Task:
From the data the growth of tumor spheroids determine doubling time
Link to the data.
My idea was to use least squares method and Mathematica to helps me find result. But I think that this is nonlinear problem so I will have to use nonlinear least squares method but I don't know how to start. Also I have a question how does my result change if I add some data or throw away.
2026-03-26 16:56:48.1774544208
From the data the growth of tumor spheroids determine doubling time using Mathematica and by hand
57 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in STATISTICS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Fisher information of sufficient statistic
- Solving Equation with Euler's Number
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Determine the marginal distributions of $(T_1, T_2)$
- KL divergence between two multivariate Bernoulli distribution
- Given random variables $(T_1,T_2)$. Show that $T_1$ and $T_2$ are independent and exponentially distributed if..
- Probability of tossing marbles,covariance
Related Questions in MATHEMATICAL-MODELING
- Does Planck length contradict math?
- Solving the heat equation with robin boundary conditions
- How to use homogeneous coordinates and the projective plane to study the intersection of two lines
- inhomogeneous coordinates to homogeneous coordinates
- Writing Differential equations to describe a system
- Show that $z''+F(z') + z=0$ has a unique, stable periodic solution.
- Similar mathematic exercises about mathematical model
- What are common parameters to use when using Makeham's Law to model mortality in the real world?
- How do I scale my parabolas so that their integrals over [0,1] are always the same?
- Retrain of a neural network
Related Questions in NONLINEAR-SYSTEM
- Solving special (simple?) system of polynomial equations (only up to second degree)
- Determination of Invertibility
- Question about stability of a nonlinear dynamical system
- The equation $x^T A x = (x^2)^T A x^2$
- 1D viscous flow upwards against gravity
- Convergence of fixed-point in a gauss-seidel style
- Intuition behind dense orbits
- Determine the stability properties and convergence in the origin using Lyapunov Direct Method
- Is $x(t/2)$ a causal/memoryless system?
- Why this field with non-zero curl has closed orbit?
Related Questions in LEAST-SQUARES
- Is the calculated solution, if it exists, unique?
- Statistics - regression, calculating variance
- Dealing with a large Kronecker product in Matlab
- How does the probabilistic interpretation of least squares for linear regression works?
- Optimizing a cost function - Matrix
- Given matrix $Q$ and vector $s$, find a vector $w$ that minimizes $\| Qw-s \|^2$
- Defects of Least square regression in some textbooks
- What is the essence of Least Square Regression?
- Alternative to finite differences for numerical computation of the Hessian of noisy function
- Covariance of least squares parameter?
Related Questions in MATHEMATICA
- Approximate spline equation with Wolfram Mathematica
- Entscheidungsproblem
- checking for sufficient condition for an unconstrained maximization problem.
- Does Mathematica have a function for the composite numbers not divisible by a squared prime?
- May someone of you provide me (if possible) an expression for the F.T. of $\tan(x)$?
- What does the floating point arithmetic contribute to the rounding error in Mathematica?
- Is it possible to obtain the closed-form expression of this differential equation?
- Numerical integration of triple integral
- Using Mathematica to find arc length of implicit function
- How to make a number out of other numbers in mathematica?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I put (approximately) your data into Minitab statistical software:
@Did's hint to take the log of Volume works fine. (It doesn't matter whether natural logs or base 10.) Here is a plot of the data with Volume on a log scale (original numbers shown, scale distorted appropriately). The header shows the regression equation. The dotted band shows 95% prediction intervals for V at each T. Roughly, R-sq = 97.2% means that 97% of the variability in $\log_{10}V$ can be explained by regression on $T.$
However, notice that the residuals towards the center tend to be positive, while those at the extremes of T tend to be negative. That suggests that a slight improvement might be made by using $T^2$ as a second predictor variable. Results below. By eye, this looks a little better, and
R-Sq(adj)is a little larger. You could use one of the usual criteria for a formal test whether the quadratic regression is a statistically significant improvement (for your exact data). If your only purpose is to find doubling time, then the quadratic regression makes that a little more complicated.Notes: (1) Based on what I see here, I can't imagine why you would want to 'throw away' any of your data, except possibly the observation at $T = 11.$ Throwing away points might result in a loss of precision. (2) A quadratic fit to $V$ (instead of $\log V$) is pretty good.