Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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1answer
82 views

Standard error of a statistic

the standard error of a standard deviation is given as : s/n^(1/2). Would the standard error of kurtosis and skewness follow the same idea? For example, se of kurtosis = kurtosis/n^(1/2)?
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218 views

How to find the formula of a spiral using least-squares(regression)?

Assume data from a plane which are roughly showing a spiral. I want employ the rationale of regression to find the parameters for the best fit by some spiral. That means, I have to estimate the ...
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2answers
38 views

Where is the square in the Least square regression method?

I'm having a serious doubt in the least square regression problem. I guess its got to do with the notation of norm. Is the least square formulation $||b - \mathbf{A}x||^2$ or is it $||b - ...
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1answer
50 views

Plane vertices from normals and centroid

I am trying to visualize a best fit plane for a set of points which is defined by the normals and the centroid. I have to find the boundary vertices of the plane given the extent of the plane. Is ...
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1answer
251 views

Predict the height of a student whose weight is 60 kilograms.

The average height and weight of a group of students turned out to be 5 ft 6 inches and 65 kilograms respectively. The correlation between heights and weights was found to be 0.6. Using the regression ...
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1answer
112 views

Linear regression for normal distributions

Basically, I have that $\ Y_i = \alpha +\beta(x_i-x_{bar}) + \epsilon_i $ where $\epsilon_i$ are i.i.d normally distributed with mean 0 variance $\sigma^2$ $\ Y_i ~~has ~a~normal~distribution~as ...
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1answer
62 views

Expressing Series-Element in Terms of its Index

Consider the following recursion: $$C_{i+1} = a \sum_{j=1}^iC_j + b$$ where $a$ and $b$ are constants. Can series-element $C_i$ be expressed in terms of only its index $i$, $a$ and $b$? In case ...
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0answers
110 views

Covariance and variance

Within the context of simple linear regression, I came across this: $$\hat{\beta}=\frac{\sum y_nx_n}{\sum x_n^2}=\frac{cov(xy)}{var(x)}$$ where I assume $cov(x,y)$ means the covariance between $x$ ...
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1answer
90 views

Regression on Linear Model?

I have 50 or so training examples involving a set of 200 or so real numbers (x1,x2,...,x200) (normalized to a 0 mean and std dev 1), and a single output real (y) in the range 0.0..1.0. I want to fit ...
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1answer
138 views

Explain Least-squares plotting with Ones -matrix

I am stuck to this code and particularly the point F=[ones(size(x)) x x.^2]. What does it do mathematically? I cannot understand what the heck the matrix has to do ...
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1answer
4k views

How different is Beta computation using Covariance and Linear Regression?

I wanted to compute Beta for a Stock against an Index (Say Stock X against S&P 500). I computed the daily returns for over one year applied the following logic : Beta = COVAR(X, S&P ...
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2answers
6k views

Unconditional expectation vs conditional expectation in regressions - does it really matter?

I refer here to a simple linear regression whose true representation is given by the equation: $y_i=x_i'\beta+u_i$, where as usual $x_i$ is a $Kx1$ vector of independent explanatory variables, ...
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1answer
144 views

Why is $(x'x)^{-1}x' = x(x'x)^{-1}$

If $(AB)'=B'A'$ then $(x'x)^{-1}x'$ should be equal to $x((x'x)^{-1})'$ . However most econometrics textbooks say that this is equal to $x(x'x)^{-1}$ . What happened to the transpose of $(x'x)^{-1}$? ...
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1answer
25 views

Using least squares regression for line of best fit

Use the least square approximation to find the closest line (the line of "Best Fit") to the points: $$(-6,-1), \quad (-2,2), \quad (1,1), \quad (7,6)$$ I'm attempting to use the least squares ...
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0answers
23 views

Averaging between different formula of same kind

There is a dataset of 8 books. We examined the similarity of each book, using a technique, with other 19 books (8*19 number of distinct books). We stored the data and then, we used ...
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0answers
21 views

(x/y) v (y/x) as predictor in regression

I am trying to predict a variable 'score' with x and y. I believe it is related to (x/y)/z and z/(x/y), but I'm not sure which. Here is some data: ...
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1answer
15 views

For the three measurements b=0, 3, 12 at times t=0, 1, 2 find the best parabola y=C+Dt+E$t^2$

So I know how to do least squares regression using matrices to solve for Ax=b. I simply do $A^TAx=A^Tb$. However I don't really know how to account for the second power in a typical parabola ...
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1answer
43 views

How to proof that least square estimator $\hat{B}$ doesnt exist when $x$ is linearly dependent?

For the linear regression model $Y=xB+e$, prove that if the columns of $X$ are linearly dependent, the least square estimator $\hat{B}$ does not exist I know that since $\hat{B}$ is an unbiased ...
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1answer
20 views

Linear Regression question 1

I would really be grateful if someone could let me know how to answer Part (a) of Question 1. I believe i should scatter plot both x and y values separately for year 2000 and year 2001 on same graph ...
-1
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2answers
911 views

“taking the derivative of both sides” ln(Y)=ln(x) (to interpret log transformed regression variables or better understand elasticities or % changes)

In a linear regression of the form Y=bX we often have ln transformed Y and X. ie., lnY=b*lnX This is interpreted as a 1% change in X resulting in a b% change in Y (approximately) The derivation of ...
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2answers
377 views

Extrapolation with exponential curve

I would like to extrapolate time series using exponential curve while getting the parameters via linear regression. Exponential curve is given as $g=e^{~a + b \cdot t}$. Since I want to use linear ...
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1answer
654 views

How to work out orthogonal polynomials for regression model

I put this question here as it has a pure maths element to it, even though it has a statistical twist. Basically, I have been given the table of data: $$\begin{matrix} i & \mathrm{Response} \, ...
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2answers
130 views

Proving that the estimate of a mean is a least squares estimator?

I think this is a really simple question so please bear with me -- I just had my first class in regression and I'm a little confused about nomenclature/labeling. Does anyone recommend some good ...
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0answers
12 views

how to find the corelation or regression between two tables [closed]

I have two tables , I need to find the dependence or relation between these two tables table one ... $3$ sport v/s four regions with value as sales table two .. same $3$ sport v/s same four regions ...
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2answers
178 views

Guess the functional form of a graph

Can you guess the functional form of the following curve y is 0 at x= Infinite ; y is very small ( +ve near to zero) at x=0 Thanks and regards