 without the trend line. That's sour chasm because it is they all land on the line. And obviously if we think about this this makes sense because if we're looking at the distance, the distance traveled as or the distance remaining as the distance remaining goes up then the distance traveled is going down. You can look at it the other way as well if you're looking at the distance traveled as the distance traveled goes up the distance remaining goes down right distance travels goes up to 80 distance remaining goes down to 20 distance travels goes up to 100 distance remaining goes down to zero so you have that negative perfect negative relationship. Alright so now let's let's let's see this mathematically with our formulas I'm gonna pull this to the side get it out of the way get out of the way we're done with you we don't need you here and I don't want to delete you though because you're still we might you're still you're still good but we'll put you over on the side here. Alright so then what we want to do is let's make like a large eye over here I'll pull this to the side and make a large eye and then I'll squish these up into the area so they're in there and so they have their space everything has to have their space everything has just like when you're eating you have to put everything everything needs its own area you can't just you can't just squish everything together you know it has to the plate is there to space out the stuff on it okay so now we're gonna pick out I'm gonna pick the same data so we'll take this data control shift down and copy it right click and copy and I'm just gonna put that same data over here and right paste it I think I could just paste it normal cuz it's just data no well this one has a formula in it will that mess us up no that's fine that's fine that's okay so I'm gonna make this a little bit larger let's let's I'm gonna insert a column between the case I'm gonna I'm working my math here which is means we're gonna take the Z score of X all the X's and the Z score of all the Y's multiply them together sum them up and then divide by the count in minus one and then so to do that I'm gonna do another column selecting column K right click and insert and I'm gonna call this is the Z of distance or traveled traveled and this is gonna be equal to the way we calculate our Z brackets the 94 miles traveled in this case minus the mean which is 53 92 F4 on the keyboard making a dollar sign before the G and the two so it doesn't move down when I pull it down divided by the standard deviation for the sample which is over here and we're gonna say F4 on the keyboard dollar sign before the G and the three so it doesn't move down when I copy it down and enter let's decimalize it so we can recognize it home tab number group and decimalize couple decimals and then we'll just fill handle double click drag it down there it is movie B to the N BN as they say in a span your and so we're gonna say this is the Z this dance remaining and home tab clipboard let's do the paint brush and paint brush it so that's good little wider and so then we're gonna do our Z score Z score for the distance remaining this is gonna be equal to brackets the six so that's six miles remaining minus the mean which is this one F4 in the keyboard dollar sign before the H and the two closing it up divided by the standard deviation of a sample and it's gonna be F4 in the keyboard dollar sign before the H and the three and enter and decimalize it home tab number group decimalize and then double click the fill handle to drop it down dropping it down like dropping a beat when I'm making my music video and I'm trying to trying to put down the base beat so that I can play like the guitars on it or something dropping dropping the base anyway I don't know what I'm talking about so they're not multiply these two together so now we can sum these two columns up and we've got the distance between each data point and the middle and divided by so we've got the Z right we've got the Z's I can sum them up but now I need to multiply them together so this is the Z I'm just gonna abbreviate the travel times asterix the Z remaining I'll just call it rem remaining and then we'll say home tab clipboard format paint to here boom and multiply it out this equals the Z distance travel times the Z distance remaining enter let's add some decimals home tab number decimalize and double click on the handle to drag it down fill it on down handle and we get the negative numbers given the nature of what we're looking at here alright so that so that is good so now let's make a skinny O column and then I'm gonna say we'll do our correlation calculation correlation we have all the tools necessary to get the job done so now let's just take those tools home tab font group here and do the job black and white so we're gonna say then this is going to be the sum of the Z the Z travel times the Z remaining the sum of that column so we'll say that's gonna be equal to the sum and control shift down enter let's decimalize it home tab number group decimalize and so so now we've done the whole summing the top bit the top part now we just need to make the numerator so the numerator I'll just put a subtitle here in minus one colon to indicate that I'm going to do a little sub calculation in the middle by the way turning these formulas into like I would call this like a tax worksheet kind of format just a worksheet is actually quite useful so to because then that lets you see all the steps that are being made in the in the problem and it could be useful in practice when you're if you're trying to put some kind of worksheet together that you might use multiple times and run different things but in case here's an n the n is just the count so I can count any of these that we want I'm just going to use our count formula equals count tab and I'm just counting the rows I'll choose the first one control shift down it's just counting them so how many rows were there 205 you'll recall that 205 when we first started the practice problem in generated 205 data points so then less one because that's what it has here in the numerator minus one so there's the one and that's going to give us the n