Types of regression and linear regression equation

1.The term regression was first used as a statistical concept in 1877 by Sir Francis Galton. 2.Regression determines ‘cause and effect’ relationship between variables, so it can aid to the decision-making process. 3.It can only indicate how or to what extent variables are associated with each other. 4.There are two types of variables used in regression analysis i.e. The known variable is called as Independent Variable and the variable which we are trying to find out or predict is the dependent variable. 5.To increase accuracy level; we can increase the no. of independent variables. 6.Scatter diagrams:-

To determine a relationship between two variables is to examine the graph of the observed ( or known )data. This graph is called as a ‘Scatter diagram’. a.Direct Linear relationship

Here as Y increases, X also increases. It is because of high degree of association of data.

b) Inverse linear relationship

In this relationship as Y decreases X increases so it called as inverse linear relationship C) Direct curvilinear relationship

In this diagram it shows a positive curvilinear relationship between X and Y axes. The values of Y increases as X increases; but this increase tapers off beyond certain values of X. This you can say it is “Learning curve”. The employees of many industries, experience learning curve; that is as they produce new product, the time time required to produce one unit is reduced by some fixed proportion as the total no. of units doubles. E.g. Aviation Industry, as manufacturing time per unit for a new aircraft tends to decrease by 20 per cent each time the total no. of completed new planes doubles.

d) Inverse Curvilinear relationship

e) Inverse linear with more scattering

e) In this diagram, it shows widely scattered patterns of points. The wider scattering indicates that there is a lower degree of association between Independent and dependent variable....

...for new house or automobile is very much affected by the interest rates changed by banks.
Regression analysis is one such causal method. It is not limited to locating the straight line of best fit.
Types:-
1. Simple (or Bivariate) Regression Analysis:
Deals with a Single independent variable that determines the value of a dependent variable.
Ft+1 = f (x) t Where Ft+1: the forecast for the next period.
This indicates the future demand is a function of the value of the economic indicator at the
present time.
Demand Function: D=a+bP, where b is negative.
If we assume there is a linear relation between D and P, there may also be some random variation in this relation.
Sum of Squared Errors (SSE): This is a measure of the predictive accuracy. Smaller the value of SSE, the more accurate is there regression equation
EXAMPLE:-
Following data on the demand for sewing machines manufactured by Taylor and Son
Co. have been compiled for the past 10 years.
YEAR | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 | 1977 | 1978 | 1979 | 1980 |
DEMAND (in 1000 Units) | 58 | 65 | 73 | 76 | 78 | 87 | 88 | 93 | 99 | 106 |
1. Single variable linear regression
Year = x where x = 1, 2, 3... 10
Demand = y
D = y + ᵋ Where D is actual demand
ᵋ = D –y
To find out whether this is the line of best fitted or not it is to be made sure that this sum of squares is minimum.
2. Nonlinear Regression...

...
Logistic regression
In statistics, logistic regression, or logit regression, is a type of probabilistic statistical classification model.[1] It is also used to predict a binary response from a binary predictor, used for predicting the outcome of acategorical dependent variable (i.e., a class label) based on one or more predictor variables (features). That is, it is used in estimating the parameters of a qualitative response model. The probabilities describing the possible outcomes of a single trial are modeled, as a function of the explanatory (predictor) variables, using a logistic function. Frequently (and subsequently in this article) "logistic regression" is used to refer specifically to the problem in which the dependent variable is binary—that is, the number of available categories is two—while problems with more than two categories are referred to as multinomial logistic regression or, if the multiple categories are ordered, as ordered logistic regression.
Logistic regression measures the relationship between a categorical dependent variable and one or more independent variables, which are usually (but not necessarily) continuous, by using probability scores as the predicted values of the dependent variable.[2] As such it treats the same set of problems as doesprobit regression using similar techniques.
Fields and examples of...

...Applied Linear Regression Notes set 1
Jamie DeCoster
Department of Psychology
University of Alabama
348 Gordon Palmer Hall
Box 870348
Tuscaloosa, AL 35487-0348
Phone: (205) 348-4431
Fax: (205) 348-8648
September 26, 2006
Textbook references refer to Cohen, Cohen, West, & Aiken’s (2003) Applied Multiple Regression/Correlation
Analysis for the Behavioral Sciences. I would like to thank Angie Maitner and Anne-Marie Leistico for
comments made on earlier versions of these notes. If you wish to cite the contents of this document, the
APA reference for them would be:
DeCoster, J. (2006). Applied Linear Regression Notes set 1. Retrieved (month, day, and year you
downloaded this ﬁle, without the parentheses) from http://www.stat-help.com/notes.html
For future versions of these notes or help with data analysis visit
http://www.stat-help.com
ALL RIGHTS TO THIS DOCUMENT ARE RESERVED
Contents
1 Introduction and Review
1
2 Bivariate Correlation and Regression
9
3 Multiple Correlation and Regression
21
4 Regression Assumptions and Basic Diagnostics
29
5 Sequential Regression, Stepwise Regression, and Analysis of IV Sets
37
6 Dealing with Nonlinear Relationships
45
7 Interactions Among Continuous IVs
51
8 Regression with Categorical IVs
59
9 Interactions involving Categorical IVs
69...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly Auto Insurance Premium
5 2 12 9 15 6 25 16
$64 87 50 71 44 56 42 60
a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables? b. Compute SSxx, SSyy, and SSxy. c. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. d. Interpret the meaning of the values of a and b calculated in part c. e. Plot the scatter diagram and the regression line. f. Calculate r and r2 and explain what they mean. g. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. h. Compute the standard deviation of errors. i. Construct a 90% confidence interval for B. j. Test at the 5% significance level whether B is negative. k. Using α = .05, test whether ρ is different from zero.
Solution a. Based on theory and intuition, we...

...Determinants of Production and Consumptions
Determinants of Industry Production (Supply)
Supply is the amount of output of production that producers are willing and able to sell at a given price all other factors being held constant.
The following are the determinants of supply:
Price (P), Numbers of Producers (NP), Taxes (T)
Model Specification
Specification of model is to specify the form of equation, or regression relation that indicates the relationship between the independent variables and the dependent variables. Normally the specific functional form of the regression relation to be estimated is chosen to depict the true supply relationships as closely possible.
The table presented below gives the hypothetical quantity supplied for a particular product (Qs) of a particular place given its price per kilo (P/kl), the Numbers of producers (NP), and tax per kilo (T/kl) for the period 2002 to 2011. (The quantity Supplied is expressed as kilo in millions)
Table
|Year |Qs |P/kl |NP |T/kl |
|2002 |21.4 |23 |39 |1.15 |
|2003 |23.9 |25 |41 |1.25 |
|2004...

...Chapter 13
Linear Regression and Correlation
True/False
1. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a rather weak correlation.
Answer: False Difficulty: Easy Goal: 1
2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable.
Answer: True Difficulty: Easy Goal: 1 AACSB: AS
3. An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
Answer: True Difficulty: Medium Goal: 1 AACSB: REF
4. There are two variables in correlation analysis referred to as the dependent and determination variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables.
Answer: True Difficulty: Easy Goal: 2 AACSB: AS
6. The purpose of correlation analysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7. Originated by Karl Pearson about 1900, the coefficient of correlation describes the strength of the relationship between two, interval or ratio-scaled...

...l
Regression Analysis
Basic Concepts & Methodology
1. Introduction
Regression analysis is by far the most popular technique in business and economics for
seeking to explain variations in some quantity in terms of variations in other quantities, or to
develop forecasts of the future based on data from the past. For example, suppose we are
interested in the monthly sales of retail outlets across the UK. An initial data analysis would
summarise the variability in terms of a mean and standard deviation, but the variation from
outlet to outlet could be very large for a variety of reasons. The size of the local market, the
size of the shop, the level of competition, the level of advertising, etc.. would all influence the
sales volume from outlet to outlet. This is where regression analysis can be useful. A
regression analysis would seek to model the influence of these factors on the level of sales. In
statistical terms we would be seeking to regress the variation in sales ⎯ the dependent
variable ⎯ upon several explanatory variables such as advertising, size, etc..
From a forecasting point of view we can use regression analysis to develop predictions. If we
were asked to make a forecast for the monthly sales of a proposed new outlet in, say, Oxford,
we can simply compute the average outlet sales and put this forward as our prediction ⎯ i.e.
ignoring specific characteristics of the Oxford...

...Nonlinear regression
From Wikipedia, the free encyclopedia
Regression analysis
Linear regression.svg
Models
Linear regression Simple regression Ordinary least squares Polynomial regression General linear model
Generalized linear model Discrete choice Logistic regression Multinomial logit Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Multilevel model Fixed effects Random effects Mixed model
Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal components Least angle Local Segmented
Errors-in-variables
Estimation
Least squares Ordinary least squares Linear (math) Partial Total Generalized Weighted Non-linear Iteratively reweighted Ridge regression LASSO
Least absolute deviations Bayesian Bayesian multivariate
Background
Regression model validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem
Portal icon Statistics portal
v t e
See Michaelis-Menten kinetics for details
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.
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