Nutrients by the Numbers

Good morning. Thank you so much for joining joining me today. I sure appreciate you being with us. My name is Gaye Wilson. I'm a registered dietitian and the food data curator here at Wolfram Research. And today we're going to be talking about one of my favorite topics, food that's shared an interest shared by many of us, as well as statistics. So it's called Nutrients by the Numbers, food and nutrition statistics with the Wolfram language. So I'm very excited about sharing this topic with you today and certainly appreciate you joining us. The reason I mentioned that I'm a registered dietitian because the thing I love, many things I love about the Wolfram language, but one of the things I really love about it is you can come to it from whatever your background is. So if you're, whether you're in manufacturing or retail or finance or healthcare, as myself, you can come to the Wolfram language and do your statistical analysis, do your research, do all sorts of analysis. So I think that that's a really neat part about it. So today we're going to be doing food, food and nutrition and using the statistical distributions that are available with the Wolfram language. So I'm very excited about that. And as I mentioned, you also can use these statistical functions in whatever your specialty is, your unique specialty is. So, so let's go ahead and get started here. The way we have food organized in the, in the Wolfram language is in these entities. So the hold that date hold data behind the entity, whether it's the strawberry or the blueberry and so forth, all of that nutrition data, all those, whether it's sodium, potassium, carbs, protein, all of that is held within that entity. And there are hundreds of specific brands in those foods and USDA entities behind that food entity. So, for example, I'm going to be pulling together some groups before we start analyzing the data. We're going to pull together some groups of types of food so we can analyze those groups against one another in statistical distributions today. So, for example, I've said let's go find these berries. We're going to have a group of berries that we're going to analyze. And you can see quickly look at what this entity looks like. And here's for example, the strawberry, the blueberry, et cetera. And so that's where all of our data is held within, with that, with that particular type of berry. And so, for example, just looking at the length of the berry of the strawberries, let's see how many strawberries, brand strawberries, USDA Strawberries. How many do we have behind this yellow box right here? And we've got 259 different strawberries, whether it's branded and so forth. In fact, what I've done here is I said let's just. Of the 259, let's randomly look at five of those berries and see there's basically, here's a variety. USDA has lots of strawberries in their database that we use. So if we also want to see low, who else have we got here behind? We've got a, you know, all these different branded strawberries of those 259. So this is just showing you the variety of actual explicit data that's behind each entity of food that we're going to work with today. So, as I said, we're going to. Before we get started, I want to quickly get our groups one of, I guess, a good data analysis. We want to get our groups put together first of what we're going to look at. So you can see we've already defined our berries. I've gone ahead and defined our citrus. We're going to do some analysis of citrus fruits. So we're going to take a look. You can see we've got our lemons, our entities. So we've pulled that. So next we're going to do a group of greens. We're going to be looking at some folate, all kinds of nutrients in our kale and our spinach and so forth. So I've gone ahead and let's get our greens put together, get our. Our entities. So we get our data ready to go. Gonna do the same with meats here. We've pulled together a variety of meats, bacon, beef, chicken, et cetera. So we've pulled that together. Some of my favorites, pastrami, bratwurst. So. And then also we're going to pull together some fish, some varieties of fish. So you can see, got our salmon in there. Good, good source of those omega 3s. So. And anchovies and a variety of fish here that we're going to be taking a look at. And down here, where I'm from, got a lot of catfish. So we're going to. Those are our food groups ready to go. We've pulled together all that data is behind it. And then we're going to start our analysis with the statistical distributions and functions that are available in the Wolfram language, which is. I sure wish I'd had this a couple of decades ago when I had known about this, when I was doing my thesis. It would have made my thesis analysis a lot more straightforward. So we're going to start with a T test. And you probably, you may be familiar with T test. It's basically asking the question. A T test is asking the question, is there a statistically significant difference between the averages or the means of two different groups? Or is that difference in their means just due to random chance? Right. So what we're going to do is we're going to take the T test function in wolfram language, and we're going to say, are the zinc and folate means of berries significantly different from the zinc and folate in green vegetables? So that's going to be our question. So berries and green vegetables are not significant sources of zinc, but we're going to use the statistics function to evaluate those trace amounts of this really vital nutrient in berries and green vegetables. Okay, so we start with the null. As all of you probably recall from your research methods classes, we start with the null hypothesis that there's no meaningful difference between berries and greens in terms of their zinc. So that's our null hypothesis. No meaningful difference. So first thing I need to do is I need to. I've already pulled together my berries groups, my zinc groups, you know, that I'm going to be looking at. So now I need to pull the zinc amount for the. The berries and for the greens. Okay? So the nice thing about the T test, it does not require your sample length to be the equal length, which is. Which is good. And then what we're going to do is I've pulled here using the. The relative zinc content for all those berries and greens that we pulled. And then also I'm going to use the quantity magnitude function, which you'll find very helpful in the Wolfram language because it's pulling out my milligrams, because these are milligrams per gram. So this is milligrams per gram of berries, milligrams per gram of greens. But we don't want that because we're going to want to do some visualization. So we want to pull our units out by saying, I'm going to use the quantity magnitude function. That'll take those milligrams out so we can do some visualizations, some charting. So I've already pulled, as you can see, we basically have just run these functions and pulled the actual data for relative zinc content in berries and greens. So what can I do with this now that I have this data for each of those entities, each of those varies, each of those types of vegetables? Well, I can easily We've got a mean function, you know, what's my mean? So that certainly, you know, that's certainly. Very quickly and quick, get a quick picture of your mean. Now, one thing the T test does require, as you may recall from your statistical methods classes, it does require normal distribution of the data. So that's the requirement. Now the nice thing is if the, the T test function in the Wolfram language will automatically test for normal distribution. But what I wanted to do here today, so it'll tell you if it's not normally distributed, but I want us to check it ourselves because I want us to use the distribution fittest function. So you see, when you don't want to check it yourself, you see how that works? So what that's going to do, it's going to return a P value, which is. So there are default null hypothesis. Is that the norm? The data is normally distributed, right? So I'm going to run the fit test, the distribution fit test on my data for berries and green zinc. And I want to just double check, you know, just know that it, you know, we're double checking that it's normally distributed so that we can use the T test. Okay? So we're going to use the 5% significance level that's very, very common. You've probably used it before to determine whether we're going to reject or fail the null hypoth or fail to reject the null hypothesis. Okay? Okay. So if we look at our distribution fit test, we can see that they're greater than 5%, greater than 0.05. So because they are greater than 0.05, we fail to reject that null hypothesis and we can conclude that the zinc is normally, data is normally distributed for both groups. Okay? So it says, yeah, great, we're going to go ahead and use the T test. It's appropriate. So I've run, when I run T test, very straightforward in the Wolfram language T test, run it. That's really handy if I'm going to run my T test and I get 0.04. And so what I found is I am less than 5%, right? So I am less than 0.05. I can reject the null hypothesis and I can conclude there's a significant difference in the average zinc of berries versus the average zinc of green vegetables. So I thought one good way to visualize this, easily visualize this in the Wolfram language is a paired smooth histogram. And you can see the spread. You can see how the greens is spread a little bit farther out, different heights. So you can sort of see that significant difference in the two groups visually. Next, we're going to examine that folate. We talked about looking at the folate difference in berries versus greens. Right. So I'm not going to. I'll show you. I went ahead and ran the data. We use quantity, magnitude, just like we did before. And I've pulled that relative. You can see my property that I'm pulling relative folate food, folate content for each of those groups. Okay, so quickly, I like doing the distribution fit test. You don't have to. The Wolfram language will tell you if the T test is appropriate. But I like to say, let's take a look. Okay. Again, they're both above 5%. Okay. So it's good. We can use the T test just like we did before. And when I ran the T test, you can see with folate, it is below that 5%, quite a bit below that 0.05. That means we can reject the null hypothesis again because the folate difference between the two groups is statistically significant. This is something I really thought was very cool that I like using is the Wolfram language will write the T test, the test conclusion for you. I like that. And it'll either give you a full length description of the test conclusion, or you can even ask for the short test conclusion. So you can see I set my difference. I want to know zero. Set my difference is zero, meaning I don't. Is there any difference? Right. And it says the null hypothesis. You can reject it based on the T test. And then I like the short conclusion. It just says reject. So that's. I think that's a neat way to basically do a. Conclude. Do your conclusion. A paired histogram I found is. I like the way this visualized. I'm very proud of myself. I use the chart style, growth colors. I was able to get my green folate as green and my berries folate as berry colored. So I was very, very proud of my styling there. So you can see a paired histogram is a great way to see that significant difference in the folate content. And you can see how they compare real quickly. And you can tell that there certainly is a significant difference there. Okay, so now that we can. We can go on and look at. We're going to look at iron. We're going to go into another test, but first we're going to look at iron for the berries and the green vegetables. So let's get a new. We're going to get a new. A new nutrient. And we're going to pull, we're pulling this relative iron content here. So as you can see, we've gone ahead and pulled it just like we did before. Our iron content for berries, our iron content for green vegetables. So that's what we're going to be working with now. Now, I wanted to quickly, before we go in to run the test, to check for significant difference, I wanted to show you some visualizations. I try to mix up my visualizations in the Wolfram language and we've got a lot of them we can choose from, which is really great. I like that. This, if you want something, you don't have much space. You want something very succinct. You don't want to use up a lot of space. This, the number line plot is a great little visual and so you can see the spread there between the berries and greens just in terms of the distribution there. So scatter plots we're very familiar with. That's the list plot function and the Wolfram language. And so that's very, very popular, as we all know. And you can do, you can do specific markers. I've just used automatic, but you can specialize your plot markers in your legends. And lots of options available to you with the list plot function. So you can see that's our iron data kind of scattered around there. Box and whisker you're probably very familiar with as well that's available. So you could see, you know, your box represents your middle 50% of the data values. The white line in the box is the median. So and then your vertical lines, you know, or your whiskers where your data lies. Now, the default excludes the outliers, but there is an option in the Wolfram language for you to include those outliers in the chart. But they, I didn't want my chart like going if there was a berry that was far out lying everybody else. So I've stayed with the default, which. But you can include the outliers if you, if you so choose. So that is an option. So, so this is where we, you know, looking at our berries and iron, you can not surprisingly, we, our instinct says greens have more iron. Right. So you cannot surprisingly see that that's a, that that box is a higher value there in greater range. Okay, we're going to keep going. Quick distribution. And here's the difference. I wanted us to look at distribution fit test one more time because I wanted to see on the previous ones, so and on the previous ones that you, you know, we had, they were significantly different. They were all above 5%. Right? So but here's the difference here. If we look at greens, the distribution fit test where we're below, we've dropped below that 5% level. Therefore that. What's that telling us is telling us that data is not normally distributed. Okay? So when that data is not normally distributed, that data is skewed. We are going to, we can use the Mann Whitney U test in the Wolfram language which many of you probably are very familiar with as well. That's a non parametric test that's going to tell us whether those two population distributions have about the same shape and location. Okay. And it does not require a normal distribution like that T test does. So. I know, I know. I remember using the Mann Whitney in my thesis and I'm sure many of you have as well. So. But I certainly wish I'd had known about the Wolfram language to use it at the time. So that's why I wanted to share it with everybody else. So you can see, you can choose what options you want to what options you want to use. I chose a P value table and then I for a short test conclusion. Here I'd like my short test conclusion. Love that feature. So you can see our p value is 0.066% and our conclusion is do not reject the null hypothesis that there is no significant difference. Okay? So we're going to fail to reject that null hypothesis. And we therefore we conclude that there is no statistically significant difference in the average iron content of berries versus green vegetables. Okay. Now I thought a smooth histogram was a real. Is going to be a really good way I feel like to show this that there is no statistically significant difference in the average content because you can see that overlap which I think is quite, you know, we can kind of see how the iron and berries and green vegetables are matching up there quite similar and heavy overlap. So we can kind. It's easy to visualize why the conclusion was not to reject the null hypothesis. This is a really handy feature. If you got some troublesome outlier data outlier that are skewing your data and messing with your evaluation, you can trim that mean. There's a very easy function here called trim the mean and you can trim the ends of the outlier from both ends and decide what percentage you want to trim that by. So here you can see I took the GR the mean for green vegetable iron and I've trimmed it by 10% on each side and you can see my new mean there. So that's really handy. If you got those outliers you just want to go ahead and, go ahead and trim off before you do your analysis. So I'm taking a quick look at. Oh, excellent. And I'll take a look at, they're moderating the chat over here for me and we'll take a look at that afterwards. And I certainly appreciate that input over there. And if I don't have the answer today, I'm going to get that answer for you. Like I said, I'm not a statistician, I'm a registered dietitian. But if I don't have the answer, I'll get the answer for you. And if it's nutrition related, I will dig deep and find the answers for you. So I certainly appreciate your input on chat. And we'll take a look at those. We're going to move on to analysis of variants anova and that's comparing the means of three or more groups. Okay. To determine if there's statistically significant differences among those three or more groups. Okay. So first, when you're using this in Wolfram language, load up, you know, the package. Okay. Now we're going to use a one way analysis of variance because we're going to look at one categorical value variable. Okay. We're going to be looking again, we're still on relative iron content. Okay. We already defined our berries and iron group beforehand. I'm going to throw meat and fish into the mix here. So here you can see we're going to do the same thing we've been doing before, quantity, magnitude, pull off our units so we can do some visualization. And we're going to. We pulled it for meat and I pulled it for fish. So those are the three groups we're going to be looking at. Iron and berries, meats and fish. Okay. Again, this is me. I love to take a look at distribution fit test. So I want to look at the distribution fit test for the meats, the iron and meats and fish. We can see they're Both above the 5% level. Okay, so, so therefore, now let's run the ANOVA and let's see what sort of table we get back when we run this anova. So I'm gonna, I'll just go ahead and hit that again. And you can see we get a lot of data back. We get means for the group, so forth. Over here, this is what we're looking for over here. There's our P value right here. So we can conclude from this ANOVA with including all the other data that you get back that there is a significant, statistically significant difference among these three groups because we're below that 5% level. The one thing the ANOVA does not specify is which group means are significantly different from which group. Okay, but after the anova, you can use post hoc test to make that pairwise comparison, right? You want to see which groups are different from other groups. Okay, so what I've done, got some homework in the notebook for you here and homework for me too. I need to spend some time researching it myself because I would like to become more familiar. We have post tests available in the Wolfram language and you can see here that I've included a link to the documentation which I'll be spending some time with myself and learning more about these post tests that you can then make determinations about more in depth determinations based on what you found from your ANOVA analysis. So that's homework for all of us there. Okay, so let's get down to correlation, linear correlation next. Okay, so as you probably as probably know, and many of you probably already done research on correlation, and that's when the statistical relationship between two variables in which one change in one variable is associated with a proportional, that's the key word, proportional change in another variable. Okay, so a positive correlation says as one variable increases, the other variable tends to also increase negative correlation. Obviously, one variable decreases, one variable increases, the other variable tends to decrease the negative correlation. They go in the opposite directions. Okay. Okay, so let's examine the correlation. We're going to look at fat and calories in meats. Okay, so first we did what we've been doing all along. We grabbed our, we're going to, this is the property we're looking at now. Relative total fat content and relative total calories. Okay. Then in order to do our correlation, we've got our data. We're going to do the transpose function and we're going to pair the fat and calorie value values for each type of meat and then we're going to plot those pairs. So it's very easy to take that data and pair it up with the transpose function, which is great, which is excellent. Easy to do. So you can see what we've done here is I've paired it up all that group meat, fat, calories, pairs for meats and then apply if list plot is a great easy way to see, you know, to see that, you know, how is there a correlation? Are they, are they moving together? Are these moving together? And you can see our plot. We are sloping upward, but we can and not surprisingly, right. We can conclude fat and calories in meats are positively correlated. Right. As total fat increases, so do calories. Okay. Yeah. So, yeah. So certainly this is not a big surprise. Not a big surprise. But let's look at one that's less obvious. Why don't we do that? What about, let's look at vitamin C and potassium. Okay. They're, they're really vital nutrients in citrus fruits. Right. But are they correlated? Right. You generally don't think of vitamin C and potassium as being associated with one another. But, but is there a hidden statistical correlation? Maybe. Why don't. Let's look. Let's find out. So let's, we've got, we've pulled our vitamin C, our property here, look at what we're using. Relative vitamin C content. And then also we're going to pull relative potassium content and we're going to apply that to our citrus groups that we defined at the start of a, start of our, our day together. Here again, I'm going to use the transpose function. I've paired them to pair those up. Right. And then I want to take a look. Let's plot them. And our instinct was correct, as you can see. Uh, the plot. And there's no, no correlation between the, the vitamin C and the potassium and citrus. All important nutrients. Both important nutrients, but no statistical correlation between of in their relationship to each other. But it was worth trying. And then you, if you think of other possibilities, whether, especially if it's in nutrition or some. Or is this nutrient and this nutrient related. This is a great way. Or even in finance or your manufacturing or your retail sales or anything that you work in. This is a great way to quickly see is there a correlation between the two. Are they particularly related to one another in this case? This confirmed our assumption that there was no statistical correlation between vitamin C and potassium. Next, let's get to linear regression. And this is, this is great especially if you're not only in nutrition but also if you're going to be modeling, you know, say in, in sales or, or making projections, then you, you're probably familiar with linear regression as, as a way to model those relationships. And that's, you're going to, we're going to find the base best fitting straight line to represent the relationship between two variables. So our example today, since we're on our. We're with food today, food and nutrition is we are again we're going to look at the total saturated fat and the monounsaturated fat content of meats. Okay. So let's do that. You can see our two, our, our Wolfram language properties here. Relative total saturated fat content and relative total monounsaturated fat content. So I, you can see I've applied that to our meets we defined earlier. Again, I've used the transpose function to pair those up and now let's. What we're going to do in linear regression is we're going to use the Wolfram language linear model fit function. This is great. Again, wish I'd had this in, in grad school access and known about it. So go spread the word, tell your friends. So this is the linear model fit function. I want the best fit to get my intercept and my slope and then I'm going to put that in a list plot. You can see I've already done that here and this is a really great way you can, you know, style it however you like. I may want to make sure that my trend is red here and pops off. So you can see this is a great, you can see that not surprising trend, you know, not surprising relationship between saturated fat and monounsaturated fat. This is not a big shocker but, but it is a great way to model that relationship between saturated fat and monounsaturated fat in meats. So again, think of, can think of all kinds of ways to use this linear regression model. So one other thing that's very, that's very useful is you want to see how strong is that correlation and you can use the correlation function that gets you the correlation coefficient that tells you the strength and tells you the direction of that relationship. So I got excited and just stomped on my keyboard there. So that coefficient is going to be between negative 1 and 1 and 1 is at perfect positive correlation. Negative 1 is that perfect negative correlation. So your general guideline is if it's above 0.5 or below negative 0.5, it's strong correlation. If it's in between, it's weak or no correlation. What is our correlation between the saturated fat and the monounsaturated fats in meats? That's 0.9. I call that a pretty strong positive correlation, right? Which not surprising. We probably could have guessed that, right? But let's look at it. This I think is a really cool visualization you can do in the Wolfram language, the smooth 3D histogram. So we can, you can see that big old everybody, you know, the big correlation, the correlation there in this particular model visualization. You can see how strong that correlation is between that. Let's do another One that, you know, obviously not all correlations are positive. So what do we, when we think about breakfast cereals, you know, what do we think? Let's think about that. Breakfast cereals. If you think about sugar and fiber and breakfast cereals, your assumption, right, is that as sugar goes up in a, in your, in your breakfast cereals fiber is going to go down. Right. And as sugar goes down, fiber goes up. Right. Let's, let's think about, let's see if that's actually correct. Okay. In terms of the relationship between sugar and fiber and the myriad of breakfast cereals available to us these days. So again I'm going to pull my breakfast cereal, my, my entity and out of curiosity, I'm going to say how many, how many actual branded breakfast cereals do I have of data behind that? And right now in the Wolfram knowledge base, I've got 232 branded and USDA and different data points behind that actual specific breakfast cereals behind that, that entity there. So like we did earlier with the strawberries, I said, you know, hey, give me four of those. You know, here's my, I've got Cocoa Puffs, Cap' n Crunch, I've got Mini Wheats. That's personally I thought it was mini Whe. So let's look at another, another random set. What else is back here? Oh, Fruit Loops. Do we remember those? Cheerios. Very popular. So you can see we can just keep going because we've got 232. So it's amazing the range. We've got honey bunch of bunches of oats, etc. So you can see we've got a lot of foods behind with a lot of data behind our breakfast cereals entity. Next, I'm not going to make you wait on this because it's pulling all the data. The total, this is our property relative total fiber for all those 232 breakfast cereals. So I went ahead and pulled that. I put a semicolon so you wouldn't have to look at that list of all 232. But when you download the notebook, feel free to run that again and look at the more Etsy everything that's behind that. So what we did and we've, we've now pulled down the relative total fiber content for those 232 breakfast cereals like we did in the example. I'm going to get the data. So again I'm, because there's so much data behind this, I went ahead and ran it, put the semicolon. So I learned that's very valuable. We don't, I don't use up all my screen space to show you all those results. So I've gone ahead and pulled the total sugar content and the other Wolfram language property, food property, relative total fiber content. So we've got that data pulled into the notebook. I've paired that up just like transpose function, just like we did before I tested the correlation. First of all, let's look at the correlation. Negative 0.4. So what did that tell us? The negative 0.4, that, that's in that week, right. If it was a less, you know, less than negative 0.5 or greater than 0.5, it's considered strong. So negative 0.4. It's, it's strong, but it's still, you know, it's not the strongest and it's a negative correlation as we sort of had guessed right around the best fit. You know, where's my energy intercept and where's my slope? And so then let's take a look. And we just want to take a look at. And you can see, and I'll just hit that again. And you can see it's not, it's, it is a downward float. It is a negative correlation. And again, it's not a super steep, steep dive. Right. So you can see that that's negative, you know, 0.4. It's, it's downward slope, but it's not the, not this a steep decline. So you can see it's there is that, you know, negative correlation. Whereas sugar goes up in breakfast cereals, fiber goes down and vice versa. But it's not maybe as strong of a negative correlation as my instinct, you know, told me it might be. So maybe they are, maybe the manufacturers are moderating how much sugar they put in and bumping up how much fiber they put in. So I consider that that's a positive sign. So also I didn't want to go into it today, but when you get the notebook, download the notebook, I put in a link for the non linear model fit function. So you can see we're using linear, the straight line. But there is a very easy, you know, where you just change that to nonlinear model fit. If your data is not necessarily going to, you know, fit a straight line. It's, it's going to fit better with some, you know, with some curves there. The Wolfram language does give you that option very easily to change that, to model that as the curve nonlinear model as well. So what I wanted to do is also quickly just talk to you about the, I Highly recommend. There's a lot of great self paced statistics courses at the Wolfram U really recommend that you visit those. This is how I really I took this Introduction to Statistics statistics class. Got me very excited about these functions and that's how I ended up going down this path and and saying what can I do with all these statistical distribution functions and how can I apply that to to food and nutrition statistics that we have in the Wolfram knowledge base? So I took that one great class. They're all great classes. I highly recommend. Oh I took this one as well. I do highly recommend that and spend some more time learning more about all these statistics functions and putting them to use in your daily life because it's been a lot of fun. It's been a lot of fun. I'm going to look over let me check real quick over here on an inquiry from Rebecca Metadata on the source data and what is the source of data for Vitamin C. And I can. We're primarily a usda. We do have some. Let's see. Okay great. We do we have up. Oh they have included by the way the notebook is in the that we'll also have it in Wolfram community as well. And but certainly but reply to Rebecca's query about the metadata the source data. We're primarily. We do try to keep the fairly current. We're kind of always what we're doing is we really monitor what users are asking for and we're adding to it in that way. We have primarily USDA data. We have European data as well. But we also are monitoring because there's a lot more queries coming in on plant based foods that looking for those trends and adding those foods as we see more of them. So that's one of my, one of my things that I do is monitor those queries and start pulling that pulling in that data for those foods that are really coming on in popularity and becoming, you know, as you know, a lot of more plant based foods and so forth and watching for those trends and making sure that the Wolfram knowledge base includes that data. But as, as in answer to your question, we are trying USDA is our, is our primary source. We also have European food data as well and then we are also adding foods as we see the queries more and more queries for those increase as well. So I've had a great time today and I'm very, very excited about this topic. I hope you are too and do download please download the notebook and just use those functions. They're great. And stay in touch with us through Wolfram community we're keeping an eye on that and we're always looking for ideas if you do something amazing you know with the Wolfram food nutrition share share it in the in the Wolfram community with us because I'm always checking that and I'm checking for anything to what are people doing with food what are people doing with nutrition and we can and work together on that and if you have specific questions post those and and because we're very excited about food is something that touches all of us we all have a common interest in and it's a science food science is an exciting area to be in and I hope everyone who works on all industries can see that these statistical functions in the Wolfram language are useful in so many different areas whatever area you work in so thank you so much have a wonderful rest of the day looking one more time over at the chat have a wonderful rest of the day and thank you so much for being with us today take.