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Consider the linear regression model, Bo + B1Xi+ Ui . What s the first order condition of min Zu; _v-Bi xZ?(xi-x) (Vi - Zkxi --2Ei(i-Bo- B1x,)=0227x vi- Bo- B1*,)=0...

Question

Consider the linear regression model, Bo + B1Xi+ Ui . What s the first order condition of min Zu; _v-Bi xZ?(xi-x) (Vi - Zkxi --2Ei(i-Bo- B1x,)=0227x vi- Bo- B1*,)=0

Consider the linear regression model, Bo + B1Xi+ Ui . What s the first order condition of min Zu; _ v-Bi x Z?(xi-x) (Vi - Zkxi -- 2Ei(i-Bo- B1x,)=0 227x vi- Bo- B1*,)=0



Answers

Compute the least squares regression line for the data in Exercise 1 ofSection 10.2 "The Linear Correlation Coefficient".

In this problem, the answer will be interaction intel election. It is because it teach, because these models, obtained by obtained by introducing explain naturally variables variables better explains the variability in the response variable in the response variable. Like so I hope you understand the solution.

Alright this question says consider the situation of exercise 11.3 but suppose n is equal to two, that is only two data points are available. You have an argument that the least squares regression line will result in Y one minus Y. Para one is equal to Y two minus y white cap too. It's close to zero. And also show that for this case r squared is equal to one. Right? So we are saying When there are only two data points there are only two data points. Okay let me get by when there are only two data points here where X one and X two are the only two. The points but they're saying they're not equal right? We know that your Y one and Y one kept plus your Y two right? They will always give you as they reasoned it. Okay now by ah method of least squares and least squares method. Right. Right. Check this is the same thing that we have here. Right, we're just not playing by X one and we're not playing by X two. Right right we've multiplied by x one. N multiplied by X two were saying this still it yields there zero like we have a saturday now we are saying um both these two equations, if you use the least squares method, these two equations they will you'd Right X 2 -11. Right and Y two- Why one kept here. So if you mix these two questions they will yield this one and the same call to sell. So which implies that this is equal to zero or this is equal to zero X one. So, but you are mainly interested in this one. So we're saying hence y two minus y one cap is is called zero. Therefore Therefore our way one minus Why one cap is also equals two zero day. So if these are equal to zero then we are saying all right, S. E. Our S S. E. Which is maybe uh maybe given us probably the sum of yeah residual squares squares there. There's some of residual residual squares, right? This this you can take it as taking the residuals there. Right? This adding residuals and the residuals here. It it yields zero from what we got from above because this is giving us zero and this is giving us zero. So our some of and our S. S. E. Will give us a zero day. So which then implies that since our r squared is equal to one minus S. S over S S. T. Right? Our S S is already zero there. So we have your r squared being equals two to one day because this will give us zero there. Right? So that's the argument that you can give their that and we have shown that our other squared is equal to to one day. Right?

In this problem, we are asked to calculate the minimum Very or five For Wister, manager of results in the waiter would be equals to zero. So in this case, we need to find the minimum value of five. In this case, we have a number of factors. Our soldiers assume they say any Sequels to six And that brother feather diagram swore First diagram can be drawn here. This is our waxes and then we have here XX is now the first way to will be here which makes an angle off 60 degree with XX is and the second will be this one. Our third waiter will be anti Beller to the XX is and the fourth way too will be this one While the fifth actor will be opposite to the second one I say this is first one, Then the then this will be fourth and this will the opposite to the second While the last worker will be opposite to this one are we consider the last worker is palate to the XX is now in this case we can white Our end is equals to six and then we can ride The fire is fights equals two 3 60 degree, divided by six. So this is equals to 60.0 degree. Using this relation, we can generalize and write the value for these fires. Files equals two. She's 60 degrees divided by. And so when the angle phi is equals to 3 60 divided by and then we can write the resultant white Chris Magnitude as er is equals to our submission off. Let's see, eyes equals to one to end And here we can white he not sign off Omega T plus, uh, hi fi is equal to zero. Thank you.

The following a solution to number one on section 10.4. And it says to compute the least squares regression line from 10.2. Number one. And I went ahead and put that data set into my tea I 84. So if you go to Staten edit the X. Values here on L. One and then the Y values here are in L. Two. So that should look familiar. Okay, that's that's from section 10.2, number one then if you go back to stat and then air over to couch. Now the way this book is set up, uh It writes it just like we would with like a like a normal algebra one, Y equals mx plus B. So I'm going to choose this option for A. X plus B instead of A plus B. X. So click number four. Excellent. Should be L. One. While it should be L. Two. Unless you put it in different columns and then we go ahead and calculate. And I'm not concerned with this R and R squared right now. I'm just looking at the A. And the B. So the a. is the slow .743 And then the b. is the y intercept of 2.675. So let's go write that down. So we write it as why? Hat? Okay. That's the estimation. Why hat is 0743 x Plus 2.675. And that is the least squares regression line for number one.


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