I'm taking Physics 11 and we're doing a graphing exercise. The graph is Cricket Chirps per minute(as dependent variable) on the Y-Axis versus Degrees Celsius(Independent Variable) Along the x-axis. I've drawn my line of best fit. The exercise asks that I find the y-intercept of the line of best fit. I've found it to be -65 chirps/minute. The next question asks how would one interpret the y-intercept. This doesn't make any sense to me.. I'm positive I've done the graphing and calculations correctly as the equation works find for finding points on the graph. I've asked my physics teacher some questions and he says they're not correct. I've asked: Is it possible the cricket stops chirping and begins processing chirps. He said no, which leaves me at a dead end. I could just put 'undefined' not sure if that'd be correct though. Also, how would I show this on a graph?
Welcome to PF, The bottom line is that for a discrete, countable thing like cricket chirps, it just doesn't make sense to have a negative value. Your result is unphysical, and it indicates either that you have done something wrong, or that the graph should be a piecewise function (meaning that it is linear with some non-zero slope down to the temperature at which the crickets stop chirping altogether, and then linear with zero slope (i.e. flat) below that temperature). So, assuming you have done the fitting right, then maybe the best interpretation of your data is, "below some positive temperature, the crickets stop chirping altogether." EDIT: Another way to express what I'm saying is that the cricket chirp rate is only well-modelled by a linear function over a limited temperature range. Below some temperature, there is a cutoff.
So say the cricket chrips 0 times a minute at 10 degrees, could I say: The y-intercept is undefined because the temperature must be above or equal to 10 degrees?
No, there is nothing preventing the temperature from being below 10 degrees. Did you read the edit I made to my post? And the y-intercept is certainly not undefined. After all, if the cricket chirp rate is zero at 10 degrees, then presumably it is zero at every temperature below that as well. What I'm saying is that the true y-intercept cannot be obtained by simply extrapolating the best fit line of the data down to T = 0, because the cricket chirp rate is not linear with a single slope over this entire temperature range. In other words, the model that most accurately describes the cricket chirp rate is not simply a single linear function, in spite of the fact that that is what the limited data set you have would indicate. Again, all of this ASSUMES you've done the earlier parts of the homework exercise properly, which is not a given. EDIT: Yes, DaveC is right. Taking a look at what you've done so far is the best way of making that determination.
Where Temperature is the Independent Variable Chirps Per Minute : Degrees Celsius 7 : 11 20 : 13 36 : 15 47 :17 61 : 19 69 : 20 Using this data I created a line if best fit. The mathematical equation of the line is: y = 6.7x - 65
Alright, so it would it be fair to say: There is not a sufficient amount of data to accurately determine the true y-intercept, as the rate of chirps per degree Celsius does not grow or decline at a consistent enough rate. So than my equation for finding chirps per minute is only accurate between a given range of temperature. Would this mean I would have to add a limit to the temperature value in the equation? i.e (Mathematically) Y: Chirps/min X: Temperature y = 6.7x - 65 20>x>=10 Would that be correct?
Well no, even if it your data were perfectly consistent and your best-fit line were razor-sharp, you still could not report a realistic y-intercept.
Ohh, okay. So than one should interpret a negative 65 chirps per minute as 0 chirps per a minute. Or presumably 0 chirps per a minute, though I can't be sure because I haven't been given enough data?
Well, your original statement that, "There is not a sufficient amount of data to accurately determine the true y-intercept" (without any of the stuff that came after it) is probably the safest thing you can say. What you're saying in the quote above is equivalent to my original advice to model it as being piecewise linear. However, this is at best an approximation, since you don't know where the turnover point really is. If you had more data for temperatures below 11 C, then you'd be characterizing the shape of the function in the vicinity of the turnover point better.
Alright. Thanks cepheid & DaveC426913. I just started in Physics and I know my teacher is trying to trick me with this question, lol. I don't want to be tricked w\ it though.