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Flashcards in regression analysis Deck (27)
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1

when did lenarde create method of least squares 

1805

2

when did gauss use method of least squares 

1809

3

when did sir galton coin 'REGRESSION'

1822-1911?? how long he lived 

4

when was George Yule's joined distrubution assumed to be Gaussian

1851-1952

5

when was Karl pearson's joined distribution assumed to be Gaussian

1857-1936

6

when did sir ronald fisher weaken the assumption of yule and pearson 

1980-1962

7

what 's the earliest form of regression 

method of least squares by 

  • LEGENDRE 1805
  • GAUSS 1809

used for astronomic observations - orbits of comets and minor planets around the sun

 

8

what did gauss do in 1821

Gauss published a further development of the theory of least squares, including a
version of the Gauss–Markov theorem

9

what did Francis galton do in 1890

the term "regression" was coined by Francis Galton to describe a biological phenomenon which was 

'heights of descendants of tall ancestors tend to
regress down towards a normal average'

10

when did  Udny Yule and  Karl Pearson extend Galton's work in   

1897-1903 

 

Galton’s work was later extended by Udny Yule and
Karl Pearson to a more general statistical context.
In the work of Yule and Pearson, the joint
distribution of the response and explanatory
variables is assumed to be Gaussian.

11

when did R.A. fisher weaken pearson and yule

1922-1925

  • his assumption is simular to Gauss's in 1821
  • he states that 'conditional distribution of the response
    variable is Gaussian, but the joint distribution need not
    be'

 

12

when did Economists use electromechanical desk calculators to calculate regressions.

1950s-1960s

13

before what date did it take up to 24 hours to
receive the result from one regression

before 1970

14

types of statistical modelling 

deterministic and probabilistic models 

15

types of probabilistic models 

  1. regression models
  2. correlation models
  3. othe models

16

types of regression modells 

  • simple: 1 explanatory variable
    • linear or non-linear
  • multiple: 2+ explanatory variables
    • linear or non linear

17

what is regression analysis 

the nature and strength of of the relationship betw/ variables can be examined by regression and correlation analysis

regression: 

assessment of the specific forms of the relationship between variablles in order to predict/estimate the value of one variable corresponding to a given value of another variable.

18

7 steps of regression modelling 

  1. Define the problem or question
  2. Specify model

  3. Collect data

  4.  Do descriptive data analysis

  5. Estimate unknown parameters

  6. Evaluate model

  7. Use model for prediction

19

simple vs mx  regression analyis 

 

simple

  • 𝛽 is the unit change in Y per unit change in X
  • doesn't take into account any other variable besides the single independent variable

multiple

  • 𝛽𝑖 is the unit change in Y per unit change in Xi

  • takes into account the effect of other 𝛽𝑖s

  •  it is the net regression coefficient

20

 6 assumptions required for regression analysis

  1. CONTINUOUS V: the two variables should be either interval or ratio variables

  2. LINEARITY: the Y variable is linearly related to the value of the X variable

  3. INDEPENDENCE OF ERROR: the residual error is independent for each value of x

  4. NO SIGNIFICANT OUTLIERS: outliers can have a negative effect on the analyisis

  5. HOMO-SCEDASTICITY: the variation around the line of regression is constant for all values of X (random errors have a constant variance) 

  6. NORMALITY: the values of Y be normally distributed at each value of X

21

what is the goal of regression analysis 

to be a statistical model that can  predict values of a dependant(response) variable based on the values of the independent (expanatory) variable

22

what is SİMPLE LİNEAR REGRESSİON

describes the linear relationship between a predictor/independant variable, plotted on the x-axis, and a response/ dependant variable, plotted on the y-axis

23

what is the simplest model of the relationship
between two interval-scaled attributes,Straight line

 a Straight line= 

  • it's slope shows the  existence of an association between them.
  • thus an objective way to investigate an association betw interval attributes is to draw a
    straight line through the center of the cloud of points and measure its slope.
  •  

24

what if the slope is 0

line is horizontal and we conclude that there is no association.

non zero= association

 

25

which 2 problems must be solved when drawing a straight line 

  1. determine how to draw a straight line that best models the relationship between attributes and
  2. how to determine whether its slope is different from zero.

 

26

what is the linear regression model 

staetes that : Relationship Between Variables Is a Linear Function

 

 

27

what is the THE ORDINARY LEAST SQUARE METHOD

  • square errors occur w/ best fit because  although the diff bet/w actual Y & predicted Y are minimal but positive differences off-set negative.???
  • LEAST SQUARE minimizes the Sum of the Squareds and reduces square errors/ deviations around the line 
  • used to determine the line of best fit