Multiple linear regression, also known as multiple regression, is a statistical technique. This technique uses explanatory variables for predicting an outcome of a variable. It aims to check the relationship between dependent and independent variables. The explanatory variables are independent, while the response variable is dependent. The formula for multiple regression is as follow:
Here i mean the number of observations
Yi is the dependent variable
Xi is the independent variable
β0 is y-interception that is a constant term
βp is the slope of coefficients for every independent variable
ϵ means error term
This way, we know the relative relationship of one variable on the other. The multiple regression model allows us to predict more variables. We can predict them based on their relationship. There are two major purposes of using regression analysis, and those are:
- To predict the value of a dependent variable
- To check the effect of the independent variable on the dependent variable.
Regression analysis is very useful in real-life scenarios. We, as researchers, can use it to get valuable insights about consumer behavior. This way, we will know how consumers make choices. Apart from this, we can use it to understand the business better. It also helps to identify the factors that can lead to profit or loss.
We need to follow several instructions to formulate research questions for multiple regression. This article aims to discuss how we can develop them. So, let’s discuss the steps in detail:
Develop Research Questions for Multiple Regression:
To formulate research questions for multiple regression, we need quantitative data. It will help us to identify and quantify the variables. These questions also require hypotheses that we develop while developing research questions. The key to writing research questions for regression is to understand the regression model. Using the model, we find the relationship between x and y variables. However, if you face still any confusion, you can get help from best dissertation writing services.
Example of Multiple Regression Research Question:
What factors can affect the punishment length of a convicted murderer? Use sample data from no more than 50 metropolitan areas of the UK. The dependent variable is punishment length in days that a murderer received. We can examine this dependent variable with several independent variables. Our independent variables can be age, sex, and race. Characteristics and criminal history of murders can also be our variables. Keeping these factors in mind, we will collect the relevant data. This way, we check the relationship between the independent and dependent variables.
While working on multiple regression, we have to follow assumptions too. Several assumptions will help us to find a relationship. Here are a few assumptions of the multiple regression model:
- Between dependent and independent variables, there must be a linear relationship. We can check this aspect after using scatterplots and partial regression plots. If there is a non-linearity among the variables, we should go for non-linear analysis.
- All variables must be multivariate normal. We can check this with the help of a histogram.
- According to the third assumption, there is a little multicollinearity between variables. We will only know this aspect when variables are highly correlated to each other. Further, we can text this aspect with three different criteria. Correlation matrix, tolerance and variance inflation factors will help us to test this aspect. If there is multicollinearity in the data, it will help to solve the problem.
- Another assumption is no or little autocorrelation in the data.
- Homoscedasticity is the final assumption about multiple regression. We can check this assumption with the help of the scatter plot technique. The Goldfeld-Quandt test is another to test this aspect of the data.
So, these are the top five assumptions for multiple regression. We must keep them in mind to formulate research questions. These assumptions will also help while collecting the data.
Data Analysis Tool and Interpretation of Results:
There are several tools that can help to analyze the collected data. But, SPSS and Stata are widely used tools for regression analysis. Students and researchers can use these tools in regression as well as business analysis. After analyzing the data, the researcher interprets the results to prove the established hypothesis. The value for the level of significance is 5%. This way, we either accept or reject our hypotheses.
Regression analysis is a statistical technique. We use it to find a relation between dependent and independent variables. This article summarizes different ways to formulate research questions for regression analysis.The regression analysis is run on different tools like SPSS, STATA etc. These tools and techniques are considered an important part of dissertation and require some professional expertise. If you are unsure about your skills then you can also seek online help.