 1.65208
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.3677 2.5911 2.457 0.0185 *
## anxiety$age -0.1831 0.1127 -1.624 0.1124
## anxiety$number_of_platforms 3.0691 0.1439 21.330 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9208 on 39 degrees of freedom
## Multiple R-squared: 0.9551, Adjusted R-squared: 0.9528
## F-statistic: 415.1 on 2 and 39 DF, p-value: < 2.2e-16
# In the model with two predictors, anxiety.nohours, the adjusted R-squared is 0.9528
anova (anxiety.full, anxiety.nohours)
## Analysis of Variance Table
##
## Model 1: anxiety$anxiety_score ~ anxiety$hours_social_media + anxiety$number_of_platforms +
## anxiety$age
## Model 2: anxiety$anxiety_score ~ anxiety$age + anxiety$number_of_platforms
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 38 5.089
## 2 39 33.068 -1 -27.979 208.94 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# p-value < 2.2e-16
# Clearly, with a much different adjusted R-squared and very small p-value, hours of social media has a statistically significant impact on anxiety!
# An additional variable that I would consider adding to this model would be sleep quality. This could be a variable that the participants rate themselves on on a scale of 1-10, maybe over the course of a few weeks. The average of their scores would be used to determine their sleep quality, which could then be assessed for whether it impact anxiety scores.
# ------------------------------------------------------------------------------------------------------------
# NUMBER 4: Predicting Type 2 diabetes using logistic regression
# Article being referenced: https://pmc.ncbi.nlm.nih.gov/articles/PMC8306487/
# I was having trouble including my review and analysis of this article into my KNIT file, so please access this response via this Google Doc link: https://docs.google.com/document/d/1kjJXSCNUWRiSJ6aQ_J3hxcEaqHkqjOoyEgFq7AKTCwU/edit?usp=sharing
# ------------------------------------------------------------------------------------------------------------
# NUMBER 5: BONUS
# The following dataset demonstrates the linear acceleration on the x, y and z axes when doing a short TikTok dance (video attached to final submission). I have split up the dance into three segments, which I will call: 1) elbows, 2) shake, 3) dance. In the video, these three segments correspond to the following times respectively: 0 to 3 seconds, 3 to 4 seconds, 4 to 10 seconds.
tiktok <- read.csv("/Users/yahavmanor/Desktop/ENP164/Exam2/tiktokcsv.csv")
tiktok
## Time..s. Linear.Acceleration.x..m.s.2. Linear.Acceleration.y..m.s.2.
## 1 0.001062125 2.407927e-02 -0.033608918
## 2 0.011070125 7.478384e-02 0.011853476
## 3 0.021079125 1.039813e-01 0.055735367
## 4 0.031088125 -1.123075e-02 -0.066965530
## 5 0.041096125 -1.703613e-01 -0.200525583
## 6 0.051105125 -2.794775e-01 -0.219890099
## 7 0.061114125 -3.434612e-01 -0.188841677
## 8 0.071122125 -2.423751e-01 -0.063562158
## 9 0.081131125 -1.140061e-01 -0.008713228
## 10 0.091140125 -4.742384e-02 -0.061224733
## 11 0.101148125 1.420406e-02 -0.029962595
## 12 0.111157125 6.387747e-02 0.035067799
## 13 0.121165125 1.342271e-01 0.108269091
## 14 0.131174125 1.272117e-01 0.076947311
## 15 0.141183125 1.092276e-01 -0.022156270
## 16 0.151191125 1.043007e-01 -0.085584234
## 17 0.161200125 9.949242e-02 -0.127760785
## 18 0.171209125 1.022174e-01 -0.122738904
## 19 0.181217125 1.419083e-01 -0.149441676
## 20 0.191225750 1.861340e-01 -0.137759231
## 21 0.201233750 1.781258e-01 -0.130573880
## 22 0.211242750 1.719185e-01 -0.189320271
## 23 0.221251750 1.625991e-01 -0.263099561
## 24 0.231259750 1.577158e-01 -0.354271979
## 25 0.241268750 1.618382e-01 -0.346260709
## 26 0.251277750 3.393366e-01 -0.586976252
## 27 0.261285750 3.080208e-01 -0.862891155
## 28 0.271294750 2.397364e-01 -1.207189539
## 29 0.281303750 1.995951e-01 -1.533824653
## 30 0.291311750 1.471363e-01 -1.718998371
## 31 0.301320750 1.535771e-01 -1.982587052
## 32 0.311328750 1.265754e-01 -2.387491241
## 33 0.321337750 3.097811e-02 -2.790779552
## 34 0.331346750 -8.079566e-02 -3.177221157
## 35 0.341354750 -2.947201e-02 -3.389060518
## 36 0.351363750 6.067081e-01 -3.214331096
## 37 0.361372750 8.223005e-01 -3.520891257
## 38 0.371380750 6.648439e-01 -3.975514321
## 39 0.381389750 5.063287e-01 -4.337130403
## 40 0.391397750 3.055055e-01 -4.147529757
## 41 0.401406750 3.225288e-01 -3.769571000
## 42 0.411415750 4.100608e-01 -3.571444822
## 43 0.421423750 5.273775e-01 -3.490820197
## 44 0.431432750 5.614102e-01 -3.315902202
## 45 0.441441750 4.757518e-01 -3.201846121
## 46 0.451449750 9.060433e-01 -2.510017306
## 47 0.461458750 8.808749e-01 -2.271692836
## 48 0.471467750 9.512546e-01 -2.070094289
## 49 0.481475750 1.029338e+00 -1.989382248
## 50 0.491484750 1.128774e+00 -1.872366599
## 51 0.501492750 1.232357e+00 -1.677853269
## 52 0.511501750 1.340693e+00 -1.396698821
## 53 0.521510750 1.433634e+00 -1.275675929
## 54 0.531518750 1.520235e+00 -0.978752564
## 55 0.541527750 1.637669e+00 -0.430374222
## 56 0.551536750 1.752337e+00 0.048451564
## 57 0.561544750 1.953171e+00 0.474918384
## 58 0.571553750 2.114820e+00 0.716440477
## 59 0.581561750 2.086178e+00 0.864605632
## 60 0.591570750 1.855672e+00 1.007303641
## 61 0.601579750 1.674440e+00 1.142863735
## 62 0.611587750 1.520139e+00 1.076387178
## 63 0.621596750 1.217137e+00 1.144304196
## 64 0.631605750 9.073949e-01 1.429610313
## 65 0.641613750 6.331353e-01 1.536336325
## 66 0.651622750 2.284811e-01 1.520699554
## 67 0.661631750 -1.959805e-01 1.589180244
## 68 0.671639750 -3.438467e-01 1.801939956
## 69 0.681648750 -5.114723e-01 1.900622391
## 70 0.691656750 -6.756686e-01 1.880380646
## 71 0.701665750 -7.963972e-01 2.238161539
## 72 0.711674750 -8.965395e-01 2.529559870
## 73 0.721682750 -1.063409e+00 2.625833691
## 74 0.731691750 -1.211428e+00 2.528421125
## 75 0.741700750 -1.332968e+00 2.392993032
## 76 0.751708750 -1.413249e+00 2.380167311
## 77 0.761717750 -1.434801e+00 2.441563514
## 78 0.771725750 -1.572635e+00 2.383277591
## 79 0.781734750 -1.436104e+00 2.358347110
## 80 0.791743750 -1.469925e+00 2.203567950
## 81 0.801751750 -1.508198e+00 2.079792627
## 82 0.811760750 -1.618949e+00 1.848228854
## 83 0.821769750 -1.621166e+00 1.665285410
## 84 0.831777750 -1.560310e+00 1.565798105
## 85 0.841786750 -1.491021e+00 1.505131781
## 86 0.851794750 -1.324893e+00 1.353473718
## 87 0.861803750 -1.020861e+00 1.263427036
## 88 0.871812750 -6.260012e-01 1.187542017
## 89 0.881820750 -9.681703e-02 1.167786322
## 90 0.891829750 7.052204e-01 1.443462075
## 91 0.901838750 1.364807e+00 1.526305865
## 92 0.911846750 1.802843e+00 1.196814532
## 93 0.921855750 1.842680e+00 0.849504978
## 94 0.931864750 1.569607e+00 0.617141599
## 95 0.941872750 1.585893e+00 0.551225644
## 96 0.951881750 1.415101e+00 0.485368016
## 97 0.961889750 1.194818e+00 0.690079036
## 98 0.971898750 8.429247e-01 0.722313566
## 99 0.981907750 7.033089e-01 0.465643603
## 100 0.991915750 6.649571e-01 0.116038579
## 101 1.001924750 4.552379e-01 -0.276285325
## 102 1.011933750 3.011912e-01 -0.572348272
## 103 1.021941750 3.417049e-01 -0.678107739
## 104 1.031950750 6.402187e-01 -0.560568472
## 105 1.041958750 1.060421e+00 -0.348530598
## 106 1.051967750 1.335560e+00 0.008681946
## 107 1.061976750 1.368336e+00 0.158911242
## 108 1.071984750 1.391281e+00 0.085633350
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## 1097 10.970526500 -3.256342e+00 -3.013957248
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## 1099 10.990543500 -3.609804e+00 -1.999074154
## 1100 11.000551500 -3.704606e+00 -1.941027675
## 1101 11.010560500 -3.293613e+00 -1.123776961
## 1102 11.020569500 -2.986087e+00 -0.784968236
## 1103 11.030577500 -2.395531e+00 -0.499083830
## 1104 11.040586500 -1.329981e+00 -0.334122766
## 1105 11.050595500 -2.436406e-01 0.085374611
## 1106 11.060603500 -4.460084e-01 0.094231389
## 1107 11.070612500 3.477465e-01 0.557348995
## 1108 11.080621500 -7.295249e-02 0.236852580
## 1109 11.090629500 -7.035452e-01 -0.138451542
## 1110 11.100638500 -1.067688e+00 -0.291971358
## 1111 11.110646500 -7.415375e-01 -0.177889257
## 1112 11.120655500 3.212712e-01 0.487006990
## 1113 11.130664500 1.556035e+00 1.711666548
## 1114 11.140672500 2.231219e+00 3.092835603
## 1115 11.150681500 2.217454e+00 4.095640104
## 1116 11.160690500 2.046570e+00 4.625853925
## 1117 11.170698500 1.951451e+00 4.708189738
## 1118 11.180707500 1.458293e+00 4.717616619
## 1119 11.190716500 3.561551e-01 4.014486598
## 1120 11.200724370 -3.457576e-02 3.763976676
## 1121 11.210733370 -1.993667e-01 3.604332486
## 1122 11.220741380 -2.634463e-01 3.419917737
## 1123 11.230750370 -4.137379e-01 3.120144439
## 1124 11.240759370 -7.438097e-01 2.682566301
## 1125 11.250767370 -1.002804e+00 2.206332221
## 1126 11.260776370 -1.205305e+00 1.700970236
## 1127 11.270785370 -1.485194e+00 1.088838093
## 1128 11.280793370 -1.797220e+00 0.345958115
## 1129 11.290802370 -2.147939e+00 -0.237619150
## 1130 11.300811370 -2.465594e+00 -0.661931709
## 1131 11.310819370 -2.680443e+00 -1.042930434
## 1132 11.320828370 -2.766052e+00 -1.440052271
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## 1140 11.400897370 -4.658755e+00 -4.384630551
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## 1142 11.420914370 -4.085440e+00 -5.327657797
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## 1144 11.440931370 -3.485885e+00 -5.229940299
## 1145 11.450940370 -2.084151e+00 -3.626944254
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## 1148 11.480966370 -5.667735e-01 -1.955697462
## 1149 11.490975370 6.794248e-01 -2.199323456
## 1150 11.500983370 2.000448e+00 -2.218755362
## 1151 11.510992370 3.119977e+00 -2.168938692
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## 1153 11.531009380 4.741730e+00 -1.699050303
## 1154 11.541018370 6.209870e+00 -0.267466481
## 1155 11.551026370 7.133938e+00 1.074715533
## 1156 11.561035370 7.272910e+00 1.857527973
## 1157 11.571044370 7.124100e+00 2.452420478
## 1158 11.581052370 6.647963e+00 2.718709111
## 1159 11.591061370 6.678351e+00 2.908097794
## 1160 11.601070370 5.413893e+00 2.359012377
## 1161 11.611078370 5.234746e+00 2.336335706
## 1162 11.621087370 5.263705e+00 2.484785109
## 1163 11.631096380 5.132958e+00 2.489212913
## 1164 11.641104370 5.468586e+00 2.460070390
## 1165 11.651113370 6.182880e+00 2.496516670
## 1166 11.661122370 6.093015e+00 2.892868429
## 1167 11.671130370 5.517125e+00 3.563281817
## 1168 11.681139370 4.851327e+00 4.200490621
## 1169 11.691147370 4.146161e+00 4.422537466
## 1170 11.701156370 3.297393e+00 4.324515327
## 1171 11.711165370 2.131170e+00 3.868426074
## 1172 11.721173370 8.385451e-01 3.234185609
## 1173 11.731182370 -1.172823e-01 2.638410175
## 1174 11.741191370 -5.618782e-01 2.319818637
## 1175 11.751199370 -4.300691e-01 2.510387435
## 1176 11.761208370 2.171574e-01 2.933469448
## 1177 11.771216370 1.031161e+00 3.041494710
## 1178 11.781225370 1.793928e+00 2.555309839
## 1179 11.791234370 2.001848e+00 2.041720383
## 1180 11.801242370 1.842668e+00 1.830362979
## 1181 11.811251370 1.313847e+00 1.664501006
## 1182 11.821260370 6.530147e-01 1.557583060
## 1183 11.831268370 1.288832e-01 1.701564459
## 1184 11.841277380 -1.474463e-01 1.615255902
## 1185 11.851286370 -1.455600e-01 1.551651498
## 1186 11.861294370 2.652467e-01 1.651791206
## 1187 11.871303370 6.183723e-01 1.723517100
## 1188 11.881311370 8.750803e-01 1.445585345
## 1189 11.891320370 9.158511e-01 0.850853858
## 1190 11.901329370 7.095777e-01 0.300636639
## 1191 11.911337380 4.250745e-01 0.101096093
## 1192 11.921346370 2.389073e-01 0.059194635
## 1193 11.931355370 3.531227e-01 0.140604633
## 1194 11.941363370 3.663813e-01 0.024211493
## 1195 11.951372370 7.620325e-01 -0.008967326
## 1196 11.961381370 4.832379e-01 -0.490785461
## 1197 11.971389370 -3.819986e-03 -0.986811782
## 1198 11.981398370 -3.631396e-01 -1.625026307
## 1199 11.991406370 -6.930050e-01 -2.210087303
## 1200 12.001415370 -1.011292e+00 -2.611475269
## 1201 12.011424370 -1.131018e+00 -2.749035402
## 1202 12.021432370 -1.059886e+00 -2.600902918
## 1203 12.031441370 -1.100098e+00 -2.318084937
## 1204 12.041450370 -1.174996e+00 -2.052421957
## 1205 12.051458370 -1.245725e+00 -1.874860144
## 1206 12.061467370 -1.330176e+00 -1.919953579
## 1207 12.071476370 -1.333912e+00 -2.076066927
## 1208 12.081484370 -1.131789e+00 -2.160172547
## 1209 12.091493370 -9.004361e-01 -2.156296573
## 1210 12.101502370 -8.624146e-01 -1.992101349
## 1211 12.111510370 -6.955965e-01 -1.614891328
## 1212 12.121519370 -4.225701e-01 -1.277493975
## 1213 12.131527370 1.185424e-01 -1.090693853
## 1214 12.141536370 4.952141e-01 -0.919093569
## 1215 12.151545370 5.825844e-01 -0.724781237
## 1216 12.161553370 7.118716e-01 -0.518287547
## 1217 12.171562370 1.041903e+00 -0.243074163
## 1218 12.181571370 1.034975e+00 -0.287325453
## 1219 12.191579370 1.448107e+00 0.174538364
## 1220 12.201588500 1.548820e+00 0.368714602
## 1221 12.211597500 1.740602e+00 0.722039624
## 1222 12.221605500 2.095199e+00 1.230713034
## 1223 12.231614500 2.720921e+00 1.798901597
## 1224 12.241622500 3.409121e+00 2.501991418
## 1225 12.251631500 3.696305e+00 2.928468324
## 1226 12.261640500 3.650596e+00 2.753359711
## 1227 12.271648500 3.562075e+00 2.018805875
## 1228 12.281657500 3.303553e+00 1.247094301
## 1229 12.291666500 2.855195e+00 0.806407052
## 1230 12.301674500 2.356854e+00 0.506392849
## 1231 12.311683500 2.017858e+00 0.178602325
## 1232 12.321692500 1.785931e+00 -0.069640923
## 1233 12.331700500 1.489990e+00 -0.290399042
## 1234 12.341709500 1.241229e+00 -0.459183015
## 1235 12.351717500 9.902687e-01 -0.670844620
## 1236 12.361726500 7.657502e-01 -0.950956070
## 1237 12.371735500 5.514626e-01 -1.384651072
## 1238 12.381743500 2.834847e-01 -1.915831730
## 1239 12.391752500 -3.186148e-02 -2.366996750
## 1240 12.401761500 -3.047721e-01 -2.622763611
## 1241 12.411769500 -4.910813e-01 -2.553146369
## 1242 12.421778500 -4.131561e-01 -2.305849493
## 1243 12.431787500 -1.861385e-01 -2.043278227
## 1244 12.441795500 -1.576766e-01 -2.099102764
## 1245 12.451804500 2.073306e-02 -1.513187490
## 1246 12.461812500 1.052499e-04 -1.547684308
## 1247 12.471821500 -1.259525e-01 -1.752820421
## 1248 12.481830500 -1.756550e-01 -1.844813203
## 1249 12.491838500 -5.426216e-02 -1.720170153
## 1250 12.501847500 7.291127e-02 -1.388953161
## 1251 12.511856500 1.545735e-01 -0.857671638
## 1252 12.521864500 2.262364e-01 -0.252072882
## 1253 12.531873500 1.051534e-01 0.158701326
## 1254 12.541882500 7.361645e-02 0.396540916
## 1255 12.551890500 2.292366e-01 0.549253524
## 1256 12.561899500 3.621134e-01 0.860687632
## 1257 12.571907500 4.942780e-01 1.273040881
## 1258 12.581916500 6.648138e-01 1.754915771
## 1259 12.591925500 6.502946e-01 2.076872528
## 1260 12.601933500 6.873922e-01 2.254377330
## 1261 12.611942500 5.486086e-01 2.331205359
## 1262 12.621951500 2.590042e-01 2.381207238
## 1263 12.631959500 -9.579493e-03 2.695235171
## 1264 12.641968500 -2.259107e-01 2.891344352
## 1265 12.651977500 -3.355284e-01 2.879114901
## 1266 12.661985500 -3.239124e-01 3.024847687
## 1267 12.671994500 2.319064e-02 2.354017393
## 1268 12.682002500 5.057649e-01 1.427454737
## 1269 12.692011500 5.519544e-01 0.950331295
## 1270 12.702020500 1.667310e-01 0.712336170
## 1271 12.712028500 -4.611149e-01 0.392782326
## 1272 12.722037500 -2.146618e-01 0.699488375
## 1273 12.732046500 2.515294e-01 0.786921791
## 1274 12.742054500 8.393298e-01 0.517512207
## 1275 12.752063500 4.857683e-01 -0.063779967
## 1276 12.762072500 1.974219e-01 -1.084704404
## 1277 12.772080500 3.472957e-01 -2.080795425
## 1278 12.782089500 3.860726e-01 -2.499015770
## 1279 12.792097500 2.067140e-01 -2.528178758
## 1280 12.802106500 8.608799e-01 -2.589871269
## 1281 12.812115500 1.990542e+00 -2.381670630
## 1282 12.822123500 1.670347e+00 -2.447577960
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## 1284 12.842141500 -6.852978e-01 -3.686842546
## 1285 12.852149500 -1.810500e+00 -2.998295481
## 1286 12.862158500 -1.745523e+00 -2.981067537
## 1287 12.872167500 -4.408992e-01 -3.550655924
## 1288 12.882175500 9.634850e-01 -3.245832678
## 1289 12.892184500 1.399537e+00 -2.834433987
## 1290 12.902192500 1.563589e+00 -2.869678664
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## 1295 12.952236500 8.423507e-01 1.355481360
## 1296 12.962244500 1.216726e+00 1.995887129
## 1297 12.972253500 9.907796e-01 1.793831037
## 1298 12.982262500 2.712348e-01 1.375268337
## 1299 12.992270500 2.840186e-01 1.461849229
## 1300 13.002279500 1.209324e+00 -0.628190936
## 1301 13.012287500 1.195260e+00 -0.871904054
## 1302 13.022296500 7.826425e-01 -0.585753891
## 1303 13.032305500 5.861087e-01 -0.695458767
## 1304 13.042313500 2.867095e-01 -1.011695777
## 1305 13.052322500 -1.291496e-01 -1.138269870
## 1306 13.062331500 -5.747810e-01 -1.240335065
## 1307 13.072339500 1.761820e-01 -0.651010280
## 1308 13.082348500 6.139663e-01 -0.179870586
## 1309 13.092357500 4.929839e-01 0.060287132
## 1310 13.102365500 7.220240e-01 0.271075163
## 1311 13.112374500 6.826075e-01 0.412733903
## 1312 13.122382500 7.736748e-01 0.582935826
## 1313 13.132391500 3.127030e-01 0.326753813
## 1314 13.142400500 -3.396745e-01 0.036146025
## 1315 13.152408500 -7.108576e-01 -0.065999862
## 1316 13.162417500 -8.658523e-01 -0.007180088
## 1317 13.172426500 -9.198957e-01 0.053060558
## 1318 13.182434500 -8.830989e-01 0.036124391
## 1319 13.192443500 -2.689086e-02 -0.056130054
## 1320 13.202451670 -3.448980e-02 -0.154430520
## 1321 13.212459670 2.567786e-02 -0.041981547
## 1322 13.222468670 9.754911e-02 0.028538505
## 1323 13.232476670 -8.256300e-03 0.047220359
## 1324 13.242485670 -3.863977e-02 0.093233854
## 1325 13.252494670 7.442071e-02 0.059498051
## 1326 13.262502670 1.704005e-01 -0.024869378
## 1327 13.272511670 7.333125e-02 -0.079428577
## 1328 13.282520670 -1.654851e-01 -0.310931247
## 1329 13.292528670 2.327589e-01 -0.373919793
## 1330 13.302537670 1.284993e-01 -0.261388081
## 1331 13.312546670 1.263772e-01 -0.230492271
## 1332 13.322554670 1.405821e-01 -0.163997442
## 1333 13.332563670 1.001814e-02 -0.370387782
## Linear.Acceleration.z..m.s.2. Absolute.acceleration..m.s.2.
## 1 0.179841642 0.1845329
## 2 0.170617075 0.1866636
## 3 0.207270931 0.2384948
## 4 0.178349433 0.1908377
## 5 0.016100893 0.2636147
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## 7 -0.264427464 0.4728093
## 8 -0.144827346 0.2894146
## 9 0.063127125 0.1306076
## 10 0.200624986 0.2150532
## 11 0.235969065 0.2382875
## 12 0.248350545 0.2588205
## 13 0.178195066 0.2479770
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## 15 0.083967771 0.1395427
## 16 0.069415805 0.1517296
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## 18 -0.007069284 0.1598850
## 19 -0.031995379 0.2085533
## 20 0.194386007 0.3023398
## 21 0.237986939 0.3246785
## 22 0.246094689 0.3549095
## 23 0.252065865 0.3989950
## 24 0.189537495 0.4316334
## 25 0.185732127 0.4249524
## 26 0.133672612 0.6910563
## 27 0.260949540 0.9526556
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## 29 0.252117321 1.5671692
## 30 0.091351635 1.7277007
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## 32 -0.276734684 2.4068066
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## 36 -0.450388218 3.3019492
## 37 0.019744878 3.6156940
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## 40 -0.384404143 4.1764941
## 41 -0.347991777 3.7993142
## 42 -0.501140295 3.6296707
## 43 -0.879780838 3.6384017
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## 47 -1.166131852 2.7011835
## 48 -0.877871137 2.4414818
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## 50 0.148070796 2.1913040
## 51 1.013261077 2.3152956
## 52 1.861020223 2.6854465
## 53 2.001783754 2.7730479
## 54 1.772131435 2.5317034
## 55 1.752259673 2.4367181
## 56 1.771981162 2.4925792
## 57 1.917665709 2.7781047
## 58 2.351198158 3.2425121
## 59 2.495515627 3.3656023
## 60 2.452085432 3.2358772
## 61 2.620679955 3.3132840
## 62 2.404773272 3.0417704
## 63 1.942020532 2.5616984
## 64 1.660994577 2.3719305
## 65 1.200224043 2.0498116
## 66 0.827034275 1.7460574
## 67 0.449611123 1.6631453
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## 69 -0.284112700 1.9886401
## 70 -0.841693829 2.1681347
## 71 -0.832333606 2.5172197
## 72 -0.755770749 2.7881258
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## 74 -0.589730290 2.8650051
## 75 -0.744741731 2.8386370
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## 77 -0.666010727 2.9092020
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## 80 -0.080957040 2.6500837
## 81 -0.086980256 2.5705572
## 82 -0.258502480 2.4705808
## 83 -0.498205578 2.3768812
## 84 -0.484168167 2.2628987
## 85 -0.509208868 2.1789584
## 86 -0.629955041 1.9960147
## 87 -0.498221365 1.6990082
## 88 0.045980750 1.3432229
## 89 0.635161402 1.3328647
## 90 1.670911455 2.3179438
## 91 2.887132018 3.5394687
## 92 3.304565036 3.9500325
## 93 3.183532642 3.7751831
## 94 2.811847655 3.2788742
## 95 2.815159810 3.2778089
## 96 1.059992317 1.8334876
## 97 0.172294933 1.3904977
## 98 -0.491091855 1.2138493
## 99 -1.040617275 1.3395342
## 100 -1.245047629 1.4162544
## 101 -1.516861296 1.6076204
## 102 -1.811782282 1.9237603
## 103 -1.823030570 1.9748501
## 104 -1.123334619 1.4092543
## 105 -1.176599830 1.6218366
## 106 -1.652052722 2.1243995
## 107 -1.409920984 1.9711601
## 108 -0.841028708 1.6279821
## 109 -0.312478420 1.5363141
## 110 0.102927368 1.5972792
## 111 0.096629332 1.8752368
## 112 -0.292205831 2.0147447
## 113 -0.533250865 1.7798198
## 114 -0.736792442 1.8719006
## 115 -1.507458973 2.6723155
## 116 -1.719791254 3.2453832
## 117 -1.126360846 3.7056162
## 118 -0.968129343 3.6098480
## 119 1.541500585 5.0982808
## 120 2.638630323 5.3088458
## 121 2.781079021 4.7365710
## 122 2.491680730 3.7383503
## 123 1.972730986 2.6955550
## 124 1.231858503 1.6210443
## 125 0.821211033 0.8344815
## 126 0.475930610 0.7695976
## 127 0.472804688 1.0386292
## 128 0.641421723 1.4636068
## 129 0.482475544 1.8562687
## 130 0.426198140 2.3281896
## 131 0.422519657 2.7526192
## 132 -0.092560108 3.0249982
## 133 -0.488237245 3.3932484
## 134 -0.777190855 3.7845764
## 135 -0.759773315 3.8846195
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## 1169 -1.031883728 6.1493308
## 1170 -0.956145767 5.5216348
## 1171 -0.619546266 4.4598702
## 1172 -0.327493047 3.3571366
## 1173 -0.107305909 2.6431946
## 1174 -0.020286330 2.3869808
## 1175 0.104629054 2.5491080
## 1176 0.440211139 2.9742539
## 1177 0.535073149 3.2558080
## 1178 0.551390097 3.1704601
## 1179 0.782615828 2.9645413
## 1180 0.925632949 2.7572538
## 1181 0.537296005 2.1875660
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## 1183 -0.378983774 1.7480164
## 1184 -1.110770999 1.9658597
## 1185 -1.266451946 2.0081610
## 1186 -1.844316482 2.4900348
## 1187 -1.841907429 2.5972136
## 1188 -1.904704771 2.5462488
## 1189 -2.087205142 2.4329326
## 1190 -2.187848003 2.3196038
## 1191 -2.089998942 2.1351825
## 1192 -1.925979280 1.9416428
## 1193 -1.975624480 2.0118542
## 1194 -2.057163903 2.0896758
## 1195 -2.452209978 2.5678995
## 1196 -3.029429566 3.1067399
## 1197 -3.257089738 3.4032992
## 1198 -3.378841631 3.7668490
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## 1205 -3.229187702 3.9363162
## 1206 -3.268975373 4.0176847
## 1207 -3.395549758 4.1975153
## 1208 -3.366406650 4.1569203
## 1209 -3.005354825 3.8069092
## 1210 -2.461807013 3.2821823
## 1211 -2.200242638 2.8165220
## 1212 -1.902570537 2.3303071
## 1213 -1.688589049 2.0137026
## 1214 -1.260677236 1.6368498
## 1215 -0.921189065 1.3089315
## 1216 -0.676074954 1.1101624
## 1217 -0.289654399 1.1083983
## 1218 -0.237310709 1.1000210
## 1219 0.754139961 1.6420122
## 1220 0.969586761 1.8641067
## 1221 1.203444690 2.2359150
## 1222 1.430497336 2.8197230
## 1223 1.447560973 3.5685975
## 1224 1.680539187 4.5504151
## 1225 1.945680304 5.1013988
## 1226 2.085801811 5.0257743
## 1227 2.027895372 4.5690608
## 1228 1.950900406 4.0341936
## 1229 1.948537546 3.5495392
## 1230 1.870818987 3.0514187
## 1231 1.634211698 2.6027483
## 1232 1.261660738 2.1877355
## 1233 0.853765114 1.7416423
## 1234 0.466681776 1.4033139
## 1235 0.120014686 1.2021098
## 1236 0.126996262 1.2275255
## 1237 0.445543507 1.5555959
## 1238 0.804061734 2.0969716
## 1239 1.073484182 2.5992416
## 1240 1.178942225 2.8916569
## 1241 1.325550925 2.9183561
## 1242 1.657817785 2.8698431
## 1243 1.934536681 2.8199407
## 1244 1.924105248 2.8518898
## 1245 2.026016662 2.5288159
## 1246 2.064436377 2.5801597
## 1247 1.993115549 2.6572078
## 1248 1.863061778 2.6277728
## 1249 1.831820982 2.5134633
## 1250 1.691165917 2.1896459
## 1251 1.407189457 1.6551966
## 1252 1.091708784 1.1430449
## 1253 0.873085484 0.8936004
## 1254 0.802316340 0.8979842
## 1255 0.683242764 0.9061178
## 1256 0.862070206 1.2708558
## 1257 1.105068794 1.7567359
## 1258 1.118821153 2.1848267
## 1259 1.197842472 2.4841717
## 1260 0.934334775 2.5352922
## 1261 0.605097358 2.4701483
## 1262 0.594068924 2.4678227
## 1263 1.065159793 2.8980942
## 1264 1.322946575 3.1876473
## 1265 0.703616509 2.9827769
## 1266 -0.012020706 3.0421649
## 1267 -0.240141054 2.3663481
## 1268 -0.247638354 1.5345194
## 1269 0.153397025 1.1096458
## 1270 0.934165791 1.1865445
## 1271 2.130412558 2.2148505
## 1272 2.136588387 2.2584007
## 1273 1.821711146 2.0002861
## 1274 -2.082318040 2.3039839
## 1275 -2.895728887 2.9368835
## 1276 -2.758699973 2.9708559
## 1277 -1.809037306 2.7790178
## 1278 -2.261062160 3.3921282
## 1279 -2.901870217 3.8542534
## 1280 -4.140411065 4.9589869
## 1281 -4.613212245 5.5602465
## 1282 -3.786821163 4.8084000
## 1283 -3.463427453 4.8439884
## 1284 -3.762169302 5.3119073
## 1285 -5.171793832 6.2462097
## 1286 -6.051169458 6.9678021
## 1287 -5.271307595 6.3708895
## 1288 -3.481011785 4.8560453
## 1289 -1.052564306 3.3317579
## 1290 1.783864458 3.7231759
## 1291 4.570761459 5.7970973
## 1292 11.581989350 12.5660605
## 1293 8.128751253 8.7381219
## 1294 8.096439539 8.8140754
## 1295 -5.754772342 5.9719586
## 1296 -2.309775313 3.2861908
## 1297 0.299876794 2.0710867
## 1298 -1.125083814 1.7974273
## 1299 -1.165437788 1.8910090
## 1300 1.200243339 1.8159494
## 1301 0.648738636 1.6154646
## 1302 1.097455135 1.4697090
## 1303 1.502857214 1.7566349
## 1304 1.321364903 1.6887084
## 1305 1.405497565 1.8132185
## 1306 1.231306672 1.8398153
## 1307 0.410523655 0.7895468
## 1308 -0.297275367 0.7054648
## 1309 -0.546349797 0.7383534
## 1310 -0.580900994 0.9655290
## 1311 -0.224557639 0.8286907
## 1312 -0.141888535 0.9790399
## 1313 0.124890679 0.4692003
## 1314 0.224932446 0.4089987
## 1315 -0.146917140 0.7288752
## 1316 -0.406283839 0.9564614
## 1317 -0.123958633 0.9297254
## 1318 -0.117950619 0.8916732
## 1319 0.081857511 0.1028317
## 1320 0.575800468 0.5971470
## 1321 0.215518429 0.2210656
## 1322 -0.180105937 0.2068053
## 1323 -0.030365176 0.0567448
## 1324 -0.115383106 0.1532933
## 1325 -0.476053986 0.4854955
## 1326 -0.614890274 0.6385490
## 1327 -1.973560413 1.9765189
## 1328 -2.105034472 2.1342993
## 1329 -0.473888177 0.6469642
## 1330 0.427774111 0.5175195
## 1331 0.415230079 0.4914407
## 1332 -0.036709405 0.2191029
## 1333 -1.027819474 1.0925659
plot(tiktok$Time..s, tiktok$Linear.Acceleration.x..m.s.2.,
main="Linear Acceleration on X-axis vs Time",
xlab="Time", ylab="Linear Acceleration on X-axis", col="blue")
plot(tiktok$Time..s, tiktok$Linear.Acceleration.y..m.s.2.,
main="Linear Acceleration on Y-axis vs Time",
xlab="Time", ylab="Linear Acceleration on Y-axis", col="red")
plot(tiktok$Time..s, tiktok$Linear.Acceleration.z..m.s.2.,
main="Linear Acceleration on Z-axis vs Time",
xlab="Time", ylab="Linear Acceleration on Z-axis", col="green")
# Throughout all of these plots, it is very apparent that there are 3 distinct segments to the dance. X, y and z linear accelerations all experience a lot of variation during segment 2 of the dance, which makes sense since this involved the most hand motion out of all. It also make sense that segments 1 and 3 are most extreme (have the most changing accelerations) on the y axis, as I did move the phone and my hand back and forth a lot during those times.
# The following is an attempt at Fourier analysis based on the module from Canvas:
signal <- c(tiktok$Linear.Acceleration.x..m.s.2.)
fft_result <- fft(signal)
period <- 4
time <- seq(0, 10, by = 0.1)
sine_wave <- sin(2 * pi * time / period)
fft_result <- fft(sine_wave)
par(mfrow = c(2,1))
plot(time, sine_wave, type = "l", xlab = "Time", main = "Original Sine Wave")
plot(Mod(fft_result), type = "l", xlab = "Frequency", main = "FFT Magnitudes")
par(mfrow = c(2,1))
plot(time, sine_wave, type = "l", xlab = "Time", xlim = c(0,8), main = "Original Sine Wave")
plot(Mod(fft_result), type = "l", xlab = "Frequency", xlim = c(0,8), main = "FFT Magnitudes")
magnitudes<- abs(fft_result)
max_index_sine <- which.max(magnitudes)
paste("Highest Amplitude: ", magnitudes[max_index_sine])
## [1] "Highest Amplitude: 34.0785278077598"
paste("Frequency of Highest Amplitude: ",max_index_sine)
## [1] "Frequency of Highest Amplitude: 3"