Regression that includes two or more non-constant independent variables.

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19 views

Setting predictor values in MLR

I am just getting started with Multiple Linear Regression (MLR), and had a question regarding setting predictor values while using the prediction equation. Suppose, I have two predictors $x_1$ and ...
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1answer
16 views

Confidence that Optimum Lies Within a Given Region

I have an ordinary least squares regression equation. Through calculus or simulation, I can find the combination of explanatory values that maximize the estimated mean response; I can also establish a ...
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12 views

How to properly set up my spreadsheet and determine which analysis to use

I am trying to determine if over a 2-day school day, if 72 elementary students' (first & second grade) physical activity (%sedentary, %light, %moderate) have any influence on students' on/off-task ...
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11 views

Testing Various Hypothesis Test for Coefficients in R [migrated]

I Know in R it returns for a Multiple Regression it returns hypothesis test for $\beta_i=0$ but what if you want to test such tests like $\beta_i=1$. Is there any easy command for this or if not how ...
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1answer
44 views

P value of multiple linear regression

I have extremely large number of observations (8524152) of soil moisture, precipitation, evapotranspiration, delta precipitation, and delta evapotranspiration. I ran a multiple linear regression model ...
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1answer
14 views

Standard Error of Intercept in Multiple Linear Regression

How do I calculate the standard error of the intercept (b0) when the model has two explanatory variables (say x1 and x2) for y = b0 + b1x1 + b2x2? Thanks!
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1answer
21 views

Multiple linear regression: does BIC drop (vaguely) collinear variables?

Say I have the following multiple linear regression: Y ~ X1 + X2 + X3 + X4 All X variables are independent, but X1 and X2 look kind of linearly related when ...
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12 views

Degrees of freedom with duplicate data points

The degrees of freedom of the residual in an OLS model is $n - p - 1$, where $n$ is the number of samples, and $p$ is the number of independent variables. I.e., the data matrix $X$ is $n\times p$. If ...
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1answer
20 views

Regression and contrast codings with multiple categorical variables

In regression with multiple explanatory categorical variables, how should I model the problem to compare the effects of the categorical variables with each other? Most contrast coding schemes (e.g. ...
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5answers
85 views

A Book for Multiple Regression and Multivariate analysis

I have done a course in Simple Linear Regression and I am aware of linear statistical models (I follow the book by C.R. Rao). Keeping this background in mind, please suggest some good book(s) for ...
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1answer
55 views

Generating data from Probit regression, cut off 0 and variance 1 necessary?

I am trying to create a dataset using a Probit regression model in R, where I have an intercept and three covariates. I first fix a set of coefficients for the three covariates, generate these ...
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1answer
17 views

Terminology: output of a regression model as input to another regression model

I have a question about terminology. I've constructed a multiple linear regression model for a variable X. This model is in turn used to estimate values of X that are used as input when constructing ...
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4answers
251 views

Why Multiple Linear Regression cannot be built when p>n?

My question is why Multiple Linear Regression (MLR), based on least squares, cannot be built when the number of variables $(p)$ are larger than the number of samples $(n)$? Can one explain why is it ...
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1answer
42 views

How to emphasize on specific data points in Linear Regression?

I'm now solving linear regression problems. $y = wx + b + e$ So I have $(x, y)$ data set and want to learn weights $w, b$. Additionally I know that certain data points are not polluted by noise ...
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0answers
3 views

Help with multiple landmark and Non-Metric Data INPUT [closed]

Thank you all in advance for being so kind as to put up with my extremely beginner level R-Studio (and statistics programming in general) skills. I am struggling with the most basic of tasks-combining ...
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0answers
11 views

Anti-correlated regression predictors

Intuitively perfectly anti-correlated predictor variables in regression would have the most stable coefficients since they contain no shared information, e.g. \begin{equation} \begin{bmatrix} y_1 \\ ...
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1answer
22 views

Deriving a restricted efficient GMM estimator with common coefficients

I'm having a bit of trouble in doing exercise 3. For us to compare with Pooled OLS, and Random effects model, it seems that we must assume that we're under conditional homoskedasticity, and the set of ...
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0answers
36 views

Multiple linear regression [closed]

I have a data frame in which I have several columns and rows. For example the data frame below shows column 1 to 4 is my soil moisture data, 5 to 8 is evapotranspiration (ET), and column 9 to 12 is ...
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1answer
27 views

A doubt on SUR model

On page 279, Hayashi begin by defining the SUR model. See picture below. If I compare with these slide-notes(slide number 34), we define the instrument vector $x_i$ equal not only to the union of ...
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1answer
38 views

Cook's D, testing for outliers

I am working on a multiple linear regression and I want to check for outliers using Cook's D. I have a problem interpreting it, as there are many points above the 4/N line, but only one is >1. How ...
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24 views

Explanation of the formula for calculating adjusted R squared of linear model

The classcial formula for calculating the adjusted $R^2$ of a linear model is as follows: $$R^2_{adj} = 1 - ((n-1)/(n-p-1)) \times (1-R^2)$$ where $n$ is the sample size and $p$ is the number of ...
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0answers
12 views

Positive correlation coefficient, but negative Beta weights in multiple regression [duplicate]

I have a situation where IVs positively correlate with the DV, and the IVs also correlate with eachother. I do not explain how the beta weights are negative. No multicollinearity is detected, and the ...
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1answer
45 views

Is regression good for river(with dams) flow prediction

I am trying to analyse the patterns in water flow from differnt dams on the same river at different hours of the day. I have gathered the spillway release hourly data of 11 dams for 2013. I know that ...
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23 views

ANCOVA; CIs for the intercepts of each treatment

I am currently doing an ANCOVA, and I need to calculate CIs for the intercepts of each treatment (categorical) group. So, instead of using lm(y~x+group), which gives me SEs of treatment contrasts, I ...
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0answers
17 views

multiple linear model validation

Hello I am a beginner in R. I have a dataset of fish and environmental parameters and anthropogenic pressures from 11 lakes. I have modeled some fish parameters (like fish biomass) as function of ...
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0answers
21 views

GLM over two groups with unequal variance in the dependent variable

I have a dataset of patients and controls and would like to model the group specific effect of a certain predictor PRED (brain imaging, marker of structural connectivity) onto one behavioral measure, ...
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0answers
17 views

How to remedy seasonality in a multiple regression model

I am trying to build an economic model using multiple regression, and I am not sure how to remedy seasonal effects. I am collecting data across several different variables, and building three models ...
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1answer
19 views

Using regression tree on time series data

I have been looking around for resources on applying a regression tree in an attempt to understanding how various spend variables impact a companies revenue overtime. Is this type of analysis ...
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15 views

Multivariate Non-parametric Regression

What is the most well known(or most effective) method for multivariate nonparametric regression? I am surprised that there is no 'popular' support vector machines' based method.
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0answers
26 views

Multicollinearity? Non-significant multiple-linear regression, highly correlated regressors but low variance inflation factor

I have a small sample (30 obs) and 4 independent variables, 3 of which are significantly correlated to each other. I have tried to run the simple linear regression on each of them separately and it ...
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0answers
10 views

Finding the amount of error with a multiple regression formula that is determining stock returns

I'm brand new to statistics and I'm using C# and Math.Net to perform multiple regression on a formula with 3 inputs and 1 output. I was told that finding an rsquared value isn't recommended for a ...
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1answer
30 views

Variance / Covariance Matrix - mean of squared errors

I'm trying to build a stats library. I'm following along with the tutorial on multiple regression analysis here: http://reliawiki.org/index.php/Multiple_Linear_Regression_Analysis I have the ...
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0answers
30 views

Standard error/deviation of the coefficients in OLS

In OLS, the variance of the regression coefficients are computed as $$ \mathrm{Var}(\hat{\beta}) = \sigma^2(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}. $$ Now, if I need to compute the standard ...
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2answers
77 views

What information can be retrieved from the slope in linear regression

Here is the problem: The question is weird in the fact that we're using categorical variables, but I see it this way: Since one extra year of education has 4 times the effect on income as going ...
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2answers
361 views

How seriously should I consider the effects of multicollinearity in my regression model?

I have a model y ~ x + z and the correlation between x and z is 0.2. This is only weakly positive. So, how seriously should I consider the effects of ...
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0answers
8 views

risk of entering group level predictors in regression to predict individual outcomes?

My GOAL: I have been running a multivariate linear regression analysis to predict student outcomes (grades; measured at the individual student level) from several variables measures at the student ...
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0answers
17 views

Best effect size estimator in simple linear regression?

Using a metric developed by someone else, I have calculated vegetation condition scores from a set of measured variables (about 1000 sites). I am using simple linear regression to determine how ...
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2answers
51 views

Creating groups using two continuous variables without using median-splitting?

I have two continuous variables, one of individuals' retrospective childhood anxiety and another regarding their current level of anxiety. Research has demonstrated that during a snapshot of ...
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1answer
37 views

Which one to compromise between MAPE and Adj R square in multiple regression

I'm trying to forecast sales of a product based on the other variables like Competitor sales, Fuel Price and CPI (Consumer Price Index). The below given output (based on 1 to 44 months) gives me the ...
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0answers
8 views

mixed measure predictors in multiple regression

I was recently told that it was not appropriate to mix psychological constructs (interval scaled personality traits) with socio-demographic variables (e.g. age) as multiple predictors in a linear ...
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1answer
46 views

Why is there no intercept in a regression model equation with standardized coefficients?

Let's say my model is this: $y = -0.372 + 0.045x_1 + 0.03x_2 - 0.205x_3 + 0.114x_4$, and my standardized model is this: $y = 0.635β_1 + 0.618β_2 - 0.466β_3 + 0.232β_4$. Why is there no intercept in ...
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30 views

In linear model, if you add one more variable, then what happens to the constant?

I have a linear model $$y=a+bX_1+cX_2+dX_3+eX_4+m,$$ where the expected value of $m$ given $X_1,X_2,X_3,X_4$ is zero. If you add one more variable $X_5$ to this model, is the constant $a$ expected ...
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0answers
10 views

Multiple linear regression calculating initial error [duplicate]

I'm a programmer and have to implement the following regression. I have the equation, Y = βa * A + βp * P + βd * D + e Here e is the error and βa, βp and βd are regression co-efficients. We have ...
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35 views

Constant dummy variable multiplied into linear multiple regression model

I have been running a multiple linear regression to determine the weightings given to certain sports statistics in a player's fantasy sports score. This part I have no problem with and is within my ...
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1answer
32 views

Antilog of a semilog regression model with dummy variables

I have a semi-log regression model, with two continuous predictors, two categorical predictors (0 or 1 dummy variables) and a non-zero intercept. The response variable is log10 transformed, none of ...
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0answers
17 views

Multiple Transformations of a Dependent Variable

Assume you have a data set with a continuous output variable (y), five continuous predictors (x1, x2, x3, x4, and x5), and a few additional categorical predictors. x1 through x4 have a weak ...
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1answer
49 views

General mathematics for confidence interval in multiple linear regression

I have 30 observations and 4 (edited: numerical) variables (x1, x2, x3, x4). Also I have a linear model to predict y value. I want to calculate confidence interval for predicted (edited: and ...
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1answer
16 views

Multicollnearity in backward selection approach

When I build my most parsimonious model using a backward selection approach, do I have to worry about multicollinearity. I mean, do I first check for multicollnearity and drop the variables which has ...
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1answer
25 views

Multiple regression with raw and derived variables as predictors

Extending my previous question ( Multiple regression with correlated variables ), can I do multiple regression with height, weight, waist, BMI (body mass index) and BSA (body surface area) as ...
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1answer
30 views

Can I add more cases and/or predictors to existing set of data?

If I have a set of data with 40 cases and 3 predictors can I add more cases and/or predictors later to the existing set of cases if I want to explore the effect of more possible predictors? The data ...