# Discussion responses

Instructions: There are 4 responses, Write a 75 word response for each.

Response 1.) Deborah

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Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest.   Regression analysis is used to predict the value of a dependent variable based on the value of at least one independent variable.  The dependent variable is the main factor that you’re trying to understand or predict.  The independent variables are the factors that you hypothesize have an impact on your dependent variable.

For Example,  medical researchers often use linear regression to understand the relationship between drug dosage and blood pressure of patients.  Linear regression is one of the most commonly used techniques in statistics. It is used to quantify the relationship between one or more predictor variables and a response variable.  Researchers administer various dosages of a certain drug to patients and observe how their blood pressure responds. They might fit a simple linear regression model using dosage as the predictor variable and blood pressure as the response variable.

Reference

:

Alchemer.  What is Regression Analysis and Why Should I Use It?

Levine, D. M., Stephan, D. F., K. A. (2021).  Statistics for managers using Microsoft Excel(9th ed.). Pearson.

Response 2.) Bryana

The regression intercept is a constant variable that depicts the point on the y-axis where the line of greatest fit crosses. When the independent variable is zero, it represents the value of the dependent variable y. When there is a unit change in the independent variable, the slope of regression reveals the unit change in the dependent variable.

The intercept of the regression line is its height when x = 0, corresponding to men with 0 years of education. Such men are 12.5 years below average in education. And each year costs \$1,400-that is what the slope says. A man with no education is predicted to have an income which is below average by

12.5 years x \$1,400 per year = \$17,500.

So, his income is predicted as \$19,700 – \$17,500 = \$2,200. This is the intercept: the predicted value of y when x = 0. (See figure 3.)

Zero years of education may sound extreme, but there were several men who reported having no education, and their incomes ranged from \$0 to about \$12,000; their points are in the lower left corner of figure 1.

Associated with each unit increase in x there is some average change in y. The slope of the regression line says how much this change is. The formula for the slope is

Response 3.) Korrickia

Levine et al., (2020) defines simple linear regression as models which examines the straight line (linear) relationship between a dependent Y variable and a single independent X variable.  We can use this example, the director of planning for Overcomers Organic Burger Bar suspect that the greater the number of profiled households who reside within a fixed radius of a store, the greater the store sales will be.  We want to determine if a linear relationship between the number of profiled customers, as the numerical independent X variable, and annual store sales, as the dependent Y variable, exists.

Linear regression analysis is based on six fundamental assumptions:

• The dependent and independent variables show a linear relationship between the slope and the intercept.
• The independent variable is not random.
• The value of the residual (error) is zero.
• The value of the residual (error) is constant across all observations.
• The value of the residual (error) is not correlated across all observations.
• The residual (error) values follow the normal distribution.
• Multiple regression models use two or more independent variables to predict the value of a dependent variable.  Overcomers Organic Burger Bar’s objective is to determine the effect that price and in-store promotional expenses will have on sales, calls for examining a multiple regression model in which the price of an OOBB in cents (X1) and the monthly budget for in-store promotional expenses in dollars (X2) are the independent variables and the number of OOBB sold in a month (Y) is the dependent variable.  The only exception with this model in comparison to the simple linear model is independent variables should show a minimum correlation with each other. If the independent variables are highly correlated with each other, it will be difficult to assess the true relationships between the dependent and independent variables.

References

CFM Team (2022, April 26).

Regression Analysis – Formulas, Explanation, Examples and Definitions (corporatefinanceinstitute.com)

Levine, David, M. et al. (2020). Statistics for Managers Using Microsoft Excel. Available from: Yuzu, (9th Edition). Pearson Education (US)

Response 4.) Mary

An example of simple linear regression.  The equation to predict weight if we knew an individual’s height. In this example, if an ind ividual was 70 inches tall, we would predict his weight to be: Weight = 80 + 2 x (70) = 220 lbs.  This simple linear regression is examined for the impact of one independent variable on the outcome.

Linear regression is a statistical modeling process that compares the relationship between two variables, which are usually independent or explanatory variables and dependent variables. For variables to model useful information, it’s helpful to make sure they can provide meaningful insight together. For example, variables about brand engagement and product demand levels might be useful, while variables about brand engagement and production time may not produce as much insight.  When solving linear regression, it’s important to use these types of visuals to help you locate the values you need to complete calculations for evaluating different business metrics. If you plan to use linear regression regularly, regression analysis software can streamline this process.

For example, researchers might administer various dosages of a certain drug to patients and observe how their blood pressure responds. They might fit a simple linear regression model using dosage as the predictor variable and blood pressure as the response variable.

Reference

Levine, D. M., Szabat, K. A., & Stephan, D. (2021).  Statistics for managers using Microsoft Excel.  Pearson.  ISBN-13: 978013596854

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