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### If first degree polynomial models are linear models, why do results of linear model differ from that of poly(x,1)? [duplicate]

As the title reads, the results from the linear and first degree polynomial model are different and I am not sure why. Any ideas why this might be? ...
24 views

### R poly what family of polynomials? [duplicate]

The R poly function documentation says that it gives orthogonal polynomials, but it's not clear what orthogonal polynomials it gives. Are they Legendre? Are they ...
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4k views

### How can I calculate the variance of interaction term from an equivalent model without interaction?

Lets say that you have access to a model that estimates the mean of four independent groups like m2 below, but these groups have been formed from two factors (a & b) and you want to instead ...
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769 views

### R - Interpretation of coefficients and written form of fitted model in lm() linear regression when using poly()

I've tried reading several resources on poly(), I'm not able to see an answer to my question. My question pertains how I might present my fitted linear model in a way that the coefficients are ...
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224 views

### Theoretical reason for multiple linear regression predictions being the same when adding and subtracting predictors

Say I have two variables $x_1$ and $x_2$, now I build a linear regression model as below $$\hat{Y} = n_1 x_1 + n_2 x_2.$$ Then I build another model as below \hat{Z} = m_1 (x_1 + x_2) + m_2 (x_1 - ...
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591 views

### Calculating predicted value from polynomial regression by hand

I have the following output from from R. I know we can calculate predicted values using the predict() function. How can we calculate the predicted value by hand if X=2 or 3? I'm using the below ...
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381 views

### How to manually compute response variable using regression with poly [duplicate]

I believe I can manually compute response values from coefficients obtained using 'raw' polynomial predictor variables. Example R code is ...
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275 views

### Difference between contr.poly e poly in regression and interpretation

I am confusing regarding the differences between poly and contr.poly in regression. Both should generate the orthonormal polynomial transformation of a vector. But poly is influenced by the length of ...
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