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In a simple regression; the ordinary least squares estimate of the slope coefficient is expected to be more precise the greater is the variation in the dependent va...

Question

In a simple regression; the ordinary least squares estimate of the slope coefficient is expected to be more precise the greater is the variation in the dependent variable and the lesser is the variation in the independent variable:TrueFalse

In a simple regression; the ordinary least squares estimate of the slope coefficient is expected to be more precise the greater is the variation in the dependent variable and the lesser is the variation in the independent variable: True False



Answers

True or False: In a least-squares regression, the response variable is normally distributed with mean $\mu_{y | x}$ and standard deviation $\sigma$.

Over here. This question when you talk about the statements, you to check if they're toward force. So if I start with the 1st 1 Huh? I would say that the coefficient off correlation is given as ah minus 0.80 Now, this means that there exists a negative correlation between a pool table. So we send. Therefore, there exists O negative correlation between the to be animals. Right? And, um so we can see that the regression line that we will have it'll have ah, negative slope, right. And therefore, we can say that if one available because is a definition of negative correlation that if one variable in Greece is the other will degrees So also, we can see why servers are like a fun available decreases the devil in Greece. Right. So because of this, I'm going to say that the given statement over here in the first part is our false statement not similar, leaving one for the next part. Now, if you're we see it at the type of correlation that is, not only do Diab State, one is deep positive on and the other is the negative that we have, right? It actually does not depend on the size off one valuable, uh, with respect to the size with respect. Oh, the size off other valuable. There is no such relation that we have. Okay. And other differences off observations from their respective means decide whether the correlation is going to be a positive one. Order. Negative. So therefore, uh, I'm saying that if why is the lesser next right? Then the coefficient off correlation between X and Y can be positive or negative. So therefore then, no correlation coefficient between them can be either. Was it a bar? Make it do. And because of this reasoning, I therefore say that this statement that they have given it wasn't the question is a false statement.

This question is a three part true or false question on us. Just wants toe explain briefly our answers, especially their books. So for the first park, it states that we choose a lily a model that path through the most eight points discussed. Hey, I have drawn to grass trying Jennifer refreshment. Look. Assume responsible, Senator. It once isn't the case. So if a hit, it s the 1st 1 If you want a drawer liner, go to the most points. We possibly go three. You look something, and it's a bit like that, but you can see, uh, you go through three points, these points and now really far away from the prediction. There's a model. It doesn't fit very well, whereas with same one were to go through just wonderful in the gaps between the residuals, as in the gaps between the prediction on the actual ones, we should call the residuals total on much smaller mouth. So this would actually be a better fit than this, even though it goes through fewer points. So the 1st 1 is vos so part two states that, um, the residuals are the observed by values minus the y values predicted by the model. No, this we don't need no explanation for, as it is in fact, true the residuals. That is exactly the definition of them. They are the difference between the actual values. I predicted values by the model Andi. A lot of questions. We'll ask you to calculate residuals or else what it means here is a joke on we need to do is take the actual way on minus predictive value. So fee is true on the final pop. See states that the least squares means that the square of the largest residual is a small as a possibly big. So that's giving you a definition of the least squares. But it is in fact, false. This definition least squares and this is an important definition is a message well fitting a graph. So you fit the growth to minimize the sum of the square. The differences between observed on estimated bodies. So what that means is, you take your residuals, which is the difference between the observed estimated about you. You want the some residual square and the reason we square them so that negative and positive residuals cancel out because you don't really mind whether they're negative or positive. You just care about the magnitude. So you want some of the residuals squares to be a small as possible. That's really important. It is a way of 15 a graph, so the definition given in the question is definitely false. So just to recap the offices of false a true for biddy on false the Sea.

We need to determine if the following statement is true. If the correlation coefficient is close to negative one, then the regression line can't be used. This is a false statement because the closer to positive one or negative one, that means your data is more of a it's more of a nice straight line and follows the equation given. So a perfect positive one. So far correlation coefficient was a positive one. That means it would be a perfect straight line, and if it's a negative one, that means it would be a perfect straight line going in a downward direction. So the closer to the positive one or negative one, that means your data is good data and you can use the line after doing the regression. So in this case the statement is false.

This question is a three part true or false question on it says if he owns it. If you believe that's to be force, explain it. So part A states that some residuals from a least squares and any model will be positive and some will be negative on this is most certainly true. So let's take Let's just have a quick look at WASA case. That's a You have part that looks a little bit like this on your mini model. Looks something like this. You can see some of the points or below seven point are buff, so some will have positive withdrawals and some will have negative residuals. I remember that a residual is the actual value minus the corrected by. So a is true. What now It's like a fee. So be says the least quest means that some of the squares of the residuals are minimized. No, While this sounds like it might be true, it it isn't. So I'm gonna just right here. This is false, and I really just explain a bit. So least waas is when you minimise this some of the residuals, the sum of the squares of the residuals because remember when you looking at residuals in terms of the whole picture, you don't really mind if they're negative? A positive. It's purely about the American Jew about how big the residual is, the sum of squares of residuals. So some of the squares the residuals are minimized isn't really true because you're summing all of them. So you're not really looking individual ones. And that's what I was on. The final one is saying that we want Why, huh? If it's a predicted Bonnie on, Just why if it is observed, This is, of course, true is very important. Remember, if you ever see a hat, it's the prediction, not the rial value. So everything just for currency, right? True. Yeah, there's, ah!


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