rowSums(my_mat)
colSums(my_mat)
mean(my_vec, trim = 0, na.rm = FALSE, ...)  
# trim is used to drop some observations from both end of the sorted vector; 
# When trim = 0.3, 3 values from each end will be dropped from the calculations to find mean. 
# na.rm is used to remove the missing values from the input vector. 
# If there are missing values, then the mean function returns NA; 
# To drop the missing values from the calculation use na.rm = TRUE.

# elementwise sum
my_vec1 + my_vec2  
# sum of vector elements: 
sum(my_vector)

mean(my_vector)
seq(a,b,length.out=n)
crossprod(x_vec,y_vec)

ceiling(x)
floor(x)
trunc(x, ...)
round(x, digits = 0)
signif(x, digits = 6)

# absolute value
abs()
# absolute difference
abs(x1-x2) 

mean()
nchar(my_vec)  
# counts number of characters in a vector of characters (strings)

max(my_data, na.rm = FALSE, ...)
min(my_data)
summary()
var()
median()

# confidence intervals: 
inference(my_dav, type="ci", method="simulation", conflevel=0.9, est="mean", boot_method="perc")
# method=simulation, theoretical
# boot_method=perc, se
# est=mean, median, proportion

# hypothesis testing: 
inference(y = nc$weight, x = nc$habit, est = "mean", type = "ht", null = 0, alternative = "twosided", method = "theoretical")
# alternative=”greater”
inference(us12$response, est = "proportion",  type = "ci", method = "theoretical",  success = "atheist")

# compare: 
by(numerical_dataset, categorical_dataset, mean/length/...)
cor(var1, var2)

# http://www.rdocumentation.org/packages/stats/versions/3.3.1/topics/sd?

# probability (in/dependent events and simulating event sequences)
# simulate: 
possible_values <- c("heads", "tails")
sample(possible_values, size=, replace=, prob=c())

# generate sample distribution: The sampling distribution is calculated by resampling from the population,
# the bootstrap distribution is calculated by resampling from the sample; 
# To construct the 95% bootstrap confidence interval using the percentile method, 
# we estimate the values of the 5th and 95th percentiles of the bootstrap distribution.
# Set up an empty vector of 5000 NAs to store sample means:
sample_means50 <- rep(NA, 5000)

# Take 5000 samples of size 50 of 'area' and store all of them in 'sample_means50'.
for (i in 1:5000) {
 samp <- sample(area, 50)
 sample_means50[i] <- mean(samp)
}

# View the result. If you want, you can increase the bin width to show more detail by changing the 'breaks' argument.
hist(sample_means50, breaks = 13)

# calculate 95 pct conf interval:
se <- sd(samp)/sqrt(60)
lower <- sample_mean - 1.96 * se
upper <- sample_mean + 1.96 * se
c(lower, upper)

# inference:
# ANOVA test: https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php, https://explorable.com/anova 

# multivariate regression, looking for the best model:
# start with a full model: 
m_full <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval + cls_students + cls_level + cls_profs + cls_credits + bty_avg, data = evals)
# check p values for each coefficient; drop one with highest p-value
# drop the variable that, when dropped, leads to the best improvement in R2

# create an array: 
array_name = np.array(list_name)
np.array([list1],[list2])
np.column_stack((list1, list2))

# subsetting arrays is the same as for lists, plus:
# conditional selection: 
bmi[bmi>23]; 
# access specific cell: 
array_name[row,col]

# check dimensions: 
a_name.shape, a_name.size
# calculate average: 
np.mean(list_name)
# calculate median: 
np.median(list_name)
# calculate st dev: 
np.std(list_name)
# check correlation: 
np.corrcoef(list1,list2)
# add: 
np.sum(list_name)
# simulate random data: 
np.round(np.random.normal(mean, stdev, #obs), 2)

import random
random.choice(strname)
random.randint(a_inclusive,b_inclusive)