# Bivariate Linear Regression Analysis

### Prompt 1

Use U.S. Census Bureau data, which you can find at the following link: https://www.census.gov/quickfacts/fact/table/US/PST045219. In the search box, enter the name of a state. Click on the state name when it comes up. You’ll see a column for that state added to the data table on the website. Choose 6-12 states. Choose two rows in the table that contain variables that you think are interesting. Copy down the values for the states you chose.

State Bachelor's degree or higher, percent of persons age 25 years+, 2014-2018 Median household income (in 2018 dollars), 2014-2018
Arizona 28.9 56,213
California 33.3 71,228
Idaho 26.9 53,089
New Mexico 27.1 48,059
Oregon 32.9 59,393
Utah 33.3 68,374
Washington 35.3 70,116
Wyoming 26.9 62,268

### Prompt 2

Identify which variable you want to be the explanatory variable and which you want to be the response variable.

For the explanatory variable (x) I chose “Bachelor's degree or higher, percent of persons age 25 years+, 2014-2018”, and for the response variable (y) I chose “Median household income (in 2018 dollars), 2014-2018”.

### Prompt 3

Compute the correlation coefficient r for your data and identify the critical value. State whether or not there is a significant linear relationship.

The correlation coefficient (rounded to three places) is 0.741, which is greater than the critical value of 0.632 for sample size 10. Therefore, we can expect a positive linear correlation with “Bachelor's degree or higher, percent of persons age 25 years+, 2014-2018” and “Median household income (in 2018 dollars), 2014-2018”.

### Prompt 4

Give the regression equation.

ŷ = 1206.28483x + 24252.7615

# Reflection

### Prompt 1

Identify specific parts of the assignment and your own process in completing it that may have applications for other classes.

Doing the mathematical calculations for this assignment manually would have been stressful and time-consuming. As is the case for many well-known formulas, there were existing and ready-made programatic approaches that I was able to find with a little exploration or research. For this assignment I used Microsoft Excel to perform the calculations, and more specifically: the CORREL function, which I used to calculate the correlation coefficient before comparing it to the critical value in the Critical Values for the Correlation Coefficient table in the formula card to determine if a linear correlation was present; and the linear regression analysis function of the Analysis Toolpak add-in, which I used to calculate the slope and y-intercept of the regression equation.

There’s a takeaway from this which applies to my chosen career of computer science. Often when solving a problem in code, there’s no need to “reinvent the wheel” by writing a solution manually from scratch. Chances are someone else has already encountered a similar problem, and posted a solution online which can be adapted to my project. Using and sharing these ready-made solutions is beneficial as it saves both time and stress.

### Prompt 2

Discuss how this assignment changed the way you think about real-world math applications. If your thinking was not changed, then discuss how the assignment supported your views about real-world math applications. (Note that this question is not about YOUR individual life or career. While you may include that if relevant, the question is about the broader world.)

I never really considered the equations or methods behind the statistics I saw plastered all over advertisements, news reports, and online articles. It was just some unknown process that happened in the background, done by experts that clearly knew what they were doing. This assignment, and the course in general, has changed my perception of statistics in the media. Now I find myself asking questions like “does the raw data support this conclusion?” and “what is the confidence level for this claim?” which I never gave much thought to before. Knowing some of what is going on behind the scenes has enhanced my ability to think critically about the conclusions that people arrive at based on mathematical processes.