Ols Definition and 15 Threads

hello, I understand that the method of ordinary least squares (OLS) is about finding the coefficients that minimize the sum ##\Sigma (y_{observed} -g(X))^2## where ##g(X)## is the statistical model chosen to fit the data. Beside OLS, there clearly other coefficient estimation methods (MLE...

Hello, Simple linear regression aims at finding the slope and intercept of the best-fit line to for a pair of ##X## and ##Y## variables. In general, the optimal intercept and slope are found using OLS. However, I learned that "O" means ordinary and there are other types of least square...

Hello soon to be saviors, 😊I have two really simple questions that I have already answered but the teacher wants more info. I am really stumped and I am not looking for the answers so much as an explanation on how to better answer the questions. I will copy and paste the problems and my answers...

Hey. I am planning on doing some research, where I predict a change based on different types of risk. The question is simple. Can I use values of standard deviation as independent variables in a linear regression analysis (OLS)? The standard deviation values over time will be calculated in...

I have a time series model constructed by using ordinary least square (linear). I am supposed to provide some general comments on how one would improve the robustness of the analysis of a time series model (in general). Are there any general advice apart from expanding data, making it more...

Say one has a regression result (ols) with significant coefficients for all independent variables. Then a new variable (Z) is added. This new variable is either something that reveals a spurious relationship among one of the initially included variables (x) and the dependent variable (y), or...

I am studying mean-centering for multiple linear regression (ols). Specifically I'm talking about the situation when there is interaction. When centering variables for a regression analysis, my literature tells me that the coefficients do not change? But when there is some sort of interaction...

I am working with multiple regression with two independent variables, and interaction between them. the expression is: y = b1x1 + b2x2 and b3x1x2 The question is: does one center both independent variables at the same time, when checking for the significance of the effect of the independent...

It is my understanding that you can use linear least squares to fit a plethora of different functions (quadratic, cubic, quartic etc). The requirement of linearity applies to the coefficients (i.e B in (y-Bx)^2). It seems to me that I can find a solution such that a coefficient b_i^2=c_i, in...

Homework Statement ΣiYi = 500; ΣiXi = 150; ΣiYi2 = 17000; ΣiXi2 = 4000; ΣiXiYi = 8000; n = 50. β0 = 3. Derive formula for OLS estimator of β1 and find estimateHomework Equations I'm new to OLS and I'm not sure where to go from: Σ(Yi - 3 - b1Xi)^2 I was able to walk through the steps in my...

So in computing the variance-covariance matrix for β-hat in an OLS model, we arrive at VarCov(β-hat)=(σ_ε)^2E{[X'X]^-1} However, I'm incredulous as to how X is considered non-stochastic and how we can just eliminate the expectation sign and have VarCov(β-hat)=(σ_ε)^2[X'X]^-1 I'm...

Hello PhysicsForums.com! I've got several sets of data that are all intended to represent the same ideal data set. I need to fit a regression to said sets of data - but have no idea of how to go about it. All multiple-regression literature I can find reads to the tune of: given...

Hi, My question is about a common procedure used to find minimum and maximum values of a function. In many problems we find the first derivative of a function and then equate it to zero. I understand the use of this method when one is trying to find the minimum or maximum value of the...

Hi, In many statistics textbooks I read the following text: “A models based on ordinary linear regression equation models Y, the dependent variable, as a normal random variable, whose mean is linear function of the predictors, b0 + b1*X1 + ... , and whose variance is constant. While...

Hi I'mwondering what's the difference between least squares method with least absolute deviation method. Assume we have y=ax+b+s where s isdeviation. Is the step to calculate even a and b is different. I read that those two methods are almost the same but hardly found a real good explanation...