chapter nine is all about correlations which are basically connections between two types of measurements and there're two quantitative measurements like in this example sales in thousands of dollars and advertising dollars spent uh also in thousands and you want to see if there's a connection between those things and that's what chapter 9 is all about the graph that goes with it is called a scatter plot grat and it's um you've seen a scatter plot and the next slide shows you some examples but um and we're not going to create one on on this slide again you've got some other examples but basically a scatter plot is just a um a graph of it looks like a bunch of dots what I want you to get from that is each one of those dots for instance if I graphed this data each one of those dots would represent a month January would have a DOT February April May all of those would have a dots and you would have two measures for instance I might have sales on my xaxis that's the horizontal one and I might have uh advertising on my y AIS you would have a number scale here like I might be going from uh $100 here all the way to uh 130 and everything in between my advertising dollars are going um in this case 5 and a half to 6.8 so maybe I would just go by maybe I could start at three I don't know three four five six so each one of these would have their own scale I might have hundreds in the bottom and I might have ones in the top and you would estimate where that dot would go how far over it would go and how far up it would go and that's where you put the dot and the graph of all those dots is called a scatter plot but what I want you to know and you're going to be using technology to do the graphs for you I just want you to understand that each one of those dots represents one person or in this case one month and there are two numerical measures used to find the location of that dot so once you start to graph a bunch of these different things you're going to see different shapes so I just want to kind of go over that there are descriptions for the types of correlations you can have uh positive correlations negative correlations here's positive uh negative correlation no correlation if those dotts don't follow any pattern or they have curvy linear nobody ever says curvy linear in this image it would be nonlinear so those are the types of relationships and then you'll notice there are descriptors like strong or moderate so where those come from is this within a scatter plot you can sort of estimate what I call an invisible line that those dots seem to be traveling along and that invisible line is called a regression line and you will learn learn in the next lesson how to find the equation of that sometimes it's referred to as the line of best fit so whether or not it's strong or moderate does not have anything to do with how steep that line is it has to do with how closely are those dots following that line so you see in the first example hello uh why is it doing that in that well I'm just going to have to get a new arrow in the first example those dots are really following really closely back and forth along that line and in the second example those dots are becoming a little bit further away from that line and so that makes the difference between strong and moderate you can have a weak uh connection and that would be where you can tell they're going uphill but they're pretty scattered back and forth above and below that line no correlation I don't even really like this image for no correlation uh and if I was was drawing this image over which I guess I probably should have done uh before I started this video I would add more dots kind of around here because you should not be able to tell whether it's going uphill or downhill so that would be no correlation um and then these two examples on the bottom I wish I could move that Arrow that's driving me bonkers but I'll just have to keep scooting it um if you again if you sort of estimate where that regression line go um if the dots are if your regression line is going downhill that's what visually how you can tell it's a negative correlation and we've already talked about the strong and moderate in the last example if I drew sort of an invisible line that it looks like the dots are following along if that actually does not make a line but makes a curve a rainbow shape that would be nonlinear that means there is a connection you can tell those dots are following a pattern but it doesn't make a straight line now if you don't have a graph if you haven't graphed information and you don't always need to graph information there's still a way to tell whether or not your data has a positive connection a negative connection and whether it's strong or weak and that's by calculating something called a correlation coefficient and we indicate that using the letter R so that's our variable that we use for the correlation Cod coefficient R and R follows a scale between -1 and positive 1 you can never have a an R value greater than the number value one um so I'm going to go through and give you the scale now these are not like industry specific the whole world uses this scale but they use a scale similar to that there's not a hard fast rule but for our purposes in a math class so that we can all be consistent with our answers I'm going to give you the scale okay so when you calculate R which you will do you've already read about how to do this um there is this massive formula but your calculator is programmed with that massive formula and it will give you the R value if your r value is between .25 and positive .25 so if your r value is somewhere within the first quarter of its way between 0o and and negative 1 or 0 one we say that that indicates that there's no correlation so you don't have to come up with a zero for there to technically be no correlation I'm going to erase that word correlation just because I'm going to run out of room so if your r value is is within that range you would say that shows that there's no correlation between those two uh data sets all right now let's go to the next indicator if your r value is between let's do a different color here so that's it gets easier to tell is between 25 and 5025 or 050 in the negative or over here in the positive you would call that a weak correlation if your r value is negative like these on the left side of zero then you would say weak negative correlation if your r value is positive and it's within that range you would call that that a weak positive correlation uh so going to the next quarter of data if it is between 50 and look that is a gross I can't even stand to see that there I got to fix that um if it's between 50 and 75 whether that's negative or positive and obviously we're talking about decimal points 05075 you would not use a descriptor so you wouldn't use weak or strong you would just it's regular you can use the word regular if you want so we would just call that a straight up negative or a straight up positive correlation without a descriptor and last but not least if it's from -75 toga 1 or the positive version of that 75 to one that's when you get too strong so strong negative if your r value is negative strong positive if your r value is positive so now let's go to our technology to learn how to actually calculate r well it might not sound exciting to you but to a a biologist it would be very exciting so this would be if you were studying uh this is grasshoppers so studying the amount of chirps per second and what the temperature is outside for eight consecutive days uh where there are gr grasshoppers present so what we're going to do is calculate the R value for this data using technology okay to do this let me just get out of this so you can see starting from fresh so we want to enter our data and we already know how to do this we've done this before you hit your stat key and you're right there at edit so you hit enter and that's what pulls up your lists now notice and and by this point in the semester you should have information filled into a lot of these if you need to clear information out of your list just put the arrow on top of whatever list you want to clear out hit clear and then enter and it will zap all those numbers out so what I want to do here is put one columns worth of numbers into L1 and we're going to put the second column into L2 actually it doesn't matter what two lists you put them in just remember where you put them so one by one I'm going to do this and I have the screen a little bit smaller so that I could still see the numbers in there so I'm going to put the chirps per second into L1 so that's one at a time I go through that uh 16 okay and you don't have to order them so you might say well these aren't in numerical order I better order them do not order them put them in exactly as they appear I'm going to pause the video because you don't need to watch me putting numbers in okay I'm going to okay so now you can see I have uh the the chirps per second into L1 I have the temperatures typed into L2 make sure you don't change the order for anything so here's how to calculate R hit your stack key immediately obviously you don't have to clear the screen this time we want it to calculate things so go over to calc and you want to go down to in this calculator it's number four Lin reg ax plus b that stands for linear regression and hit enter now what it's waiting on is it wants to know where are your lists for some of you um it it will already have them filled in but you have to remember we have two lists and so you have to put commas between them so I have this yellow L1 so I have to hit my second key and hit the number one that pulls up L1 and then my comma comma L2 and then and hit enter and notice it spits out all kinds of stuff now let me say this this is important if you do yours and there are and you just have y a b and you don't have these two you have to do what's called um turn on your Diagnostics on your calculator to turn on the Diagnostics in your calculator you have this little word down here that says catalog so you go second and then hit catalog and you have this alphabetized list of functions so you would scroll all all the way down until you see Diagnostics it's way on down there okay so you notice you see Diagnostics off and Diagnostics on you want Diagnostics on so make sure the arrow is there and hit enter twice make sure you hit it twice until you see the word done so if if that happens to you if you do not see R 2 or R turn your Diagnostics on and then go back and hit stat Cal go to your linreg L1 comma L2 enter and you'll see those values so what I'm interested in is not r s I'm interested in R and that's that number that we told you about in the previous slide that's that scale we're looking for so for this problem we have an R value of 958 if I round a three decimal places so we don't need the video anymore 958 and if you think about the scale from the last Slide the correlation coefficient is really close to positive one it's positive I know that cuz there's not a negative in front and it's between 75 and 1 or 1.0 so that's in according to our scale the range where we describe it as a strong positive correlation and so we just did two skills number one we found the correlation coefficient R and number two we used that to describe the correlation and those are the main skills we want you to get out of this section