Questions tagged [cubic]
13 questions
22
votes
2 answers
The definition of natural cubic splines for regression
I am learning about splines from the book "The Elements of
Statistical Learning Data Mining, Inference, and Prediction" by Hastie et al. I found on page 145 that Natural cubic splines are linear beyond the boundary knots. There are $K$ knots,…
Durin
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3
votes
1 answer
Given a truncated power basis function show that it represents a cubic spline for one knot
Given the truncated power basis function
$$h_1(x)=1, h_2(x)=x, h_3(x)=x^2, h_4(x)=x^3, h_5(x)=(x-\epsilon)^3_+$$
Show that a function of the form $f(x)=\beta_0+\beta_1x+\beta_2x^2+\beta_3x^3+\beta(x-\epsilon)^3_+$ is a cubic regression spline by…
user8714896
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2
votes
1 answer
RSS of different models given true relationship between X and Y
My question is if we have three models e.g. linear regression, polynomial regression and smoothing spline, what would be the expected values of their RSS (training and test) be if the true relationship is 1) linear and 2) cubic.
Let's say the data…
R1ddler
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2
votes
0 answers
Smearing estimate for cubic root transform in linear regression
I am building a cost model with cubic root transformation of the cost. Hence dependent variable is (cost)^(1/3). Now, am at a stage where i need to re-transform the predicted value to the actual cost. But while re-transforming, i have read that we…
Harsh Khad
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1
vote
0 answers
Error propagation for cubic relationship
I have the cubic relationship between two variables, x and y, and I need to find the error in x.
y = ax^3 + bx^2 + cx + d
I have the values for the coefficients and their respective uncertainties. I also have the y values and their associated…
eshbee
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1
vote
1 answer
In making scatterplot for correlations between two continuous variables, can we use the choice cubic instead of linear choice
In making scatterplot for correlations between two continuous variables, can we use the choice cubic instead of linear choice in "create a fit line at total", as shown in the copied Figure, please? does this sort of Figure acceptable scientifically…
user271931
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1
vote
0 answers
Why aren't quadratic terms considered in cubic splines?
When generalizing from linear to cubic splines, in 3 regions with two knots, I have imagined a continuous basis such as:
$$h_1(X) =1, \quad h_2(X) =X,\quad h_3(X) =X^2,\quad
h_4(X) = X^3,\\
h_5(X) = (X-\xi_0)_+,\quad
h_6(X) =…
Francesco Boi
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- 13
1
vote
0 answers
Derivation for restricted cubic splines for regression
I would like to derive the basis functions for restricted cublic splines with K knots ($\epsilon_1,...,\epsilon_K$):
$h_1(X)=1\text{, }h_2(X)=X\text{, }h_{j+2}(X) = d_j(X)-d_{K-1}(X)\text{, }j=1\text{ to } K-2 $
where…
Fed
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1
vote
0 answers
Cubic or curvilinear relationship between predictor and outcome - regression?
This isn't really a statistical problem, more like a curiosity. In any case, comments much appreciated.
I read a paper where they hypothesize the following:
Hypothesis 1. Z moderates the relationship between X and Y. When Z is high, the positive…
andree
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0
votes
1 answer
How to perform Restricted cubic spline (Cox adjusted) after multiple imputation with mice?
Hello I would like to perform restricted cubic spline (Cox adjusted) after multiple imputation with mice.I use rms package. but after imputation when I use the function datadist I get this message (Error in sort.int(x, na.last = na.last, decreasing…
Bkry
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- 3
0
votes
1 answer
how could i plot the interaction effect in a COX model
In a COX model, i included an interaction item between A(continuous variate) and B(category variate),and the p value of A:B1 (reference to A:B2) was <0.05.
Could i conclude that A and B have an interactive effect in the model, and how could i plot…
Chen
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0
votes
1 answer
Natural Cubic Spline Linearity at End-Points
How can we prove that Natural Cubic Splines are linear at the end points? We just know that the constraint is the second derivative to be zero at the end pints.
mBabaee
- 31
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0
votes
0 answers
Skewness of a non-linear distribution
Suppose, it is stated that $X$ is a random variable which has a symmetric distribution.
Now, let us consider $Y$ to be a random variable which has a distribution given by : $Y = g(X)$, where '$g$' is a non-linear function.
By a non-linear function,…
Dwaipayan Gupta
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