Weekly Math Problem! #38

Linear Regression. I scanned my current problems list and said, "Hmm...🤔... I don't see STATISTICS on here." I thought it would be fun to do a little linear regression so, here we are. I think STATISTICS is cool, however, there are many instances when performing the calculations can make you feel a little dizzy. 😵 This is why we're grateful for software. 🙃 

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to find the regression line using the Least Squares method
        ✔️     How to use the regression line
        ✔️     How to interpret the slope regression line

You'll have to lookup the formulas and so will I. Perform the calculations by hand and use software to check. I know the numbers a little big but, we'll be okay. (You may want to do the calculations in stages, if doing it in one sitting is too much.) Alright, here goes WMP! #38:

Happy solving!

Check back on Friday, February 19th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Hopefully, you're not mad at me for these calculations. 🥴 Somehow, I found this to be a little, key phrase "a little", therapeutic. Yeah, I know, I know, I'm weird...but who isn't? 🤷🏿‍♀️ I will acknowledge that mistakes can easily be made, especially if you're not paying attention. I had to check my work...a must. I entered the data in Google Sheets to do so. Let's get started shall we...

a. To find the equation of the regression line, certain calculations are needed. We'll start with squaring and multiplying the data points, as needed, organizing them in chart. That information will, then, be used to calculate the intercept and the slope of the regression line. Finally, the equation of the regression line can be written.

   

b. To estimate the blood pressure, we'll use the equation of the regression line from part a. How? Substitute the age 50 in place of x, then perform the indicated operations. The answer you get will be the estimated blood pressure, assuming no computation errors were made.

c. In our situation, the residual is the difference between the blood pressure of a 42-year old as observed in the data and the estimated blood pressure of a 42-year old as computed from the regression line equation.

d. To interpret the slope, keep in mind the context of the problem and think about how the blood pressure number changes, when the age of a person increases by one year.

I hope you found this helpful. I sure did! It was super helpful for me, actually. Part d. was my favorite part of the problem because, it required to me explain the meaning of the slope. Interpreting/explaining numbers reminds me that it isn't always about what the number is. Just as important is what the number means. This is how reports get written. This helps with decision making in certain sectors. 

But before we go, I just have one more thing to share...a scatter plot of the data from the problem with the fitted regression line.

*This plot was created using Google Sheets.*

▪️ Did you find this problem hard, annoying, or something else?

▪️ How did you feel about STATISTICS, in general?

▪️ Leave your response down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

L👀ks like WMP! #39 is quickly approaching.

Cheers!

The Younge Lady