# General Regression Questions

• JoeTarmet
In summary, the regression form of the sine function can be represented as y=asin(b(x-c))+d, where all variables except c can be determined mathematically. To determine c without graphing the data, non-linear optimization methods would need to be used to minimize a cost function, which is a statistical concept that involves minimizing the difference between the predicted and actual values. This method can be applied to all types of regression, including linear, cubic, and sinusoidal. However, understanding cost functions and optimization methods may require further explanation.

#### JoeTarmet

Sorry if this is somewhat elementary but the regression form of the sine function with data provided is y=asin(b(x-c))+d

As far as I know, all of the variables except c can be determined mathematically. My question is this, using calculus or any other method, is there a way to determine c without graphing the data?

As a follow up, is there a general formula or procedure that applies to all types of Regression (linear, Cubic, Sinusoidal, etc.)? I want to know this because I believe it is possible using statistical concepts like variance and I want to find out how many of these can be done completely by hand without graphing.

Your question is very confusing. Graphing isn't used to determine regression parameters, though it can be used to select general models for some very simple datasets. Generally, the parameters would be selected by minimizing some cost function (usually through least-squares), which in your case would require using some sort of non-linear optimization method, since your function is non-linear in its parameters.

Number Nine said:
Generally, the parameters would be selected by minimizing some cost function (usually through least-squares), which in your case would require using some sort of non-linear optimization method, since your function is non-linear in its parameters.

Please explain this further, I am interested in what you are saying about cost functions and optimization, but I don't understand these terms.

## 1. What is regression analysis?

Regression analysis is a statistical method used to identify and quantify the relationship between a dependent variable and one or more independent variables. It is commonly used to predict the value of the dependent variable based on the values of the independent variables.

## 2. What are the types of regression?

There are several types of regression analysis, including linear regression, logistic regression, polynomial regression, and multivariate regression. The type of regression used depends on the type of data and the research question being asked.

## 3. How is regression analysis different from correlation analysis?

Regression analysis and correlation analysis are both used to examine the relationship between variables. However, regression analysis also allows us to predict the value of the dependent variable based on the values of the independent variables, while correlation analysis only measures the strength and direction of the relationship between variables.

## 4. What is the purpose of regression analysis?

The main purpose of regression analysis is to identify and quantify the relationship between variables. This allows us to make predictions and understand the impact of independent variables on the dependent variable. Regression analysis is commonly used in fields such as economics, psychology, and social sciences.

## 5. What are the assumptions of regression analysis?

There are several assumptions that must be met for regression analysis to be valid, including linearity, independence of errors, homoscedasticity (equal variance), and normally distributed errors. Violations of these assumptions can affect the accuracy of the regression model.