# [✓] Manipulate of a 2-D plot?

GROUPS:
 I am trying to create a plot of a logistic function with parameters AHAT and MDIF. The values of these parameters depend up underlying parameters A and DIF and an underlying ability distribution with a covariance omega and mean vector mu. I have to go through several steps to determine AHAT and MDIF. I would like to create a plot where I can manipulate sigma, mu1 and mu2 to see how it affects the logistic curve. I can't figure out how to create the plot. Leaving the variable sigma and mu1 and mu2 in the expressions at the outside will not work. I have attached a MSWord document with the code. Does any have suggestions? A={{1.2,.4},{.8,.5},{.9,1.0},{1.3,.5},{.6,.9}};u={{μ1,μ2}}; DIF={{.5},{.7},{1.0},{-1.},{2.0}}; Ω={{σ,1},{1,σ}} L=CholeskyDecomposition[Ω] W=Eigenvectors[Transpose[L].Transpose[A].A.L] AM=List[A[[1]]] W1M=List[W[[1]]] W2M=List[W[[2]]] AHAT=AM.Transpose[W1M]/Sqrt[2.89+AM.Transpose[W2M].W2M.Transpose[AM]] MDIF=(DIF[[1]]-AM.Transpose[u])/AM.Transpose[W1M] Manipulate[Plot[{(1/(1+Exp[-1.7*AHAT*(θ-MDIF)])),},{θ,-3,3},AxesLabel->{θ,p}],{σ,1,3},{μ1,-2,2},{μ2,-2,2}]  Attachments:
 The problem seems to be to give the parameters to the plot instruction. Try this A = {{1.2, .4}, {.8, .5}, {.9, 1.0}, {1.3, .5}, {.6, .9}}; u = {{\[Mu]1, \[Mu]2}}; DIF = {{.5}, {.7}, {1.0}, {-1.}, {2.0}}; \[CapitalOmega] = {{\[Sigma], 1}, {1, \[Sigma]}}; L = CholeskyDecomposition[\[CapitalOmega]]; Manipulate[ W = Eigenvectors[ Transpose[L].Transpose[A].A.L /. {\[Sigma] -> s, \[Mu]1 -> m1, \[Mu]2 -> m2}]; AM = List[A[[1]]]; W1M = List[W[[1]]]; W2M = List[W[[2]]] /. {\[Sigma] -> s, \[Mu]1 -> m1, \[Mu]2 -> m2}; AHAT = AM.Transpose[W1M]/ Sqrt[2.89 + AM.Transpose[W2M].W2M.Transpose[AM]]; MDIF = (DIF[[1]] - AM.Transpose[u])/ AM.Transpose[W1M] /. {\[Sigma] -> s, \[Mu]1 -> m1, \[Mu]2 -> m2}; Plot[{(1/(1 + Exp[-1.7*AHAT*(\[Theta] - MDIF)]))}, {\[Theta], -3, 3}, AxesLabel -> {\[Theta], p}, PlotRange -> {0, 1}] , {s, 1, 3}, {m1, -2, 2}, {m2, -2, 2}]