Regression analysis

-

 Regression analysis

  • Regression like , relation is a study of a relationship between variables 
  • Simple regulation : single explanatory variable 
  • Multiple regression : includes any  number of explanatory variables
  • Dependent  variables : The single variable being explained/ predicted by the regression model
  • Independent variable: Explanatory  variables used to predict the dependent variable
  • Residuals :Portions of dependent variables  is not explained by the model
  • Correlation  tests or closeness and direction of relationship between the two phenomena . Regression  gives the nature and extent of this  relation, so that prediction  can be made about dependent variable, for any value of independent variable.
  • Clearly designates one  variable as cause and the other effect , unlike the correlation
  • Linear regression :straight line relationship, Y=mx+c
  •  In least square method of regulation ‘m’ and ‘b’ are calculated by equating the differencal of Loss Function (Yi-Pi) to zero
  • Formula:-

Y_i=f(X_i, \beta)+e_i
Y_i= dependent variable
f= function
X_i= independent variable
\beta= unknown parameters
e_i= error terms


  • Non linear regression : implies third relationships. e.g Logarithmic relationships
  • Cofficient of determination(R^2) : Sum of sq explained by a regression /total number sum of Squares. It lies between 0 and 1 .if R^2=1 it means 100% of variation in Y is explained by variation in X
Graph :-






Application:-

  • Spectrophotometry and similarother and analytical techniques
  • Used to model real life situation for which outcomes is  uncertain. Modelling the appropriate probability distribution can help to make predictions and inferences.
  • Probability of an event varies between 0 and 1 

Popular posts from this blog

Chapter -2 Biological classification

-
Image
  Biological classification is the scientific procedure of arranging organisms into groups and subgroups on the basis of their similarities and dissimilarities and placing the group in a hierarchy of categories. Importance of classification :-  It is not possible to study every organism. Study of one or two organism of a group gives sufficient information about the essential features of the group. It helps in identification of new organism. Classification helps in knowing the relationship amongst different groups of organisms. The organism of past cannot be studied without a proper system of classification. Classification :-  (i)Artificial system of classification (ii)Natural system of classification (iii)Phylogenetic system of classification (i)Artificial system of classification- Only one or two morphological characters for grouping of organism is used. Flowering and non-flowering plants, enaima and anaima. Aristotle classification. (ii)Natural system of classification- Takes into
Read more

Human Eye

-
Image
 Human Eye The human eye is a remarkable and complex organ responsible for vision, allowing us to perceive the world around us. It collects and processes light, converting it into electrical signals that are interpreted by the brain as visual images. Here's a detailed description of the eye's anatomy and its main components: Anatomy of the Eye: External Structures: 1. Eyebrows: The eyebrows are located above the eyes and serve to prevent sweat and other particles from falling into the eyes. They also play a role in nonverbal communication and facial expressions. 2. Eyelashes: Eyelashes are situated at the edges of the eyelids and help protect the eyes by sensing and reducing the amount of light, dust, and debris that enters. 3. Eyelids (Palpebrae): The upper and lower eyelids cover and protect the front of the eye. They also help distribute tears over the surface of the eye, keeping it moist and clean. 4. Conjunctiva: A thin, transparent membrane that covers the front
Read more

Origin of Bilateria

-
Image
 Origin of Bilateria                                        First meta zones are very likely to radial animals Believed that bilateral symmetry evolved in radical ancestor when it is started creeping There are several theories given by many scientists for the Bilateria symmetrical animals are as follows:- 1.Ctenophore polyclad Theroy  :-  Ctenophores provided a a bridge or intermediate forms between                 radiate coelonterate and ancestors  and bilateral polyclad flat warms. Based on resemblance:- Oval flat and shaped with dorsal ventral differentiation Creeping on entire ventral surface Presence of two dorsal tentacles Centrally located ventral mouth Radiating, anastomosing nervous system Swimming larval stages of polycalds have eight ciliated lobes and comparable  to 8 comb rows of ctenophore  Limitations:- Cleavage is biradical in ctenophore but spiral in polyclad  Acoel flatworms are now regarded to be a most primitive 2.Planuloid-Acoeloid Theroy:-   Ludwig Von Graft form
Read more