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Without anything passed into it, it might give you a number between zero and one, or zero and 100. And you have to be very careful on how you use this to make sure that you have an even chance of picking certain numbers. But what you would do in this situation, if you had access to some random number generator, and it ... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
And so the first student alphabetically, assign the number zero, one. And you could just say one if you're using a random number generator, but I'll use two digits for it just because it'll be useful and consistent. And in a little bit, we'll use another technique where it's gonna be nice to be consistent with our numb... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
And so the next one, zero, two, and you go all the way to 79, and all the way to 80. And then you use your random number generator to keep generating numbers from one to 80. And as long as you don't get repeats, you pick the first 30 to be your actual random sample. Another related technique, which is a little bit more... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
Another related technique, which is a little bit more old school, but is definitely the way that it has been done in the past and even done now sometimes, is to use a random digit table. You still start with these number associations with each student in the class, and then you use a randomly generated list of numbers.... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
And you start at the beginning. And you say, okay, we're interested in getting 30 two-digit numbers from one to 80, including one in 80. So one technique that you could use is you start it right at the beginning, and you could say, all right, this is a randomly generated list of numbers. So the first number here is 59.... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
So the first number here is 59. Is 59 between one and 80? Sure is. As long as we, you know, if this was a zero one, that would have worked. If this was an eight zero, that would have worked. If this was a zero zero, it wouldn't have worked. If this was an eight one, it wouldn't have worked. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
As long as we, you know, if this was a zero one, that would have worked. If this was an eight zero, that would have worked. If this was a zero zero, it wouldn't have worked. If this was an eight one, it wouldn't have worked. But this would be our, this right over here, that would be our first name that we, you could im... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
If this was an eight one, it wouldn't have worked. But this would be our, this right over here, that would be our first name that we, you could imagine the same as picking that first name out of the hat, whoever's associated with number 59. Now, you would move on. You get the next two digits. The next two digits are 83... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
You get the next two digits. The next two digits are 83. They don't fall into our range from one to 80, so we're not going to use it. Then you look at the next two digits. So we get a five and a nine. Well, that fits in our range, but we already picked 59. We already picked person 59, so we're not gonna pick 59 again. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
Then you look at the next two digits. So we get a five and a nine. Well, that fits in our range, but we already picked 59. We already picked person 59, so we're not gonna pick 59 again. So we keep moving on. Then we get a 37. Well, that's in our range. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
We already picked person 59, so we're not gonna pick 59 again. So we keep moving on. Then we get a 37. Well, that's in our range. We haven't picked that yet. We do that. Then we get a zero zero. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
Well, that's in our range. We haven't picked that yet. We do that. Then we get a zero zero. Once again, not in our range. I think you see where this is going. 91, not in our range. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
Then we get a zero zero. Once again, not in our range. I think you see where this is going. 91, not in our range. 23, it's in our range, and we haven't picked it yet. So we're gonna pick the 23. I think you see where this is going. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
91, not in our range. 23, it's in our range, and we haven't picked it yet. So we're gonna pick the 23. I think you see where this is going. We're gonna keep going down this list in the way that I've just described until we get 30 of these. We've just gotten three. We just have to keep on going. | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
I think you see where this is going. We're gonna keep going down this list in the way that I've just described until we get 30 of these. We've just gotten three. We just have to keep on going. And this isn't an exhaustive list of all of the different ways that you can get random numbers, but it starts to give you some ... | Techniques for generating a simple random sample Study design AP Statistics Khan Academy.mp3 |
In this video, we're going to get our bearings on the different types of studies you might statistically analyze or statistical studies. So first of all, it's worth differentiating between an experiment and an observational study. I encourage you, pause this video and think about what the difference is, at least in you... | Types of studies AP Statistics Khan Academy.mp3 |
Well, you might already be familiar with experiments. You oftentimes have a hypothesis that if you do something to one group, that it might have some type of statistically significant impact on them relative to a group that you did not do it to, and you would be generally right. That is the flavor of what we're talking... | Types of studies AP Statistics Khan Academy.mp3 |
An experiment where actively putting people or things into a control versus treatment group. In the treatment group, you put the people, and you usually would want to randomly select people into the treatment group. Maybe it's a new type of medication, and maybe in the treatment group, they actually get the medication,... | Types of studies AP Statistics Khan Academy.mp3 |
And then you wait some time, and you can see is there a statistically significant difference between the treatment group, on average, and the control group. So that's what an experiment does. It's kind of this active sorting and figuring out whether some type of stimulus is able to show a difference. While an observati... | Types of studies AP Statistics Khan Academy.mp3 |
While an observational study, you don't actively put into groups. Instead, you just collect data and see if you can have some insights from that data. If you can say, okay, the data, there's a population here. Can I come up with some statistics that are indicative of the population? I might just wanna look at averages,... | Types of studies AP Statistics Khan Academy.mp3 |
Can I come up with some statistics that are indicative of the population? I might just wanna look at averages, or I might wanna find some correlations between variables. But even when we're talking about an observational study, there are different types of it, depending on what type of data we're looking at, whether th... | Types of studies AP Statistics Khan Academy.mp3 |
So if we're thinking about an observational study that is looking at past data, and I could imagine doing something like this at Khan Academy, where we could look at maybe usage of Khan Academy over time. We have these things in our server logs, and we're able to do some analysis there. Maybe we're able to analyze and ... | Types of studies AP Statistics Khan Academy.mp3 |
That would be past data, and that type of observational study would be called a retrospective study. Retro for backwards, and spective, looking. So a retrospective observational study would sample past data in order to come up with some insights. Now, you could imagine there might be the other side. What if we are tryi... | Types of studies AP Statistics Khan Academy.mp3 |
Now, you could imagine there might be the other side. What if we are trying to observe things into the future? Well, here, you might take a sample of folks who you think are indicative of a population, and you might want to just track their data. So you could even consider that to be future data. So you pick the group,... | Types of studies AP Statistics Khan Academy.mp3 |
So you could even consider that to be future data. So you pick the group, the sample, ahead of time, and then you track their data over time. I'm just gonna draw it as these little arrows that you're tracking their data. And then you see what happens. For example, you might randomly select, hopefully a random sample of... | Types of studies AP Statistics Khan Academy.mp3 |
And then you see what happens. For example, you might randomly select, hopefully a random sample of 100 women, and you wanna see in the coming year how many eggs do they eat on average per day. Well, what you would do is you selected those folks, and then you would track that data for each of them every day. And then o... | Types of studies AP Statistics Khan Academy.mp3 |
And then once you have the data, you could actually do it while you're collecting it, but at the end of the study, you'll be able to see what those averages are, but you can also keep track of it while you're taking that data. And you could imagine what this was called. Instead of retrospective, we're now looking forwa... | Types of studies AP Statistics Khan Academy.mp3 |
So it is prospective, forward-looking observational study. Last but not least, some of y'all are probably thinking, what about if we're doing something now? If we go out there and we were to survey a bunch of people and say, how many eggs did you eat today? Or who are you going to vote for? What might we call that? Wel... | Types of studies AP Statistics Khan Academy.mp3 |
Or who are you going to vote for? What might we call that? Well, it's tempting to call it something with a prefix and then spective, so it all matches, but it turns out that the terminology that statisticians will typically use is a sample survey. Sample survey. That right now, you're going to take a, hopefully random ... | Types of studies AP Statistics Khan Academy.mp3 |
And they gave us a bunch of data points. And it says if it helps, you might drag the numbers around, which I will do, because that will be useful. And they say the order isn't checked, and that's because I'm doing this on Khan Academy exercises up here in the top right where you can't see there's actually a check answe... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So I encourage you to use the exercises yourself. But let's just use this as an example. So the first thing, if I'm going to do a box and whiskers, I'm going to order these numbers. So let me order these numbers from least to greatest. So let's see, there is a 1 here. And we've got some 2's here. And some 3's. | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So let me order these numbers from least to greatest. So let's see, there is a 1 here. And we've got some 2's here. And some 3's. I have one 4. Then 5's. I have a 6. | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
And some 3's. I have one 4. Then 5's. I have a 6. I have a 7. I have a couple of 8's. And I have a 10. | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
I have a 6. I have a 7. I have a couple of 8's. And I have a 10. So there you go. I have ordered these numbers from least to greatest. And now, well, just like that I can plot the whiskers because I see the range. | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
And I have a 10. So there you go. I have ordered these numbers from least to greatest. And now, well, just like that I can plot the whiskers because I see the range. My lowest number is 1. So my lowest number is 1. My largest number is 10. | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
And now, well, just like that I can plot the whiskers because I see the range. My lowest number is 1. So my lowest number is 1. My largest number is 10. So the whiskers help me visualize the range. Now let me think about what the median of my data set is. So my median here is going to be, let's see, I have 1, 2, 3, 4, ... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
My largest number is 10. So the whiskers help me visualize the range. Now let me think about what the median of my data set is. So my median here is going to be, let's see, I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 numbers. Since I have an even number of numbers, the middle 2 numbers are going to help define... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So my median here is going to be, let's see, I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 numbers. Since I have an even number of numbers, the middle 2 numbers are going to help define my median because there's no one middle number. I might say this number right over here, this 4, but notice there's 1, 2, 3, 4,... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
The same thing would have been true for this 5. So this 4 and 5, the middle is actually in between these 2. So when you have an even number of numbers like this, you take the middle 2 numbers, this 4 and this 5, and you take the mean of the 2. So the mean of 4 and 5 is going to be 4 and 1 half. So that's going to be th... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So the mean of 4 and 5 is going to be 4 and 1 half. So that's going to be the median of our entire data set, 4 and 1 half. Now I want to figure out the median of the bottom half of numbers and the top half of numbers. Here they say exclude the median. Of course I'm going to exclude the median. It's not even included in... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
Here they say exclude the median. Of course I'm going to exclude the median. It's not even included in our data points right here because our median is 4.5. So now let's take this bottom half of numbers over here and find the middle. So this is the bottom 7 numbers. So the median of those is going to be the one that ha... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So now let's take this bottom half of numbers over here and find the middle. So this is the bottom 7 numbers. So the median of those is going to be the one that has 3 on either side. So it's going to be this 2 right over here. So that right over there is kind of the left boundary of our box. And then for the right boun... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
So it's going to be this 2 right over here. So that right over there is kind of the left boundary of our box. And then for the right boundary, we need to figure out the middle of our top half of numbers. Remember, 4 and 5 were our middle 2 numbers. Our median is right in between at 4 and 1 half. So our top half of numb... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
Remember, 4 and 5 were our middle 2 numbers. Our median is right in between at 4 and 1 half. So our top half of numbers starts at this 5 and goes to this 10, 7 numbers. The middle one is going to have 3 on both sides. The 7 has 3 to the left, remember, of the top half, and 3 to the right. And so the 7 is, I guess you c... | Another example constructing box plot Data and statistics 6th grade Khan Academy.mp3 |
She then created the following scatter plot and trend line. So this is salary in millions of dollars and the winning percentage. And so here we have a coach who made over $4 million and it looks like they won over 80% of their games. Then you have this coach over here who has a salary of a little over a million and a h... | Interpreting y-intercept in regression model AP Statistics Khan Academy.mp3 |
Then you have this coach over here who has a salary of a little over a million and a half dollars and they are winning over 85%. And so each of one of these data points is a coach and it's plotting their salary or their winning percentage against their salary. Assuming the line correctly shows the trend in the data and... | Interpreting y-intercept in regression model AP Statistics Khan Academy.mp3 |
There are some outliers here that are well away from the model and this isn't a, it looks like there's a linear, a positive linear correlation here, but it's not super tight and there's a bunch of coaches right over here in the lower salary area going all the way from 20 something percent to over 60%. Assuming the line... | Interpreting y-intercept in regression model AP Statistics Khan Academy.mp3 |
But anyway, let's see which of these choices actually describe that. So let me look at the choices. The average salary was $39 million. No, no one on our chart made 39 million. On average, each million dollar increase in salary was associated with a 39% increase in winning percentage. So that would be something related... | Interpreting y-intercept in regression model AP Statistics Khan Academy.mp3 |
No, no one on our chart made 39 million. On average, each million dollar increase in salary was associated with a 39% increase in winning percentage. So that would be something related to the slope, and the slope was definitely not 39. The average winning percentage was 39%. No, that wasn't the case either. The model i... | Interpreting y-intercept in regression model AP Statistics Khan Academy.mp3 |
We're told that Maya and Doug are finalists in a crafting competition. For the final round, each of them will randomly select a card without replacement that will reveal what the star material must be in their craft. Here are the available cards. So I guess the star material is the primary material they need to use in ... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
So I guess the star material is the primary material they need to use in this competition. Maya and Doug both want to get silk as their star material. Maya will draw first, followed by Doug. What is the probability that neither contestant draws silk? Pause this video and see if you can work through that before we work ... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
What is the probability that neither contestant draws silk? Pause this video and see if you can work through that before we work through this together. All right, now let's work through this together. So the probability that neither contestant draws silk. So that would be, I'll just write it another way, the probabilit... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
So the probability that neither contestant draws silk. So that would be, I'll just write it another way, the probability that, I'll write MNS for Maya no silk. So Maya no silk and Doug no silk. That's just another way of saying what is the probability that neither contestant draws silk? And so this is going to be equiv... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
That's just another way of saying what is the probability that neither contestant draws silk? And so this is going to be equivalent to the probability that Maya does not get silk, Maya no silk, right over here, times the probability that Doug doesn't get silk, given that Maya did not get silk, given Maya no silk. This ... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
And so let's calculate each of these. So this is going to be equal to the probability that Maya gets no silk, she picked first. There's six options out of here. Five of them are not silk. So it is five over six. And then the probability that Doug does not get silk, given that Maya did not get silk. So if Maya did not g... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
Five of them are not silk. So it is five over six. And then the probability that Doug does not get silk, given that Maya did not get silk. So if Maya did not get silk, then that means that silk is still in the mix, but there's only five possibilities left because Maya picked one of them. And four of them are not silk. ... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
So if Maya did not get silk, then that means that silk is still in the mix, but there's only five possibilities left because Maya picked one of them. And four of them are not silk. They're still silk as an option. And it's important to recognize that the probability that Doug gets no silk is dependent on whether Maya g... | General multiplication rule example dependent events Probability & combinatorics.mp3 |
Suppose that each pack has probability 0.2 of containing the card Hugo is hoping for. Let the random variable X be the number of packs of cards Hugo buys. Here is the probability distribution for X. So it looks like there is a 0.2 probability that he buys one pack, and that makes sense because that first pack, there is... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
So it looks like there is a 0.2 probability that he buys one pack, and that makes sense because that first pack, there is a 0.2 probability that it contains his favorite player's card. And if it does, at that point, he'll just stop. He won't buy any more packs. Now what about the probability that he buys two packs? Wel... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
Now what about the probability that he buys two packs? Well, over here, they give it a 0.16, and that makes sense. There is a 0.8 probability that he does not get the card he wants on the first one, and then there's another 0.2 that he gets it on the second one. So 0.8 times 0.2 does indeed equal 0.16. But they're not ... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
So 0.8 times 0.2 does indeed equal 0.16. But they're not asking us to calculate that. They give it to us. Then the probability that he gets three packs is 0.128, and then they've left blank the probability that he gets four packs. But this is the entire discrete probability distribution because Hugo has to stop at four... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
Then the probability that he gets three packs is 0.128, and then they've left blank the probability that he gets four packs. But this is the entire discrete probability distribution because Hugo has to stop at four. Even if he doesn't get the card he wants at four on the fourth pack, he's just going to stop over there.... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
So we could actually figure out this question mark by just realizing that these four probabilities have to add up to one. But let's just first answer the question. Find the indicated probability. What is the probability that X is greater than or equal to two? What is the probability? Remember, X is the number of packs ... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
What is the probability that X is greater than or equal to two? What is the probability? Remember, X is the number of packs of cards Hugo buys. I encourage you to pause the video and try to figure it out. So let's look at the scenarios we're talking about. Probability that our discrete random variable X is greater than... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
I encourage you to pause the video and try to figure it out. So let's look at the scenarios we're talking about. Probability that our discrete random variable X is greater than or equal to two. Well, that's these three scenarios right over here. And so what is their combined probability? Well, you might want to say, he... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
Well, that's these three scenarios right over here. And so what is their combined probability? Well, you might want to say, hey, we need to figure out what the probability of getting exactly four packs are. But we have to remember that these all add up to 100%. And so this right over here is 0.2. And so this is 0.2, th... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
But we have to remember that these all add up to 100%. And so this right over here is 0.2. And so this is 0.2, the other three combined have to add up to 0.8. 0.8 plus 0.2 is one, or 100%. So just like that, we know that this is 0.8. If for kicks, we wanted to figure out this question mark right over here, we could jus... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
0.8 plus 0.2 is one, or 100%. So just like that, we know that this is 0.8. If for kicks, we wanted to figure out this question mark right over here, we could just say that, look, have to add up to one. So we could say the probability of exactly four is going to be equal to one minus 0.2 minus 0.16 minus 0.128. I get on... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
So we could say the probability of exactly four is going to be equal to one minus 0.2 minus 0.16 minus 0.128. I get one minus 0.2 minus 0.16 minus 0.128 is equal to 0.512, is equal to 0.512. 0.512. You might immediately say, wait, wait, this seems like a very high probability. There's more than a 50% chance that he buy... | Probability with discrete random variable example Random variables AP Statistics Khan Academy.mp3 |
The last video, we constructed an experiment where we had a drug that we thought might help control people's blood sugar. We looked for something that we could measure as an indicator of whether blood sugar is being controlled, and hemoglobin A1c is actually what people measure in a blood test. We have a whole video on... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
So that's the explanatory variable, whether or not you're taking the pill, and the response variable is, well, what does it do to your hemoglobin A1c? We constructed a somewhat classic experiment where we had a control group and a treatment group, and we randomly assigned folks into either the control or the treatment ... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
And so we would measure folks' A1cs before they get the treatment or the placebo. Then we would wait three months of getting either the treatment or the placebo, and then we'll see if there's a statistically significant improvement. Now, this was a pretty good, and it's a bit of a classic experimental design. We would ... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
We would also do it so that the patients don't know which one they're getting, placebo or the actual treatment, so it's a blind experiment. And it would probably be good if even the nurses or the doctors who are administering the pills, who are giving the pills, also don't know which one they're giving, so it would be ... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
Other people should try to prove the same thing, maybe in different ways. But even the way that we designed it, there's still a possibility that there are some lurking variables in here. Maybe, you know, we took care to make sure that our distribution of men and women was roughly even across both of these groups, but m... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
Maybe it changes their behaviors in other ways, or maybe older people, when they take a pill, they decide to eat worse because they say, oh, this pill's gonna solve all my problems. And so you could have these other lurking variables, like age, or where in the country they live, or other types of things, that just by t... | Matched pairs experiment design Study design AP Statistics Khan Academy.mp3 |
She recorded the height in centimeters of each customer and the frame size in centimeters of the bicycle that customer rented. After plotting her results, Vera noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
So she had a bunch of customers, and she recorded, given the height of the customer, what size frame that person rented, and so she might have had something like this, where in the horizontal axis, you have height measured in centimeters, and in the vertical axis, you have frame size that's also measured in centimeters... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
Oftentimes, you would use a spreadsheet or you use a computer, and that line is trying to minimize the square of the distance between these points, and so the least squares regression, maybe it would look something like this, and this is just a rough estimate of it. It might look something, actually, let me get my rule... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
So let me plot it. So this, that would be the line, so our regression line, y-hat, is equal to 1 3rd plus 1 3rd x, and so you could view this as a way of predicting or either modeling the relationship or predicting that, hey, if I get a new person, I could take their height and put it as an x and figure out what frame ... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
Well, the residual is going to be the difference between what they actually produce and what the line, what our regression line would have predicted, so we could say residual, let me write it this way, residual is going to be actual, actual minus predicted. So if predicted is larger than actual, this is actually going ... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
Well, we know the actual, they tell us that, they tell us that they rent, it's a, the 155-centimeter person rents a bike with a 51-centimeter frame, so this is 51 centimeters, but what is the predicted? Well, that's where we can use our regression equation that Vera came up with. The predicted, I'll do that in orange, ... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
Their height is 155. That's the predicted. Y hat is what our linear regression predicts, our line predicts, so what is this going to be? This is going to be equal to 1 3rd plus 155 over three, which is equal to 156 over three, which comes out nicely to 52. So the predicted on our line is 52, and so here, so this person... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
This is going to be equal to 1 3rd plus 155 over three, which is equal to 156 over three, which comes out nicely to 52. So the predicted on our line is 52, and so here, so this person is 155, we can plot them right over here, 155. They're coming in slightly below the line. So they're coming in slightly below the line r... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
So they're coming in slightly below the line right there, and that distance, which is, and we can see that they are below the line, so that distance is going to be, or in this case, the residual is going to be negative, so this is going to be negative one. And so if we were to zoom in right over here, you can't see it ... | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
And in this case, it is negative one. And so that is our residual. This is what the actual data minus what was predicted by our regression line. | Calculating residual example Exploring bivariate numerical data AP Statistics Khan Academy.mp3 |
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