assignment3
2026-09-01
Hypothesis:
There is no difference in average tire tread depth (TIRETREAD) between top tire manufacturers (TIREMANUF) and all other manufacturers.
1) Load CSV
tire_data <- read.csv("tire_data.csv")
#remove missing data
clean_data <- subset(tire_data, TIRETREAD < 90)
summary(tire_data)## source_file CASEID PSU CASENO
## Min. :1.000 Min. : 20282 Min. :10.00 Min. : 1.00
## 1st Qu.:2.000 1st Qu.: 25329 1st Qu.:18.00 1st Qu.: 34.00
## Median :3.000 Median : 30301 Median :26.00 Median : 68.00
## Mean :2.745 Mean : 882262 Mean :34.07 Mean : 73.96
## 3rd Qu.:4.000 3rd Qu.:2401844 3rd Qu.:52.00 3rd Qu.:106.00
## Max. :4.000 Max. :2406391 Max. :82.00 Max. :259.00
## CASENUMBER CATEGORY VEHNO TIRELOC
## Length :76640 Min. : 1.000 Min. :1.00 Length :76640
## N.unique :14409 1st Qu.: 3.000 1st Qu.:1.00 N.unique : 4
## N.blank : 0 Median : 4.000 Median :1.00 N.blank : 0
## Min.nchar: 16 Mean : 5.096 Mean :1.41 Min.nchar: 2
## Max.nchar: 17 3rd Qu.: 7.000 3rd Qu.:2.00 Max.nchar: 2
## Max. :22.000 Max. :7.00
## TIREMANUF TIREMODEL TIRESIZE TIRETIN
## Min. : 1.0 Length :76640 Length :76640 Length :76640
## 1st Qu.: 59.0 N.unique : 7536 N.unique : 610 N.unique :34699
## Median :103.0 N.blank : 0 N.blank : 0 N.blank : 0
## Mean :277.7 Min.nchar: 2 Min.nchar: 7 Min.nchar: 4
## 3rd Qu.:201.0 Max.nchar: 39 Max.nchar: 14 Max.nchar: 13
## Max. :999.0
## TIRETREAD TIRERESTR TIRESIZETYPE CASEWGT
## Min. : 0.00 Min. :0.000 Min. :1.00 Min. : 4.139
## 1st Qu.: 5.00 1st Qu.:0.000 1st Qu.:1.00 1st Qu.: 66.294
## Median : 6.00 Median :0.000 Median :1.00 Median : 164.057
## Mean :21.04 Mean :0.451 Mean :2.18 Mean : 617.972
## 3rd Qu.: 9.00 3rd Qu.:0.000 3rd Qu.:1.00 3rd Qu.: 455.966
## Max. :99.00 Max. :9.000 Max. :9.00 Max. :24230.454
## PSUSTRAT VERSION
## Min. : 1.000 Min. :6.000
## 1st Qu.: 4.000 1st Qu.:7.000
## Median : 7.000 Median :8.000
## Mean : 6.645 Mean :7.745
## 3rd Qu.: 9.000 3rd Qu.:9.000
## Max. :12.000 Max. :9.000Boxplot of Tire Tread Depth vs Tire Location
boxplot(TIRETREAD ~ TIRELOC, data = clean_data,
main = "Tire Tread Depth by Tire Location",
xlab = "Tire Location (LF, RF, LR, RR)",
ylab = "Tire Tread Depth")
Explanation: The tread depth distributions across all four tire
positions look nearly identical, indicating that tire location alone
does not create a dramatic difference in median tread depth across this
dataset.
2) Statistical Calculations:
Separate tread depth into Top Manufacturer (70) vs. Other Manufacturers
70 is the the numerical manufacturing code for specific tires. It is the most common frequently occuring manufacturer in my dataset.
top_manuf <- subset(clean_data, TIREMANUF == 70)$TIRETREAD
other_manuf <- subset(clean_data, TIREMANUF != 70)$TIRETREADMean and Standard Deviation calculations
mean_top <- mean(top_manuf)
sd_top <- sd(top_manuf)
mean_other <- mean(other_manuf)
sd_other <- sd(other_manuf)Print results
cat("Top Manufacturer Mean Tread:", mean_top, "\n")## Top Manufacturer Mean Tread: 6.206326cat("Top Manufacturer Std Dev:", sd_top, "\n")## Top Manufacturer Std Dev: 2.54403cat("Other Manufacturers Mean Tread:", mean_other, "\n")## Other Manufacturers Mean Tread: 6.09485cat("Other Manufacturers Std Dev:", sd_other, "\n")## Other Manufacturers Std Dev: 2.467963Simple barplot comparing means
means_vector <- c(mean_top, mean_other)
barplot(means_vector,
names.arg = c("Top Manufacturer", "Others"),
main = "Average Tire Tread Depth by Manufacturer Group",
ylab = "Mean Tread Depth")
Explanation: The top manufacturer group has a slightly higher average
tread depth (6.21) than all other manufacturers (6.09). This small mean
difference of 0.12 units suggests similar average wear levels between
the two groups.
3) Test 1:
Correlation test between Tire Size Type and Tire Tread Depth
cor.test(clean_data$TIRESIZETYPE, clean_data$TIRETREAD)##
## Pearson's product-moment correlation
##
## data: clean_data$TIRESIZETYPE and clean_data$TIRETREAD
## t = 27.864, df = 64317, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1015704 0.1168425
## sample estimates:
## cor
## 0.1092129Linear Regression Model
model <- lm(TIRETREAD ~ TIRESIZETYPE, data = clean_data)
model_summary <- summary(model)
model_summary##
## Call:
## lm(formula = TIRETREAD ~ TIRESIZETYPE, data = clean_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.3939 -2.0533 -0.0533 0.9467 16.9467
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.63575 0.01950 289.06 <2e-16 ***
## TIRESIZETYPE 0.41757 0.01499 27.86 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.462 on 64317 degrees of freedom
## Multiple R-squared: 0.01193, Adjusted R-squared: 0.01191
## F-statistic: 776.4 on 1 and 64317 DF, p-value: < 2.2e-16Extract R-squared and p-value
r_squared <- model_summary$r.squared
p_val <- model_summary$coefficients[2, 4]
cat("R-squared:", r_squared, "\n")## R-squared: 0.01192746cat("p-value:", p_val, "\n")## p-value: 7.50917e-170Scatter plot with fitted regression line
plot(clean_data$TIRESIZETYPE, clean_data$TIRETREAD,
main = "Regression: Tire Tread Depth by Tire Size Type",
xlab = "Tire Size Type",
ylab = "Tire Tread Depth",
)
Explanation: Although the p-value is extremely small because the dataset
is so large (indicating a statistically significant relationship), the
R^2 value is very close to zero (0.0119). This shows that tire size type
alone does not practically explain or predict tire tread depth.
Test 2:
Plot histogram of numerical column TIRETREAD
hist(clean_data$TIRETREAD,
main = "Histogram of Tire Tread Depth",
xlab = "Tire Tread Depth",
ylab = "Frequency",
)
Explanation: The histogram shows a right-skewed distribution for tire
tread depth (TIRETREAD). Most recorded values cluster heavily around
typical wear levels between 4 and 8, with fewer instances extending
toward higher values.
5) T.Test:
Divide data into two groups based on Manufacturer (Top vs Other)
group_top <- subset(clean_data, TIREMANUF == 70)$TIRETREAD
group_other <- subset(clean_data, TIREMANUF != 70)$TIRETREADApply two-sample t-test
t_test_result <- t.test(group_top, group_other)
t_test_result##
## Welch Two Sample t-test
##
## data: group_top and group_other
## t = 3.4621, df = 8617.9, p-value = 0.0005385
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.04835913 0.17459278
## sample estimates:
## mean of x mean of y
## 6.206326 6.094850Explanation of Results: Even though the practical difference in tread depth is small (6.21 vs 6.09), the dataset’s large sample size gives the test high statistical power to confirm that the minor difference between manufacturer groups is statistically significant rather than being random.