For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

### Scatterplots

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Roadmap
- Previous Visualizations
- Compare & Contrast
- Summary Values
- Example Scatterplot
- Positive and Negative Association
- Linearity, Strength, and Consistency
- Summarizing a Scatterplot
- Example 1: Gapminder.org, Income x Life Expectancy
- Example 2: Gapminder.org, Income x Infant Mortality
- Example 3: Trend and Strength of Variables
- Example 4: Trend, Strength and Shape for Scatterplots

- Intro 0:00
- Roadmap 0:04
- Roadmap
- Previous Visualizations 0:30
- Frequency Distributions
- Compare & Contrast 2:26
- Frequency Distributions Vs. Scatterplots
- Summary Values 4:53
- Shape
- Center & Trend
- Spread & Strength
- Univariate & Bivariate
- Example Scatterplot 10:48
- Shape, Trend, and Strength
- Positive and Negative Association 14:05
- Positive and Negative Association
- Linearity, Strength, and Consistency 18:30
- Linearity
- Strength
- Consistency
- Summarizing a Scatterplot 22:58
- Summarizing a Scatterplot
- Example 1: Gapminder.org, Income x Life Expectancy 26:32
- Example 2: Gapminder.org, Income x Infant Mortality 36:12
- Example 3: Trend and Strength of Variables 40:14
- Example 4: Trend, Strength and Shape for Scatterplots 43:27

### General Statistics Online Course

### Transcription: Scatterplots

*Hi and welcome to www.educator.com*0000

*Today we are going to be talking about scatterplots.*0002

*First we are going to talk about how scatterplots are different from previous visualization.*0007

*Because of that I will go over a little bit about what the previous visualizations all have in common.*0013

*Then I will compare and contrast this with scatterplots.*0018

*Finally we are going to go on to describing the different aspects of scatterplot versus other distributions we have been talking about before.*0023

*The previous distributions we are talking about have largely been about frequency distributions.*0030

*and here we are talking about the one continuous variable like height or age or number of friends on www.facebook.com.*0039

*We are asking how frequent is this value?*0049

*How frequent is that to have 200 friends on www.facebook.com?*0052

*How frequent is it to be 6 feet tall?*0057

*Now the frequency distribution looks like there are two variables because the x-axis and y-axis. *0061

*But it is one variable height and the frequency which is just another variable for counting how many you have.*0069

*We have looked at some cases where we compare two different variables, but usually it might be comparing two groups on some continuous variables. *0080

*We might compare male and female heights, but we are only looking at one continuous variable height.*0091

*The other variable is a categorical variable, the two groups.*0099

*That is how we get the two groups like gender.*0103

*Although we have that still the fundamental basis is that we only been looking at one continuous variable at a time. *0107

*Now these frequency distribution we have drawn like histograms and different beings, they often look like this is and they are summarized by shape, center, and spread.*0116

*Usually by center we mean something like mean and by spread we mean something like standard deviation.*0129

*Now that is going to be sort of the past. *0140

*Now we are moving on to scatterplots.*0144

*Here is how scatterplots are different.*0148

*Instead of having one continuous variable we have two continuous variables.*0150

*That is the big key difference.*0155

*And because of that one axis is going to have variable 1 and instead of putting frequency here we are going to put variable 2 here.*0157

*Some frequency distributions we had variable 1 here and we have that frequency of variable 1 here.*0172

*Notice here there is no explicit representation of frequency. *0179

*There is no number that we are planning to represent frequency and each axis is going to represent the variable.*0182

*We are summarizing these distributions by shape, strand and strength. *0193

*Here it can be called a scatterplot because each case is now going to appear as a dot. *0201

*Each case, for instance each person on www.facebook.com might have variable 1, number of friends, as well as variable 2.*0210

*How many photos they have uploaded?*0220

*Each dot represents one person, but 2 values within that person.*0223

*And because of that, it is called the scatterplot because it looked like somebody just scattered a bunch of dots on this graph.*0232

*It makes sense that it is called the scatterplot and notice that here it does not quite seem like we are really interested in the center of one dimension.*0242

*We are interested in the center of two dimensions.*0254

*Because of that trend is going to be sort of like center and strength is going to be a lot of like spread.*0258

*These concepts are concepts you have got about before but we are translating them from one dimension to 2 dimensions.*0273

*Spread used to be something like this but now we are talking about spread in 2 dimensions.*0284

*That is going to look a little bit different. *0291

*Let us talk about these particular summary values of shape, center, and spread.*0296

*Remember frequency distributions are always what we call univariate in terms of continuous variables.*0301

*It might have 2 variables but one will probably be categorical.*0309

*When we talk about shape we talked about being like unimodal, symmetric, asymptote.*0315

*Those are common features that we are looking for.*0329

*Is it normal, uniform?*0332

*Those are words that we are buzzed when we talked about shape in frequency distributions.*0336

*In scatterplot we are largely interested in putting different shapes.*0342

*One shape might be that the dots sort of fall in a line.*0347

*Is it a linear scatterplot?*0353

*Another potential distribution is that the dots might fall in a curve.*0358

*Is it curvilinear?*0366

*It is a shape that we are interested in is that there is just sort of no shape, and it sort of the love like or cloudlike.*0370

*This is not the cloud may be one way of thinking about it. *0383

*Those are different shapes that we are interested in.*0391

*How linear is it? Is it curvilinear, is it cloud?*0397

*Let us talk about center.*0403

*The way we talked about center before was that we are interested in things like the mean, median, and mode.*0404

*A lot of times we used mean.*0413

*Either signified by mu or ex-bar , depending on whether you are in the population or sample.*0415

*Trend has sort of the same idea as center.*0426

*You could think about this as a version of center, except the center of two variables not just one.*0432

*Here it is not useful to have a center of just dot because that is what we had before.*0444

*We had point mean.*0455

*It was like a particular point, but now what we are interested in it is let us say we have a whole bunch of dot scattered here.*0457

*What we might be more interested in is a line of some sort that describes the relationship between all these points on these two variables.*0466

*Here we are not just interested in a pointcenter, we are interested in a line center.*0478

*I’m goingto adjust these to be lines center rather than a point center.*0486

*That line is going to be called the official term for that is regression.*0493

*That is going to be the regression line.*0500

*The final idea that we talk about here is strength and I want to tie that to the idea of spread that we talked about.*0504

*One important idea of spread that we frequency talked about with standard deviation expressed as sigma or expressed as S.*0517

*Those are two ways we have talked about spread before and that gives you a one-dimensional spread, *0536

*but what might be more useful here is something like two-dimensional spread.*0542

*Here we have our dots, we have our line, but now we are interested in how spread out these dots are.*0549

*You could think about it at all these little distances away from the line. *0560

*What is that is spread away from the line like?*0568

*You want to think of this as a multidimensional spread.*0573

*It is not just the one-dimensional spread, it is a two-dimensional spread.*0576

*You can think about this as spread around line.*0582

*Before this was spread around the points, but now it is spread around the whole line.*0591

*We are going to call that correlation.*0598

*Is the very strong it means it hugs that line really closely.*0602

*That is a strong correlation where it hugs it closely.*0607

*A weak correlation means it is hazy like it is far out and spread out from that line and a moderate correlation is there is a little bit of spread, but not too much.*0611

*And all of that has changed because now we are talking about by variate distribution.*0626

*And what we are talking about bivariate data we are no longer just interested in points and spread around the point, we are interested in things like lines.*0632

*Here is an example of scatter plots.*0651

*Remember that the data that we have looked at in the past with 100 friends on www.facebook.com *0653

*and we wanted to look at whether the number of friends people has correspond to the year of birth.*0661

*Now this is not saying that there are lots of people necessarily born in 1997.*0669

*This is not what this means, it means that this dot is actually a particular person.*0677

*It is a case of one person and this means that this one person was born in 1993, but they also have a inordinate number friends.*0685

*They have like 1900 friends.*0712

*This scatter plot means that you cannot interpret this as being a very popular year to be born anymore. *0717

*Now you have to say this particular person was born in this year and has this number friends.*0724

*If you look at another point like this one like here they have very few friends but they are born in 1978 or so.*0732

*Right and one thing you might notice about this is that there is sort of the shape here.*0744

*It seems to rise on those.*0750

*We drew some sort of line that would cut this and maybe would be aligned like this where these people as you see the year of birth increased, these people are younger.*0756

*They were born close in history.*0777

*They seem to have more friends.*0781

*If you drew a curve that might be better where it seems like the people born in 1985 they have less number of friends than the people who are born afterwards.*0784

*That seems to shoot out more.*0797

*This is an example of a scatter plot and this lines are example of rough lines that might be regression lines.*0802

*Lines that fall in the middle of all these points.*0811

*It is where these points are roughly below it.*0815

*These points are roughly below it.*0819

*And if you count all the distances up that will average that line.*0821

*Let us think about that as the trend and the strength is that.*0828

*It seems like a matter of strength.*0836

*It is not hugging the line quite closely but it is not just a plot either.*0838

*Usually we do not plot things by birth and sometimes we do but you could easily change the year of birth or age by just using 2011- whatever the year of birth was.*0849

*Here I have age plotted on the x axis and here I have year of birth plotted on the x axis.*0863

*On the y axis on both of this box it is the number of friends on www.facebook.com.*0871

*These are scatter plots and you could know that just by looking at these variables.*0875

*If one of them says frequency and you know it is not a scatter plot.*0881

*If they are both variables then you know it is a scatter plot.*0885

*Here we see this positive association.*0889

*The higher the year of birth, the higher the number of friends.*0894

*As one variable gets greater the other variable increase and vice versa.*0900

*As one variable gets less, the year of birth gets less and the number of friends seems to be quite low.*0908

*On the other hand, if you look at this graph we see and exact opposite trend where as age goes up the number of friends come down.*0917

*They are moving in an opposite direction as the other one goes up the other one goes down and vice versa as you go this way on the x axis then you will see friends going up.*0933

*This is what we call a positive association where the variables are couple to each other in the same direction.*0952

*When we plot age instead of birth we see a negative association.*0972

*When a negative association is going up or down in a way that they are opposite to each to other because it means opposite.*0980

*As long as the other one goes up, the other one goes down.*0992

*It is important to know that these are just associations.*0997

*It is not that the year of birth is causing them to have more friends.*1000

*Maybe there are some other variables that matters like when you are introduced to www.facebook.com, something like that.*1005

*How comfortable you are using the computer?*1016

*Just having a positive association does not mean that it is a causal association and that is where you get that instinct correlation does not equal to causation.*1019

*Because a matter of association is also correlation.*1029

*Just because you have this nice association either positive or negative it does not mean that it causes the other.*1035

*Let us think about why year of birth has an opposite effect of age.*1046

*It has the opposite association with friends on www.facebook.com.*1052

*If you think about year of birth, it means that when you are increasing the year of birth you are decreasing age.*1058

*These 2 variables actually have a perfect negative association.*1072

*As one goes up, the other one goes down.*1083

*If your birth goes up 1994 or 1991, 2000 the age is going down and down.*1085

*That is what we call a negative association.*1093

*It is not really that one is causing the other but is the same idea.*1097

*They are perfectly negative associated.*1102

*That is all correlation association just not equal causation.*1105

*Here are some examples of some scatter plots that you might see.*1113

*There are a couple of few different concepts that I will go over just one of these ideas of linearity.*1119

*It is going to be very important to us and linearity is just going to talk about how to connect the line.*1126

*I want you to know this distinction between linear and curvilinear.*1137

*When you think about linearity, think about linear versus curvilinear.*1146

*When you think of strength, I want you to think of it as if we are talking about spread.*1156

*It will just come in your mind as spread so if we have these dots and a little bit of spread around the line.*1167

*You could think of it as a couple of distance away from that line.*1183

*First if you have something like this that was much more widely spread around this line.*1191

*There is a lot more spread going around here and if I added a few more spread around here, I will have even more spread.*1208

*When you think of strength think about it as spread.*1225

*I want you think of it as strong, moderate, weak.*1229

*You can think of strength in those terms.*1238

*Finally, I want to introduce these concepts of consistency that we not have been talking much until now.*1241

*Consistency just means how consistent is that strength.*1247

*Is it strong all the way through?*1254

*Is it weak all the way through?*1256

*Or is it inconsistent?*1257

*Example graph looks something like this.*1259

*This starts off looking very linear but then down here they might be more variability.*1263

*Here you could see that if we drew a regression line here we have a very little spread but here we have a lot of spread.*1276

*This would be inconsistent.*1289

*It might be constant spread versus inconsistent.*1295

*An example of constant will be something like this.*1305

*It is pretty constant, this one is less constant because there is this peak right here but here there is less variability.*1309

*This is an example of constant and this is an example of inconsistent.*1319

*You want to think of this consistency as a point of strength.*1324

*Is it consistent all the way through or is it different all the time?*1328

*Just to point out something, in all these graphs that are drawn here like coincidence, I have drawn a negative association *1333

*because there is one variable as we look at values that are greater one of the variables is consistent here.*1342

*These variables seems to be down low the values right here and these are all examples of negative association.*1352

*A long easy way you could visually see this is that it all have these negative strength where strength is pointing this way instead of that way.*1362

*Let us think about how to summarize a scatter plot.*1385

*It seems to have a different feature of it but here I use rock around a scatter plot.*1388

*It will be distributed in to 5 steps so that it will easier for us to knock through all of them.*1396

*First thing you want to do is identify the cases and the variables.*1404

*Oftentimes people look at a scatter plot and they see the shape, is it a line.*1408

*Then they forget what the dots are.*1412

*It seems like seeing the force but forgetting what the trees are.*1413

*First thing you want to do is identify what the traces are and then identify what the variables are so that you know what you are talking about.*1419

*Then you want to describe the overall shape and talk about the linearity if there are any clusters you want to identify those.*1428

*If there are any outliers you want to be able to identify those as well.*1438

*Then you want to describe the trend or you could think of this as the positive and negative association.*1443

*The strength and the positive side or strength in the negative side.*1451

*You could think of this as going that way and that way.*1456

*Step 4 is to describe the strength.*1464

*The way you could just think of it as borrowing your strong, median, or moderate, or weak, but we will talk about exactly how to do that later.*1466

*Any potential explanations for this relationship.*1477

*This is just an extra step.*1481

*Sometimes you might not need this but it is often helpful to do and it is critical that you remember not always causal.*1485

*They might be a causal relationship but not always.*1498

*It gives us potential explanations that are not causal.*1501

*One might they have this positive association.*1507

*They might be these 2 variables have these negative association.*1510

*That is going to be important for us to figure out.*1514

*But it is good for us to think about maybe it is causal but maybe it is not.*1519

*Those are harder to think of sometimes because you jump to the causal explanation.*1526

*One thing that might be the case is some third variable that explains these relationship and it might not be these 2 variables that are important.*1532

*Final thing is when we describe the trend but now we are just going to describe it in a sort of overall linear.*1545

*We are going to learn how to describe it in a way precise state of manner.*1556

*When we do that, that is going to be called finding the regression line.*1561

*In that way is it going to be the equation of that line.*1570

*We are also going to describe the strength roughly but later we are going to find precise quantitative values for strength and that is going to be called correlation.*1576

*Let us move on to some more examples.*1594

*First here is a graph and what I want you to do is just go thought those 5 steps of summarizing a scatter plot.*1597

*Remember it is to describe the cases and the variables.*1608

*Talk about the shape.*1615

*Talk about the trend.*1617

*Talk about the strength.*1619

*Think about potential explanation.*1621

*I’m going to introduce you to the thing of dotminded.org.*1625

*It is a beautiful website that puts together these different data bases that are interesting definition from all over the world *1628

*and puts it in beautiful graphs so that we can look at the data in new and very interesting way.*1638

*Here you could go to dotminded.org if you want as I already pulled it out on my browser.*1646

*You want to clip in www.dotminded world, I actually cooked some helpful recognition.*1658

*If you want to follow along you could do that too.*1671

*I want to show you this graph and show what we have on the bottom is income per person.*1673

*GDP/capital.*1681

*This is the entire amount of money that the economy of that mission makes divided by how many people are part of that mission.*1683

*That is income per person and x axis.*1697

*Notice that it is in log form but it means that it is spread out and the higher numbers is squished together because they have taken the log of the income per person.*1701

*Also here we have life expectancy so that is the average number of years that people live in this country.*1716

*Let us start with first things first.*1723

*Step 1, what are the cases?*1726

*These cases actually represent countries and if you put your cursor over these dots it will tell you what country it is.*1728

*In www.dotminder, one nice thing is that you know the population of that country just by the size of the dots.*1738

*All the dots are different sizes.*1746

*Here it tells you the geographic regions.*1751

*Yellow is the Americas.*1754

*Red is East Asia.*1757

*Violet is Africa.*1761

*Green is Middle East and Northern Africa.*1765

*Orange is Europe and Central Asia.*1769

*You could probably guess what this big one is, China and also India.*1773

*These are the big circles.*1780

*If you want to find the United States it is a yellow country and quite roughly.*1781

*We live quite a long time.*1787

*That is the United States.*1790

*If you look behind it there is Singapore which is a very small country but they are very rich and high GDP/capita.*1792

*High income per person but also high in life expectancy.*1801

*India is also in the middle of the plot and it is median in terms of income but also median in terms life expectancy.*1807

*One thing you might notice is Africa is clustered down here or maybe these countries have relatively lower income per person.*1818

*Also relatively low life expectancy compared to these other countries.*1830

*You could also see that Europe is clustered down here.*1834

*America is up in there.*1840

*Asia is also up in the higher end of this.*1843

*Immediately you see this positive association.*1850

*You see this positive association and it seems roughly linear or maybe a little bit curve but roughly linear.*1855

*Another wonderful thing about www.dotminded.org that we will be talking that much today is that it has this data from 1800 all the way to 2000.*1857

*If you hit this point button, it will play for you how this scatter plot came about over time.*1862

*You see a lot of countries started off with a very low population numbers.*1884

*All the dots are relatively small.*1891

*But the dots grow our GDP will grow and at the same time our life expectancy will grow.*1893

*You will see that European countries are hot of the pack.*1900

*Africa is down here.*1906

*China is growing faster and faster in terms of life expectancy and the GDP is catching up with it.*1908

*Finally we end up with 2009 which apparently when this data goes up.*1916

*Another thing that you could do with this visualization is that you can pick a particular country that you might be interested in. *1922

*Let us say we are very interested in Azerbaijan and we can look at just how Azerbaijan changes over time and *1934

*it will keep on running track of how Azerbaijan is growing in terms of their GDP as well as their life expectancy.*1942

*This is just a really wonderful graph and you could do a lot of different kinds of variables for these nations. *1953

*But let us answer our five questions and back to more statistics things.*1962

*The first thing is that these are nations that are represented and it is their income per person, by life expectancy.*1967

*That is the first thing.*1987

*We have figured out what the cases are and what the variables are.*1991

*The second thing is the shape.*1994

*These are roughly linear and maybe a little bit curved.*1997

*We have seen some clusters of these geographic clusters, but not really in terms of the actual of that.*2002

*If you thought of these as just blacked out and would it would create roughly this line.*2008

*Let us talk about the trend.*2016

*The trend definitely seems to be a positive association, so as GDP is greater, life expectancy is also greater.*2021

*As GDP is lower, life expectancy is also lower.*2033

*The rate in the positive way, not opposite meaning.*2038

*Let us talk about spread and we can imagine a line and see some of the spread and maybe this is a moderate spread *2042

*and it is not that you see a perfect line, but it is not like so spread out you cannot see the line either.*2054

*Maybe moderate might be a good answer for that.*2059

*And number five let us think of why that must be.*2063

*We want to consider a couple of things when we think about the the relationship between these two variables.*2067

*We want to think about how variable 1 might impact variable 2.*2077

*We also want to think about how variable 2 might impact variable 1.*2082

*Finally, we might want to think about how some third variable, variable 3, the mystery variable might impact both 1 and 2.*2090

*We might think if you have a higher income per person, if you are a richer country you have better health care, better facility, better sanitation.*2101

*You might have greater life expectancy.*2113

*Also if you have greater life expectancy, you could invest in more education and more long-term things, and because of that might increase income per person.*2116

*You might be able to share more cultural capital.*2124

*Who knows right?*2133

*There might be some third variable.*2133

*Maybe government that governs so well that you have this great income also have good health care or other things to have great life expectancy.*2135

*It might be the different things or maybe like some countries have more.*2146

*If you have a lot of work in your economy sectors, but also life expectancy suffers.*2150

*That is like a third variable.*2157

*It might be a whole bunch of different things.*2160

*It is such a long answer but we have not write it down.*2164

*You want to think about all the different ways that they might impact each other. *2166

*Here we have almost the same idea, but now we plotted income per person by infant mortality and infant mortality is the rate of infant deaths.*2175

*Infants are counted as children under the age of one.*2188

*How many infant deaths you have per 1000 births?*2193

*Here we see immediately that it seems pretty linear. *2200

*It seems to hug the line pretty closely.*2206

*We already know its nations. *2209

*This seems to be a negative association.*2217

*Remember negative in this case means opposite.*2223

*As the other one goes up, the other one goes in the opposite direction.*2227

*As income goes up, infant mortality goes down.*2231

*Countries that are very wealthy have very low rates of infant mortality.*2234

*They are not losing a lot of infants.*2239

*Countries that are more poor where their income is very low they have a higher rate of infant mortality.*2244

*So that is what we think of a negative association.*2253

*Sorry I skipped to that the three.*2256

*Step 2 is shape and I am going to write just linear because this seems to be even more linear than before.*2259

*Let us say this is moderate to strong because you could clearly see that line and let us think about why there might be the negative association.*2267

*You could think of infant mortality as the opposite of life expectancy.*2283

*Life expectancy, the greater the number of the sort of better the health.*2289

*Infant mortality, the lower the number the better the health.*2294

*Those two ideas are negatively associated with each other. *2299

*It makes sense that they would have the exact opposite relationship to income per person.*2304

*Once again we might want to think about how variable 1 impacts variable 2.*2312

*How variable 2 impacts variable 1?*2320

*And also how third variable might impact both one and two.*2323

*Income might be to better healthcare, better prenatal care and that might to better mortality.*2328

*Also having less infant mortality might somehow help the economy. *2339

*For instance, having a growth in the population often helps economies grow in their force to get more jobs and *2350

*have more things to serve more people but also there might be a third variable again, like war where there are times *2357

*or disease and that might reduce infant mortality and income per person.*2366

*Those kind of things might be much more what you want to think about for answer number five.*2373

*I think this dotminder.org data set is just really interesting.*2380

*You might want to play with the different kinds of axis that you can actually create and you could create these wonderful scatter plot from real data from the world.*2386

*You could get women's education and you can look at other aspects of the economy or health or public policy.*2400

*You can go to war, you would get a whole bunch of different things.*2410

*Example 3, we are back to sort of more mundane kinds of statistics problems and we expect that these variables to have a positive or negative relationship or trends.*2416

*Would you expect weak strength or strong strength. *2430

*Well, these are sort of online and let us think about the case of chicken eggs.*2433

*For each chicken eggs they each have a length and a width.*2440

*By length, let us talk about being the axis of being the elongation.*2443

*That would be like this length and then for the chicken egg this is the width.*2451

*With these have a positive association or a negative association.*2459

*Well, I imagine that chicken eggs you might have better chicken eggs, or small chicken eggs.*2464

*There might be chicken eggs that are skinny or fat, or larger version.*2471

*Imagine that length and width are sort of positively associated.*2480

*I would probably expect maybe a strong strength because the nice thing with chicken eggs in sort of like one shape.*2486

*I would imagine that this have each other closely.*2496

*Let us talk about US cars.*2502

*If our cases where US cars, but with those with weights and gas mileage look like.*2504

*It is helpful to just think about maybe a couple of US cars to just help us to think about this.*2511

*Most used cars are the Hummer, that is like very very strong on weight. *2520

*If we put weight here that might be way up here on the weight part.*2527

*In terms of gas mileage, the Hummer is not so great.*2532

*It has relatively have low gas mileage.*2537

*Whereas like really like tiny little cars they are less weight, but maybe they have greater gas mileage.*2540

*Maybe we would see something like this.*2550

*If we plotted all the US cars and their gas mileage and here we see something like the negative relationship.*2558

*They do the opposite of one another as weight goes up gas mileage goes down.*2569

*As weight goes down gas mileage goes up.*2574

*I’m not sure how strong the correlation that may be.*2578

*Maybe all the way to moderate or moderate to strong.*2582

*Maybe strong, just because I can imagine if you are putting more weight because your car is heavy then that might bring down your gas mileage.*2588

*That might be a strong connection there, but I’m not really sure. *2599

*I'm going with moderate or moderate to strong.*2602

*Example 4, join the trend, the strength and the shape for the following scatter plot.*2610

*Let us also threw in consistency just for ourselves.*2617

*And seems pretty linear and pretty positive.*2627

*A strong pretty strong.*2636

*It seems very constant that the spread is constant down here and here. *2640

*It is pretty constant throughout. *2647

*This one looks like a pretty weak strength. *2650

*I do not know if it is linear.*2658

*It looks like a cloud to me and you can draw line but it is really weak association.*2660

*The trend, it seems more positive than negative because at least there is more up here than down here.*2670

*And here is that with negative we see more here and here and if it is consistent it is pretty spread out here, but maybe a little bit less spread out here.*2682

*Maybe sort of consistent, but a little inconsistent.*2696

*Another one here these one looks definitely starts to curve to me.*2707

*This seems curvilinear.*2712

*It also seems like a positive association because as x goes up y goes down.*2715

*It seems pretty strong but maybe a little bit inconsistent because here it seems stronger and get a little bit less down here.*2722

*It is sort of consistent to me.*2733

*I can also see a curve but I also see the line going curve too.*2745

*When I see curved but now this is definitely a negative relationship because the low axis have high y.*2750

*And the high axis have low y.*2764

*It seems moderate or strong.*2771

*Moderate to moderate to strong and is pretty consistent.*2778

*I will go with constant.*2789

*Here we have a quite linear negative and it seems pretty strong too.*2793

*Let us go with strong and noticed that these are very light.*2812

*I’m sort of eyeballing it and it seems consistent.*2817

*This is just a way to just help us just eyeball these little bit better.*2824

*Get used to seeing them. *2829

*Get used to seeing some of these features very quickly. *2831

*That is scatter plot.*2834

*Thanks for using www.educator.com*2838

0 answers

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