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Accepted

How to interpret coefficients from a polynomial model fit?

My detailed answer is below, but the general (i.e. real) answer to this kind of question is: 1) experiment, mess around, look at the data, you can't break the computer no matter what you do, so ... ...
• 7,374
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Is there a way to use the covariance matrix to find coefficients for multiple regression?

Yes, the covariance matrix of all the variables--explanatory and response--contains the information needed to find all the coefficients, provided an intercept (constant) term is included in the model. ...
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Negative relationship but regression analytics gives positive correlation coefficient

The correlation coefficient is $r$. $R^2$ is the square of $r$, and it is of course always positive, regardless of the sign of $r$. Taking the square root gives that $r= \pm 0.8489$, and since the ...
• 3,888
Accepted

Will larger correlation coefficient values result in greater slopes between x and y?

The answer is "not necessarily" — how correlated the variables are dictates how "noisy" the scatter plot is, but not how steep. In fact, the correlation and regression slope are ...
• 20.9k

Can regression coefficients be higher than correlation coefficients?

For simple linear regression there is a relationship between slope and correlation: $\hat\beta_1 = r_{x,y}{s_y\over s_x}$ So the relationship of $\hat\beta_1$ and $r_{xy}$ is entirely dependent on ...
• 2,239
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Frequentist perspective of regression coefficients and significance (coming from Bayesian background)?

A p value is the probability of observing a test statistic as or more extreme than the researcher's own test statistic, assuming the null hypothesis, and an assumed distribution model are both true. ...
• 26.4k
Accepted

Linear regression with log transformed data - large error

If you say your model is ln(y) = b*ln(x) + a it is only part of your model. Your actual model includes an error term: $\ln y_i = b\cdot \ln x_i + a + \varepsilon_i$...
• 5,808
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What's the difference between regression coefficients and partial regression coefficients?

"Partial regression coefficients" are the slope coefficients ($\beta_j$s) in a multiple regression model. By "regression coefficients" (i.e., without the "partial") the author means the slope ...
Accepted

Interpretation of LASSO regression coefficients

Are the LASSO coefficients interpreted in the same method as logistic regression? Let me rephrase: Are the LASSO coefficients interpreted in the same way as, for example, OLS maximum likelihood ...
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Importance of predictors in multiple regression: Partial $R^2$ vs. standardized coefficients

In short, I wouldn't use both the partial $R^2$ and the standardized coefficients in the same analysis, as they are not independent. I would argue that it is usually probably more intuitive to compare ...
• 885
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Lets consider an example (here I use Stata, but the logic works the same in any other package): ...
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What is the difference between least square and pseudo-inverse techniques for Linear Regression?

In the context of linear regression, 'least squares' means that we want to find the coefficients that minimize the squared error. It doesn't specify how this minimization should be performed, and ...
• 29.7k

Interpretation of log transformed predictor and/or response

The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic ...
• 53k
Accepted

How to compute the standard errors of a logistic regression's coefficients

Does your software give you a parameter covariance (or variance-covariance) matrix? If so, the standard errors are the square root of the diagonal of that matrix. You probably want to consult a ...
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How to interpret coefficients of $x$ and $x^2$ in same regression
Such an equation describes a curved relationship between $y$ and $x$ - a parabola: (This particular set of parameters correspond to a minimum at $x= -\frac{_5}{^6}$, just off the left margin of this ...