Exam 3 Complete Set

Line of regression

line that makes the squares of the vertical distances of the data points as small as possible(from the line)

(line of best fit)

When is it appropriate to compute line of best fit?

When the scatterplot has linear form

Coefficient of Determination

R²
Explains what proportion of the variation in the y variable is explained by the regression of y on x.

R vs R² range

R= -1 to 1

R²=0 to 1

R² Interp

R² of 0 means that none of the variation of y is explained by the

regression, while an R² of 1 means that all of the variation is

explained by it.

extrapolation

the process of estimating values or predicting trends outside the range of known data points, risky

Causation

x causes y

common response

x and y are both caused by a third unmeasured variable z

Confounding

It is difficult to distinguish the effects of x and z on y

Coincidence

As demonstrated, it’s possible that The relationship is just dumb luck.

Random phenomenon

When individual outcomes are uncertain, but there is a regular distribution of outcomes when a large number of observations are made

Probability

A number between 0 and 1 that represents the proportion of times that the outcome would occur in a very long series of repetitions.

Discrete random variable

takes countable separate values (usually whole-number outcomes like 0, 1, 2, 3…).

Continuous random variable

takes any value within a range (including decimals)

Exact Probability

Exact probability is usually impossible in real life because it would require endless trials, so we use estimates from data instead.

The myth of short-term regularity

the false belief that random outcomes must quickly “even out” in a small number of trials.

The myth of streaks

Overrating the probability of something occurring due to a large streak of prior chances

The myth of surprising coincidence

The false belief that unlikely coincidences are too amazing to happen by chance, even though rare events happen often in large numbers.

Personal probabilities

personal judgements about the likelihood of certain events with no mathematical basis

Law of Averages(or high numbers)

In a large enough number of trials, the rate at which a certain event occurs will almost surely approach the probability

“One or the other occurs” rule

If two events have no outcomes in common, then the probability that one or the other occurs is the sum of their individual probabilities

“both occur” rule

If two events are independent, the probability they BOTH occur, is the product of their probabilities.

68-95-99.7 Rule

68% of data is within 1 Std

95% of data is within 2 Std

97% of data is within 3 Std

Z score formula

(observation - mean)/Std

Expected value

can be thought of as the “average outcome” of an event with numerical values

Expected value formula