Question

give two examples in any area of interest to you (other than those already presented in this chapter) where regression analysis can be used as a data analytic tool to answer some questions of interest. For each example:

a. what is the question of interest?

b. Identify the response and the predictor variable.

c. Classify each of the variables as either quantitative or qualitative.

d. Which type of regression (see table 1.15) can be used to analyze the data?

e. Give a possible form of the model and identify its parameters.

Table 1.15

Type of Regression

Univariate. Multivaritae - Only one quantiative response variable. Two or more quantitative response variables

Simple. Mutiple - Only one predictor variable. Two or more predictor variables

Linear - All parameteres enter the equation linearly, possibly after transformaton of the data

Nonlinear - The relationship between the response and some of the predictors is nonlinear or some of the parameteres appear nonlinearly, but no transformation is possible to make the parameters appear linearly.

Analysis of variance - All predictors are qualitative variables

Analysis of covariance - Some predictors are quantitative variables and others are qualitative variables

Logistic - The response Variables is qualitative

Answer 1

Hello,

Univariate-Only one quantiative response variable.

Example: success and failure of students is depends on the hours of study.

            Responce – Suceess or failure

            Independent variabl – number of study hours

Model, y=a+bx+e,

Multivaritae - Two or more quantitative response variables

Example: Grade of student in exam is depends on the hours of study.

            Response – Grade of student(A,B,C,D)

            Independent variable – number of study hours

Model, y=a+bx+e,

Simple. Mutiple - Only one predictor variable. Two or more predictor variables

Ans- The above both examples contains the one predictor variables.

Two predictor variables:
Example: Grade of student in exam is depends on the hours of study and teaching methods.

            Response – Grade of student(A,B,C,D)

            Independent variable – number of study hours and teaching methods.

Model, y=a+b1x1+b2x2+e,

Linear - All parameters enter the equation linearly, possibly after transformation of the data:

Ans –

Example-

on-linear function of model parameters and one or more independent variables. There are several common models, such as Asymptotic Regression/Growth Model, which is given by:

b1 + b2 * exp(b3 * x)

Logistic Population Growth Model, which is given by:

b1 / (1 + exp(b2 + b3 * x)), and

Asymptotic Regression/Decay Model, which is given by:

b1 – (b2 * (b3 * x)) etc.

Analysis of variance - All predictors is qualitative variables

Example: testing of the several treatments on the human.

Response: continuous

Independent variable: different treatment

Objective: all treatment has equal effect.

Analysis of covariance - Some predictors is quantitative variables and others are qualitative variables

ANS- Example

Example: testing of the several treatments on the humans considering age and sex has some effect.

Response: continuous

Independent variable: different treatment

Covariates – age and sex

Objective: all treatment has equal effect along with the covariates.

Logistic - The response Variables is qualitative

Logistic regression is used when the response variable is categorical

Logistic regression is a predictive modelling algorithm that is used when the Y variable is binary categorical. That is, it can take only two values like 1 or 0. The goal is to determine a mathematical equation that can be used to predict the probability of event 1. Once the equation is established, it can be used to predict the Y when only the X’s are known.

Response: categorical (Nominal or Ordinal)

Independent variable – both (Continuous or categorical)