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this session is going to have a look at a data handling in there's two dimensions bivariate data handling and also one dimension histograms and so on both have a look at some probability distributions so let's get out of this one and go to the 2d page now it's quite nice to introduce bivariate stats by just literally getting some points and throwing a few I'm not too many just enough to make the point okay let's select and select that lot now once we've selected these points there are various things we can do let's have a look at the right-click options the first one I going to set along as best fit it's quite nice to show that you can actually do a polynomial best fit up to order six and of course it's a particular down loading situation which is nice if you knew it was going to be a parabolic or even a straight line fit obviously double click and you just change this so we'll just select that and delete so let's select these and right click this time I want to do a regression line now we're in advanced level which means you do get options like X on Y regression and Y our next regression in the standard level it just as an eye on the best fit so we do y on X which means X is the independent variable against Y though it is and of course we move these points around that happens so now I've got these points selected what I'd like to do also is to put on the mean I think it's quite instructive to show that the mean actually lies on the calculators regression line and always does so so whenever I see those apps on the web for fitting a random straight line through data and look at the least squares it's so much nice if you can know for sure that that line is going to go through the mean and then you've only got one degree of freedom for your second point so what I'm going to do now is I've got always point selected I'm going to convert those to a dataset which is convert to a data set that means that they're now a single object i double-click I can see what I've actually done these are the points I've put on the screen and obviously that could have come out of Excel so I'm going to put a point over here somewhere somewhere and I'm going to select that point and the mean and right click I'm going to do a straight line this is giving me a random straight line through the mean nature and work but it sometimes that point can be little hard to see one of the dodge is to right click for a circle throat of 0.1 and I could say it more easily okay now what I want to do I want to hide this because I don't want to see what the answer is so they'll hide the object so now I'm going to select the data and this random line now that they've got a line and some data selected I get the residuals option now Y on X residual is the one who wants you want X to be the independent variable so again get the pen out and look at this what we actually mean is that all these differences between the actual data and the measured data is going to be in some cases positive in some cases negative so we want a system for minimizing these lengths now the last time we did this with standard deviation we took the square with the differences between the means and the values and that's what we're going to do here to get rid of the fact that summer plus or Southern Lights we're going to square each so we put a square on each one and then we're going to minimize those okay so let's now we've got the idea of it edit select all school and delete okay so I'll select that and this and right-click I'm going to do Y on X residuals and I'm going to draw lines to start with because I think that's quite instructed to show these the things we're trying to minimize but once you've got the idea put squares on and then if you select that and go to the text box option you can see what we've actually got on the screen which is which is 11 565 in sum of all these squares so I can move this around and try and get that smaller 10-9-8-7-6-5-4-3-2-1 1.9 1.8 and and once you've got that idea let's just see what we've got unhide all and see how close we were not bad so then you want to obviously deal with some real data so let's go to the data set which comes off our website as well and let's look at weights of babies there's quite a good data set this because it's about 1,100 babies from Stanford University in the States and there they are and if you have a look at it is there's lots of this equate to the babies in pounds and kilograms gestation days mothers agents on let's take these to which the next to each other luckily they're not next to each other you need to hide the ones in between but worth but birth weight and gestational would seem to have something to do with each other so I'm going to right click and copy minimize that so that you just drag from D to E and right click copy that's what happens that puts it on the clipboard and we're now going to do enter XY data set right click paste and it goes there's birth weight there's gestation now these are column headers so we want to use the X column header with the x axis label and the Y column header as the y axis label and just click OK perform auto scale I think we do want if you want the data to show on the screen but if you've got your scales already set up and obviously won't take that and there it is but actually if we think about it the birth weight is the consequence of the long gestation so I think these are the wrong way around so double click and there was the option to swap the axes I'm sure this test is well if you like and that's quite nice so there you have your regression that sort of can see we want Y on X regression which is just in there and you can see for that that the correlation is 0.4 it's quite low if we transfer that to results box let's see what the results box is now it lives over here but if it's not there use your view results box and there it comes so you've got different settings for the results box you can either have it going there see this for pin the pin goes this way it sort of interrupts but if you pin goes this way it floats on top of that's probably the best one to have so this is just text you can drag it out and you can just drag this and copy it and paste it into word or wherever you'd like to put it that's by various steps now what about mana variable static page here which says single mobile statistics one variable long here and up here goes frequency or probability so once again we'll go back to the same data set and have a look at mother's age which is a good one because that's a single variable it's not particularly normal it's got a skew at the top so I'm going to copy that and that's copying column F so what do we got here we've got right-click we've got enter group data which we don't want that's if you happen to know the groups and the frequencies enter raw data if you just know the raw numbers which is what we have enter box plot enter probability distribution that is something else that's something to discuss later the normal price on the binomial time so I'm going to right click enter raw data now this is where you can either paste it in as we're doing now they would all goes or you can actually select one of these distributions to generate data from that in the mode tick tick so what the column headers to do work for me it's quite interesting to sort by X just to see what we've got see Vasily got some young mums here and the other end you've got some older mums and up to 8:45 in this particular sample click OK now unlike the scatter diagram the frequency page doesn't draw anything because it doesn't know what to do yet there are several options it just got a bucket full of numbers so the best thing to do is to draw a drop block that just throw the up in the spacing of one by default but you can change all of that up and down is entirely arbitrary we're just deciding that one little block should equal one frequency so that will in fact measure frequency straightaway there it goes now what we could do is right click and say box block but actually isn't it better to get the pen out all the work we've been doing with the pen in the two dimensions environment that works really well here too so where's the meeting where's the mother who can say there was many mothers older as there are younger mmm then where is the mother who is in the middle of this lot and where's the mother in the middle of this lot so what we're doing we're generating a box plot by discussion and that has the desired effect of course of making the students thing up well I wanted to see how good we are if you look at the results so you've achieved your aim which is skipping purist to press the right click and see what the answer is box plot and there it goes more data or groups it's only raw data at the moment so that's fine well we didn't do too bad down the median and the upper quartile in our court I was a mess okay so edit select all scribbles and delete now if we want to draw a histogram how do we do it well right-click we need to group the data at the moment is there's nothing here about group data because it isn't grouped as if raw data don't enter a brand new group data set there's something else group data so here we go it's offering a zero to fifteen classes of five which you can change of course but that's done to spadework which is pretty good well I'll buy that this is where you put in unequal class widths if you want to and certainly there will be no need to work out the frequencies that will do it all for you now if you want to calculate you can calculate what the actual classes are going to be here which is handy you can calculate what the actual frequency is going to be again that's handy so there's a pretty good distribution so I'm happy with that but obviously who wanted to change that to ten you could do that or recalculate now continuous or discrete very important distinction age is a funny one because you are thirty until the moment of 31 so it's all about a like discrete but actually of course it's a continuous variable okay off we go now nothing's happened yet because right click all the options that require the data to be grouped are now here so histogram cumulative frequency we've done those but stem and leaf diagram that's a mess with large data so forget that one table of stats is obviously leading the data to be grouped so don't look at the histogram frequency will fix the density there aren't many quickly around the world that do fix the density at so school age but you know those that do have to get involved in this but for now we'll just stick to frequency and it brought up you could have it plotting down if you want to have two distributions draw a histogram is what we're doing the frequency polygon sits on top of it and fill it up yep now the red tick comes to your aid here and let's move that up so we've now got our histogram based on continuous variable so 2221 starts at 20 if it was discrete of a start at 19 in the half and you can show that quite nicely by clicking this button which is discrete plotting and it just shunt after the left this reading up here is the table of stats and here it all is that's quite good sort of grab this and stick it into Excel just to show you that it really does transfer very nicely we'll go to the spreadsheet that we had open just now no prep a new page and right click paste it in and you can see that you've got all the information about there nicely in columns and all the sausage at ah whenever that wakes up it's worth exploring see what it's doing it can vary the class width dynamically which is quite nice so if the class width is 6 for example this is going to get wider so it's going to go up and one thing I forgot to mention on the results box of course I'm treating it as discrete data and so it's going 0 to 4 and 5 to 9 and 10 to 9 to 10 to 14 if we made it continuous data and did the same thing it goes 0 to 5 5 to 10 10 to 15 that's on expecting the actual value of 5 itself to be in here but across that value never exists because it's a width cumulative frequency is this one and it does plots automatically you can have a curve fit or a linear fit I would think that the integral of a set of blocks like this should be a linear fit but they were out the convention is that the curve is drawn it nearly always shoots off the top so let's do the red tick to save ourselves going to find it and there it goes let's select that and right-click do a tumor to frequency diagram measurement and let's do the median now what this does is puts the median at the right place here cuz that's easy to work out half the total this is just a random function f2 move by i2 where we want it to be that's interesting because it looks at so the median as measured this way is completely different to this and remember the median here was measured from the raw data so I'm now going to right click put on the box plot that this time groups data it should have that perfect nicely this little button here is quite nice this view the stats box this compares the raw data stats to the grouped data because group data is assuming they're all of the middle point and so it's quite an approximation so you can see the meetings are very different sound deviations and so on you want this picture to go into a Word document what you could do is just show up the actually is a bit I think these are these are too close these lines here so let's go to the exes control which is the spanner and you get a chance to order everything so let's go zero to 500 I think we probably don't need that the pips here want to go in five hundreds not hundreds that's better but also I think double-click you want to put in some option subdivisions of four that's looking good what you could do of course is double click and just look at the appearance and choose a theme which is a craft paper that always does quite nicely and makes it look really good so I want to put that into word file just going to get rid of all this top here which is an X YZ key and it's a page so I want to copy that just move that away page and the copy page and the ctrl C is the best one and open up a word page and right click paste so that's a look at some of the stats for autograph and next you