Week 1: Central Tendency, Varibality Measures, Z-Score, Linear Regression, Correlation, R Squared, Predicted values, Residual

Question 1

1. What type of variables are these?
Country
Income
Temperature
IQ
PH
Cancer types
Hair color
Socio-economic statuscolor
Number of Pets
2. What central tendency and measures of variability can we calculate for each?

Answer 1

1. Country - Nominal (Mode only)
Income - Ratio (median, mode, mean, IQR, Var, SD)
Temperature - Interval (all of them)
IQ - Interval (all)
PH - Interval(all)
Cancer types - Nominal (mode only)
Hair colour - Nominal (mode)
SES - oridnal (median, mode)
nr of pets - ratio (median, mode)

Question 2

What graphs do we use for numerical/qualitative variables?

Answer 2

Qualitative - bar chart

Numeric - histogram, boxplot

Question 3

Central Tendency
What is 
1. Mean
2. Median
3. Mode

Answer 3

1. Mean - average, typical (sum of var/nr of var)
2. Median - the middle, order it ten pick middle
3. Mode - the most frequent value

Question 4

Measures of Variability
What is: (formulas)
1. Variance
2 Standard Deviation
3. IQR

Answer 4

1. Variance: how much the subject differ from each other
   Population Var: sigma^2=x1-miu^2/population size
   Sample Var: xi-mean value of all observ^2/n-1
2. SD: measure the number of variations/ dispersion of a set of values
   Formula same as Var(x) but all with root square
3. IQR: spread of data, also midpsread
   1s quartile- 2nd quartile

Question 5

What is a normal distribution?

Answer 5

mean=median=mode
empirical rule: 68/95/99.7% 1/2/3 SD
wel discribed by its SD
unimodal
symmetrical
centered
fixed score distirbution

Question 6

The Standard Normal Distibution is…

Answer 6

a ND with mean: 0 and Variance: -1

Question 7

Describe the +/- skewness

Answer 7

+ right skewed - mode>median>mean

- negaive skewed - mode>median>mean

Question 8

What is the Z-Score?

Answer 8

• How far is an observation from the mean in terms of SDs
• The nr of SDs by which the value of raw score is above or below the mean value of what is being observed
• The standardized score
  Z =(observed value-men)/SD
• if we extend 1 SD above the mean and 1 SD below=> approx 68% of the observations are within the interval
• Approx 95% of the populations would be between 2 SD above the mean and 2 SD below for a ND
• Also, if x is normally distirbuted, then 1 is ND, with mean=0 and SD=1

Question 9

What is the Correlation Coefficient?

Steps

Answer 9

Way of sum a scatter plot into an nr between -1 and 1
Steps
1. fits a straight line to the data
2. the cc rememebrs if the slope of the striaght line points downwards or upwards
if slope + => coeff (0-1)=> positive
if slope - => coeff (1-0)=> negative
is flope striaght => coeff is 0 => closer to 0 the weaker it is
3. looks at the quality of the fit of the straight line of the data

Question 10

What is Pearson Correlation (Formula)

IN LINEAR REGRESSION ONLY !

Answer 10

• summ the strength and direction of a straight-line relationship
  1. strength - the closebess of the points to a straight line
  2. direction - if one var generally increases or decreases
  rxy= (xi-x mean values)(yi- y mean values)/squar root (xi-x)(yi-y)^2

Question 11

What is Linear Regression Analysis?

Answer 11

used to predict the value of a variable based on the value of another variable
describes the average relation between y-values and x-values
the points on the regression line are predicted by y-values and denoted by y hat
explores the relation btw a quantitative response var and oneor more explanatory

Question 12

Regression Line is fully determined if:

Answer 12

• > the intercation with te y-axis is known–> intercept

- > it is known how steep the line is–> slope

Question 13

Formulas for:
Regression Line
Regression Model

Answer 13

RL: Y hat=b0(intercept)-b1(slope) x Xi
RM: Yi= Y hat i+ ei=b0+b1 x Xi+ei (residual)

Question 14

How R squared and rxy are related?

Answer 14

R^2=rxy

Question 15

About simple linear regression

Answer 15

One explanatory variable→simple regression
Multiple explanatory variables→multiple regression
- describes the average relation between Y values and X values
–> used whe y is numeric or continuous, x var as well
limited because it is useful for summ associations only

Y Hat = estimated value
Y Line = predicted value for an individual

Question 16

What is R squared? Coefficient of Determination

Answer 16

indicates the percentage of variability of y explained by the variable x
tells us how good a regression line estimates/ predocts actual values

Question 17

What is an Error? What is Residual?

Answer 17

both are obersed errors for a set of data
difference between observed y and estimated y
= (yi-y hat)
distance between regression line and theactual observed value

Question 18

What is the independ and dependent var?

Answer 18

x- independent
y - dependent
x- explained var
y - response var
e.G 
x - type of treatment (indep)
y - blood pressure (dep)
treatment --> effect--> on blood pressure

Question 19

What does a low/high variance indicate?

Answer 19

A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another.

Question 20

What is the difference between the predicted and actual Y score?

Answer 20

The residual

Question 21

How high can R squared go

Answer 21

up to 1 only!

Question 22

If the dots on a scatter plot are spread out randomly, the researcher would report the correlation as

Answer 22

close to 0

Question 23

What is a negative correlation

Answer 23

A negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.
e. g:
The more often a person visits the dentist, the fewer cavities she/he will have.