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 ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 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

Weekly Math Problem! #15

Quadrilaterals. Listen, geometry is not necessarily a favorite topic in mathematics for a lot of people. So, now you're thinking, "What about you, Lori? How do you feel about geometry?"  Well, it's not my favorite either 😅; I'm not in love with geometry. 🤷🏿 I will say, I am very visual, so I love the fact images, and the need to draw pictures, are a crucial part of geometry. I have lots of respect for this topic. Geometry is everywhere.

This week's problem was taken from the last administered NYS Regents High School Examination in Geometry before quarantine--January 2020, Part III, question 32. To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Plotting points on the coordinate plane

    ✔️  Slope, distance, midpoint formulas

    ✔️  Properties and theorems for quadrilaterals

    

WMP! #15 says...

Happy solving! 

Check back on Friday, August 14th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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In high school I learned the two-column proof method for geometry proofs. The proofs I remember doing the most were triangle proofs. I rarely, if ever, used the paragraph-style for writing geometric proofs. So, for this problem I'll complete the necessary computations and accompany them with statements that support those computations. 

There are various way to prove that a quadrilateral is a rhombus. This is because there are various ways to prove that a quadrilateral is a parallelogram, of which a rhombus is a special case. I will prove that quadrilateral NATS is a rhombus with the following method:

            I.   Prove that quadrilateral NATS is a parallelogram

            II.  Prove that the parallelogram is a rhombus.

 

But first, here is an image of quadrilateral NATS (the rhombus in question):

**This plot was created using GeoGebra's Geometry App.

I. Prove that quadrilateral NATS is a parallelogram. I will do this by showing that the diagonals of NATS bisect each other. The midpoint formula was used.

Diagonal NT and diagonal AS share a midpoint. NM = TM and AM = SM. Therefore, diagonals NT and AS bisect each other. Therefore, quadrilateral NATS is a parallelogram. ✔️

II. Prove that parallelogram NATS is a rhombus. I will do this by showing that the diagonals are perpendicular. 

The slopes of diagonal NT and diagonal AS are negative reciprocals of one another. Therefore, diagonal NT and diagonal AS are perpendicular. Therefore, parallelogram NATS is a rhombus. ∎

It's been quite a while since I've done one of these. This has me thinking 🤔 back to when I took my high school math Regents. I remember doing logic proofs. Maybe I'll explore that topic in a future WMP!

◾️ How do you feel about geometry?? 

◾️ What method did you use to complete the proof?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Without further ado, on to WMP! #16 

Cheers!

The Younge Lady