Question

Archers need to use arrows that do not bend easily. The table shows how the weight of an arrow affects its spine, or the distance the center of the arrow bends when a certain constant weight is attached. Graph the data in the table to find a linear and a quadratic model for the data. Use the regression feature on your calculator to find each model. Which model is a better fit? Explain.

Answer 1

We would need the data to fully answer this, but for each set:

set the weight values as x, and the distance values as y

graph the values

and then use the regression model to make 1. a linear model and 2. an exponential model, and see which one gives you an r^2 value closer to 1

Answer 2

This is the data

Answer 3

good, so going along with what I said, you would plot (140, 1.4), (150, 1.25), etc. into your calculator, and calculate the r^2 values. if you're having trouble you can look up regression instructions for whatever calculator model you're using.

Answer 4

I put the numbers in my calculator and I got a=-0.15... b=3.5... but I don’t know how to find the quadratic

Answer 5

what brand/model of calculator are you using?

Answer 6

Ti 84 plus

Answer 7

try this: https://www.wsfcs.k12.nc.us/cms/lib/NC01001395/Centricity/Domain/1499/Quad%20Reg%20Calc%20Directions.pdf

if that doesn't work, try this online regression calculator https://keisan.casio.com/exec/system/14059932254941

Answer 8

Ok I’m working on it now

Answer 9

Ok I got a=16.1966... b=-94.84... c=242.12

Answer 10

good, have you tried finding the r^2 values?

Answer 11

No how do I find them?

Answer 12

should be step 2?

https://www.statology.org/quadratic-regression-ti-84-calculator/

stat --> calc --> linreg or quadreg, depending on which you're doing --> set your X as L1 and Y as L2 ---> calculate ---> enter

Answer 13

For some reason I only see a b c I don’t see r^2, I followed the instructions but I still don’t see it

Answer 14

maybe try this? https://www.desmos.com/calculator/qsdscncgi6

Answer 15

Oh I fixed it for r^2 I got 0.99429...

Answer 16

alright, good, then repeat for the linear regression and see which one is higher

I think this should work for linear regression r^2

https://ncalculators.com/statistics/r-squared-calculator.htm

Answer 17

Ok

Answer 18

I got -0.9941...

Answer 19

I’m not sure if that’s correct

Answer 20

hm, I don't think r should be negative

can you send me your data points?

Answer 21

just typed out is fine

Answer 22

Ok

Answer 23

(140,1.4) (150.1.25)(170, 0.93)(175, 0.78)(205,0.43)

Answer 24

alright, so using https://ncalculators.com/statistics/r-squared-calculator.htm

inputting x-values: 140, 150, 170, 175, 205
inputting y-values: 1.4, 1.25, 0.93, 0.78, 0.43

gives R^2 = 0.9729

Answer 25

so our quadratic model: R^2 = 0.99429
linear model: R^2 = 0.9729

since the quadratic model R^2 is closer to 1, this means the quadratic model is a better fit to the data

Answer 26

Ohhhhh wow, I was definitely confused until I got help...so thank you so much