Multi Regression Problem for Wine Quality
The purpose of this regression analysis was to test wine quality. An evaluation like this would help assure quality for the wine market. We collected or data from “Machine Learning Repository” a data mining website. The data we obtained from Machine Learning Repository compares variables such as fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphate, and alcohol to help identify the quality of the wine

The first step in or regression analysis was to use SAS to run a stepwise and backward elimination test in order to remove any unneeded variables. The summary of the stepwise and backward elimination test determined that pH, total sulfur dioxide, volatile acidity, density, alcohol, and sulphate were all variables that could be removed from our models we were comparing. Once the unneeded variables were eliminated, three models were created and compared against one another to determine which model was best. The variables for model one were color, fixed acidity, citric acid, residual sugar, and free sulfur dioxide , u=5.8255 + .2117x1 - .1104X2 + 1.4832X3 - .0597X4 + .0183X5. The variables used in model two were color, citric acid, residual sugar, and free sulfur dioxide, u=5.0404 +.3279x1 + 1.1687X2 - .0607X3 + .0183X4. Model three variables were citric acid, residual sugar, and free sulfur dioxide, u=4.9968 + 1.6035X1 - .0577X2 + .02188. Once the models were set up we compared there t and p-values with one another and found that model three had the best p-values and also the lowest variance inflation factors so model three was chosen as the best model.

After running model three whose variables are citric acid, residual sugar, and free sulfur dioxide in SAS the results of the variance inflation factors showed no signs of multicollinearity. The next step was to run a complete regression analysis of model three. The residual by...

...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 Analysis...

...
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...

...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...

...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...

...employees as the source of the problem, Kaizen stresses that its objective is the process and that employees can deliver improvements by understanding how their roles fit in the process and thus recognize their ability to change it. A process-oriented approach puts emphasis on to the employees to understand why a process works, whether it can be altered, revised or replicated elsewhere in the organization and ultimately how it can be improved.
As for the employee-oriented approach, Kaizen emphasizes on the management to make the work place more humane by taking genuine interest in the employees, reward good work and encourage involvement and commitment in improvement activities. Also it must be assured that worker’s physical over exertion (classified as Muri in lean manufacturing terms) is minimized and that employees are trained and empowered to be investigative, innovative, to get involved and become knowledgeable so that they can take decisions themselves and thus be self-driven and recognize opportunities for continual improvement by themselves.
Kaizen is thus is applied by the employees which like experimenting scientists gauge the effects resulting from the purposely applied small changes on their respective areas of responsibility, and then adjusting accordingly for a desirable outcome, transforming the applied change an improvement. A good example for an organization which is people-oriented is Toyota which instructs its workers to: “Identify...

...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...

...associated with a β1 change in Y.
(iii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 ln(Xi ) + ui is as
follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a β1 change in Y.
(c) a change in X by one unit is associated with a 100β1 % change in Y.
(d) a 1% change in X is associated with a change in Y of 0.01β1 .
(iv) To decide whether Yi = β0 + β1 X + ui or ln(Yi ) = β0 + β1 X + ui fits the data better, you
cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear
model.
(d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regression functions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...
(vi) The following are properties of the logarithm function with the exception of
(a) ln(1/x) = −ln(x).
(b) ln(a + x) = ln(a) + ln(x).
(c) ln(ax) = ln(a) + ln(x).
(d) ln(xa) = aln(x).
(vii) In the log-log model, the slope coefficient indicates
(a) the effect that a unit change in X has on Y.
(b) the elasticity of Y with respect to X.
(c) ∆Y/∆X.
(d)
∆Y
∆X
×
Y
X
(viii) In the...

...Background
Wine was once viewed as a luxury good, but now it is increasingly enjoyed by a wider range of consumers. According to the different qualities, the prices of wines are quite different. So when the wine sellers buy wines from wine makers, it’s important for them to understand the winequality, which is in some degrees affected by some chemical attributes. Whenwine sellers get the wine samples, it makes difference for them to accurately classify or predict the winequality and this will differentiate their profits. So our goal is to model the winequality based on physicochemical tests and give the reference for wine sellers to select high, moderate and low qualities of wines.
We download winequality data set that is the white vinho verde wine samples from the north of Portugalthe from UC Irvine Machine Learning Repository. This white wine data set includes 4898 observations and 12 variables, among which quality is the dependent variable, and other 11 attributes- fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphates, and alcohol-are independent variables.
Technical summary...