# Colorado University Application of Correlation & Regression Discussion

1. 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.
2. Discuss how correlation or regression was used, summarize your findings, and share them.
3. Be sure to include the independent and dependent variable – discuss the impact/relevance of the independent variable.

here is an example post:

Hello Class,

For this week’s discussion I was intrigued by a real life example from a case study of SAT and College GPA scores that used a linear regression analysis. The study involved examining 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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