Hi,

I am using the following (dummy) code to generate a density plot.

densityplot(x-y^2, x=-5..5, y=-5..5, axes=boxed, style=patchnogrid, numpoints=1000, legendstyle=[location=bottom], labels=[x, y]);

While this command does generate x vs y plots with varying color shared, I cannot figure out where the function (x-y^2) value by looking at the color shades. Is there a way to produce a legend along with the plot that will demonstrate how the function is taking different values with parameters? 

I found a similar post, dated 2005, that suggests using the "s_tyle=" command. However, it does not work for some reasons. I would appreciate help in this regard. 

Thank you,

Omkar

Hi,

I am struggling with an issue of the solutions produced by the "fsolve" command for a polynomial with multiple solutions. I am running the commands that are represented as follows:

f := x^2-x+0.25:

fsolve({f=0}, x=0..1);

It produces multiple solutions as follows:

{x = 0.5000000000}, {x = 0.5000000000}

What I am looking for is as follows:

1. Store multiple solutions separately.

2. For each solution, separate the variable "x=" and the numerical value "0.50000000". 

I would appreciate inputs from the team. 

Thank you,

Omkar

Dear Colleagues,

Apologies for the generic question below.

I am trying to obtain the Nash equilibrium solutions for a two-person game. I am not sure of any in-built packages that can help me in obtaining the solutions computationally. The algorithms that I created do not seem to give good solutions that are meaningful in my application. Any suggestion would be much appreciated. 

Regards,

Omkar

Hi,

I am struggling with one task involving solve and plot commands. I would appreciate if I could get some help. What I need to do is as follows:

1. Define alpha between 0 and 1.

2. Solve an equation f(x,alpha) =0 for x by taking different values of alpha.

3. Of all values of x obtained in step 2, choose the value of x between 0 and 1 and discard all others. I have technically shown that there will be exactly one value that is acceptable and all other values of x can be discarded.

4. For different values of alpha and correspondingly selected values of x in step 3, plot and display function g(x,alpha) with function value on the vertical axis and alpha on the horizontal axis.

Regards,

Omkar

Hi, 

I am struggling with statistical analysis of a dataset. I would appreciate help from the community. Let me describe what I am looking for.

1. The linear regression model that I am trying to use is Y=b1X1 + b2x2 + e. I am interested in estimating b1 and b2 so that the estimated error is the least.

2. I am trying to randomly select 25 percent of observations from the dataset and estimate b1 and b2. 

3. The estimated coefficients are used to predict the Y values for the remainder of the 75 percent of the data and calculate the error. The idea is to use a subset to estimate coefficients, and check for the robustness of the estimates.

4. The process is iterated for say 100 times.

5. Each time, I would like to store the statistical results and export them to an excel file.

For some reason, each time I struggle with one or two steps mentioned above. Could anyone help me with the approach?

Thank you,

Omkar