Data Science 1000

Exam prep

Individuals

An object described by a set of data

Variable

A characteristic of the individual

Categorical variable

Places individuals into one of several groups or categories

Quantitative variable

Takes numerical values for which arithmetic operations make sense

How are quantitative values usually recorded?

A unit of measurement

Exploratory data analysis

The process of using statistical tools and ideas to examine data in order to describe their main features

What does the distribution of a variable tell us?

What values it takes and how often it takes these values

Stems

Non decimals

Leaves

Decimals

Time plot

Shows behaviour over time

What is the most common measure of centre?

Mean

What is the median?

The midpoint of a distribution

What happens if the distribution is exactly symmetric?

The mean and median are exactly the same

First quartile (Q1)

The median of the observations located to the left of the median in the ordered list

Second quartile (Q2)

The median of the observations located to the right of the median in the ordered list

What percentage of the observations in a distribution are greater than the first quartile?

75%

What does a five number summary consist of?

Minimum, Q1, median, Q2, maximum

Standard deviation

The most common measure of spread looks at how far apart each observation is from the mean

What are all the values that a standard deviation S can take?

Greater than or equal to zero ( 0 < s )

What is n-1 called?

Degrees of freedom

When does S = 0?

Only when there is no variability

If the scale is adjusted so that the total area under the curve is exactly one, what is this called?

Density curve

What does a density curve describe?

The overall pattern of a distribution

What is the median of a density curve?

The equal areas point which divides the area under the curve in half

What is the mean of a density curve?

The balance point at which the curve would balance if it were made of solid material

Normal curves

All are symmetric, single peaked and bell shaped

Approximately what percent of observations fall within ơ of μ

68%

Approximately what percent of observations fall within 2ơ of μ

95%

Approximately what percent of observations fall within 3ơ of μ

99.7%

What is the standardized value often called?

Z-score

What is the standard normal distribution?

The normal distribution with mean 0 and standard deviation 1

Cumulative proportion for a value x in a distribution is what?

The proportion of observations in the distribution that are less than or equal to x

Response variable

Measures an outcome of a study

Explanatory variable

May explain or influence changes in a response variable

Two variables are positively associated when?

Above average values of one tend to accompany above average values of the other, and below average values also tend to occur together

Two variables are negatively associated when?

Above average values of one tend to accompany below average values of the other, and vice versa

What does the Pearson correlation coefficient r measure?

The direction and strength of the linear relationship between two quantitative variables

If the correlation between two variables is close to 0, you can conclude that a scatterplot would show?

No straight line pattern, but there may be a strong pattern of another form

Regression line

A straight line that describes how a response variable y changes as an explanatory variable x changes

When do we use a regression line?

To predict the value for y for a given value of x, when we believe the relationship between y and x is linear

Slope

The amount by which y changes when x increases by one unit

Intercept

The value of y when x=0

The least-squares regression line of y on x

The line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

The points on a scatterplot lie close to the line whose equation is y = 2 - x, therefore the slope of the line is what?

-1

Square of the correlation r²

The fraction of the variation in the values of y that is explained by the least-squares regression of y on x

r² near 0 means there is?

A weak linear relationship

r² near 1 means there is?

A strong linear relationship

What is a residual?

The difference between an observed value of the response variable and the value predicted by the regression line

Residual plot

A scatterplot of the regression residuals against the explanatory variable which helps us assess how well a regression line fits the data

What makes an observation influential?

If removing it would markedly change the result of the calculation

Extrapolation

Predicting outside of the range of x

Marginal distribution

The distribution of values of one of the categorical variables among all individuals described by the table

Conditional distribution

Describes the values of that variable among individuals who have a given value of another variable

Baseline risk

Risk without treatment or behaviour

Relative risk

Outcome for two categories of explanatory variable is ratio of risks for each category

Simpson's paradox

An association that hold for all of several groups can reverse direction when the data are combined to form a single group

The missing third variable

Simpson's paradox