Statistics IV - Formula and Graphs

Question 1

What is the formula for the covariance of variables x and y?

Answer 1

Question 2

What is the formula for the correlation of variables x and y?

Answer 2

Question 3

What is the formula for the z-score of x?

Answer 3

Question 4

What’s the formula for the mean-centred variable?

Answer 4

Question 5

What’s the formula for linear regression?

Answer 5

Question 6

Explain all variables in this formula:

Answer 6

x … independent variable

y … dependent variable

ß0 … y-intercept

ß1 … slope

epsilon … error

Question 7

In linear regression: What consists of ß0 and ß1?

Answer 7

coefficient of regression

Question 8

The regression line always fits through the _______ of both variables.

Answer 8

The regression line always fits through the means of both variables.

Question 9

What’s the formula for the slope of a linear regression?

Answer 9

Question 10

What’s the formula for the y-intercept of a linear regression?

Answer 10

Question 11

In linear regression: What’s the formula for Var(epsilon) and where can we derive this formula from?

Answer 11

Question 12

What’s the formula of the coefficient of determination in linear regression?

Answer 12

Question 13

What is the mathematical connection between correlation and coefficient of determination?

Answer 13

Question 14

Four examples of how a regression can look like:

Answer 14

Question 15

How does a log function / Sigmoid-curve look like?

Answer 15

Question 16

How could a two point regression look like?

Answer 16

Question 17

Simply put, what is the formula for variance?

Answer 17

S²_x = 1/n * ∑ (x_i - xˉ)²

Question 18

Simply put, what is the formula for standard deviation?

Answer 18

Sx = √(Sx²)

Question 19

Simply put, what is the formula for correlation?

Answer 19

rxy = Sxy / SxSy

Question 20

Simply put, what is the formula for covariance?

Answer 20

S_xy = 1/n*∑(x_i - x¯)(y_i - y¯)