# Mis 650 discussion response

Discussion 1: Anthony coles

Univariate linear regression is used to locate a relationship between one dependent or independent variable. The intercept, which is labeled as a constant, is the point where the function crosses the y axis. Without an intercept, the regression line goes through the origin and the dependent and independent variable is equal to zero. When removing the intercept, the variable almost always become significant with a p value less than 0.05 and the R2 increases considerably. In some instances, it makes sense to remove the intercept. However, when looking to calculate predicted values, the best practice would be not to completely remove this from the analysis.

Why is intercept important in regression analysis? | (analyticsinsight.net)

Discussion 2: Meredith Carter

The intercept is often referred to as the “constant”. It is the expected mean of the dependent variable (y) when the independent variable (x) is equal to zero (Grace-Martin, n.d.). However, if the independent variable is never zero, then the intercept is of no interest since it will not help to determine the relationship between the two variables. In order for the intercept to have meaning in a dataset where the independent variable never equals zero, the independent variable needs to be rescaled so that the intercept can be calculated and meaningful.

More often than not, the intercept is actually meaningless. But that doesn’t mean that it isn’t important in linear regression modeling. A significant constant simply means that it is significantly different than zero. Whether or not the intercept is significant is of no real importance.

Frost, J. (n.d.). How to interpret the constant (y-intercept) in regression analysis. Statistics by Jim. Retrieved on September 24, 2021 from https://statisticsbyjim.com/regression/interpret-constant-y-intercept-regression/

Grace-Martin, K. (n.d.). Interpreting the intercept in a regression model. The Analysis Factor. Retrieved on September 24, 2021 from https://www.theanalysisfactor.com/interpreting-the-intercept-in-a-regression-model/

Discussion 3:David Lundholm

“Linear regression is a statistical method to find the relationship between one dependent and one or more independent variables and is widely used to explore and model the relationship between variables”. The variable analysts are predicting is called the dependent variable and is denoted as Y, while the variables being based on predictions on are known as independent variables also referred as X. Univariate linear regression is commonly used to describe the relationship between a single independent variable (x) and a dependent variable (y). For example, when wanting to estimate the relationship between a person’s weight (y) given their height (x). The intercept, also known as the constant, represents the point where the function crosses the y-axis. Depending on what analysis is being done, “some models become more significant when the intercept is removed, and the regression line reduces to Y = bX + error”. Theoretically, when the intercept term is significant, you can reject the null hypothesis that the constant equals zero. Also, when the constant is statistically significant, the confidence interval will not include zero. This matters because it is more difficult to interpret the constant and draw conclusions about it when concluding that it doesn’t equal zero.

References:

Becominghuman. (WeiQin Chuah). (April 7, 2021). Univariate Linear Regression: Explained with Examples. https://becominghuman.ai/univariate-linear-regression-clearly-explained-with-example-4164e83ca2ee

Analytics Insight. (Ashish Sukhadeve). (July 10, 2016). Why is intercept important in regression analysis? https://www.analyticsinsight.net/why-is-intercept-important-in-regression-analysis/