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Problem 24 Hard Difficulty

Biologists have observed that the chirping rate of crickets of a certain species appears to be related to temperature. The table shows the chirping rates for various temperatures.

(a) Make a scatter plot of the data.
(b) Find and graph the regression line.
(c) Use the linear model in part (b) to estimate the chirping rate at 100 $ ^{\circ} F $.

Answer

a. See the explanation and the graph.
b. See explanation for result.
c. The Chirping Rate is approximately 265 Chirps/min when the temperature is $100^{\circ} \mathrm{F}$ .

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Video Transcript

all right. So we have a problem about the chirping rate of crickets as a function of temperature, and this would be a great problem to use a graphing calculator for. So we go to the calculator and we go into the stat menu and into edit, and then we type all the data into list one endless, too. So the temperature data is enlist one. And the chirping rate data is endless, too. The first thing we want to do is make a scatter plot. So from here we can go into the stat plot menu, which is second y equals. Turn on plot one by going into the plot one menu turning it on and checking to make sure that it is a scatter plot using list one in list, too those of the defaults. But just in case you change them for some other use of your calculator, you want to make sure that those are set. The next thing your calculator can do for you is choose a good viewing window. So if you go into the zoom in you and then you choose zoom number nine zoom stat, it will set up a window that works for the data in List one and list, too. So here we have our scatter plot, so that takes care of part A For Part B. We want to find and graft the regression line. So we go back into the stat menu. We go over to calculate, and we go down to choice number four. Linear Regression. We press intern. It's going to use list one and list, too, so that's what we want. We don't need to worry about frequency list, but because we do want to graft this, we want to store the equation in the UAE one section of the Y equals menu. So from here, when you're in store regression equation, you press the variables, which is the vars button, and then over to why variables and then choose function and then choose why one. And now we can calculate. So here's the regression equation, and if we press y equals, that regression equation was pasted into our Y equals menu for us and it's ready to graph. So now we compress graph and we see the regression equation line in addition to our scatter plot. Finally, we're going to use this model to estimate the chirping rate at 100 F so we could use the graph or we could use the table, and I'm a big fan of using the table. So I'm going to go into the table set menu, which is second window. Make sure that it's on independent. Ask, which means that you can type in your own X value, and the calculator gives you the Y value. Then we go into the table menu, which is second graf. Don't worry if there are other numbers already there from last time you use the calculator, you can just type right over those numbers, and so we're gonna type in 100 degrees. So 100 for X and we see that the Y value is 264.7. So that's telling us that when it's 100 F, the crickets are chirping at a rate of about 265 trips per minute,

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