# Colorado University Application of Correlation & Regression Discussion

Your task for this discussion is as follows:

- Use the internet to find a website that shows an example or application of correlation or regression in an area of interest in your personal or professional life.
- Discuss how correlation or regression was used, summarize your findings, and share them.
- Be sure to include the independent and dependent variable – discuss the impact/relevance of the independent variable.

here is an *exam*ple post:

Hello *Class*,

For this *week*’s *discussion* I was intrigued by a real life *exam*ple from a case study of SAT and College GPA scores that used a linear regression analysis. The study involved *exam*ining high school grades (GPA) of *students* to predict college performance (GPA) of 105 computer science majors. According to Holmes et al. (2017), regression analysis is a valuable method used to determine whether or not a cause and effect relationship exists and also measures the magnitude of that relationship. Hence, a scatter plot and approximation with a line of best fit is developed from the data points that can be represented by a simple linear equation, *Y’=bX + A.* A simple linear regression refers to a method for studying the association between two variables where one variable is the predictor or independent variable (known as the explanatory variable, *X*), and the other is the dependent variable, *Y* (Gopalan, 2020). Thus, a change in one variable can be used to predict the effects on another.

Source: University GPA as a function of High School GPA (Lane, n.d.).

In order to study the relationship between high school GPA and University GPA, a scatter plot was constructed (displayed above). It was determined that there was also a strong positive relationship among the variables with a correlation of 0.78 (Lane, n. d.). The regression equation used in the case study was *Y’=bX + A:* “University GPA’ = (0.675)(High School GPA) + 1.097, where, Y` denotes the predicted value (University GPA) , b denotes the slope of the line (0.675), X denotes the independent variable (High School GPA), and A is the Y-intercept (1.097). Thus, a student with a 3.0 H.S. GPA was predicted to have a 3.12 GPA in the University [University GPA’=(0.675)(3.0)+1.097=3.12] (Lane, n. d.). The study proved that there was a strong positive relationship between the prior and future performance of the ‘observed’ sample of *students*. Holmes et al (2017) states that when X and Y have a positive linear relationship, an increase in X, independent variable, will increase Y, the dependent variable. In other *words*, the impact of higher high school GPA had a positive impact on their college GPA. Thus, we could infer that there is a strong relationship between the variables and *students* that did well in high school will be expected to do well in college.

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