non-linear-regression

I am trying to do a simple forecast of future profit of an organization based on the past records by using regression. I am following this link . For testing purpose, I have changed the sample data and it produced these results: My actual data will be date and profit, and they will be going up and down rather than in a contiguous increment way. I realized that the method above works for sample data which keep on increasing as the prediction is quite accurate. However, when I changed the data to the one in the screenshot which goes up and down crazily, the prediction is not so accurate anymore.

I am trying to estimate the constants for Heaps law. I have the following dataset novels_colection : Number of novels DistinctWords WordOccurrences 1 1 13575 117795 2 1 34224 947652 3 1 40353 1146953 4 1 55392 1661664 5 1 60656 1968274 Then I build the next function: # Function for Heaps law heaps <- function(K, n, B){ K*n^B } heaps(2,117795,.7) #Just to test it works So n = Word Occurrences , and K and B are values that should be constants in order to find my prediction of Distinct Words. I tried this but it gives me an error: fitHeaps <- nls(DistinctWords ~ heaps(K,WordOccurrences,B), data =

Assuming we have the below function to optimize for 4 parameters, we have to write the function as below, but if we want the same function with more number of parameters, we have to rewrite the function definition. def radius (z,a0,a1,k0,k1,): k = np.array([k0,k1,]) a = np.array([a0,a1,]) w = 1.0 phi = 0.0 rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1) return rs The question is if this can be done easier in a more automatic way, and more intuitive than this question suggests. example would be as following which has to be written by hand. def radius (z,a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,k0,k1,k2

This question already has an answer here: Predict() - Maybe I'm not understanding it 4 answers I have read few answers on this here but I am afraid I have not been able to figure out an answer. My R code is: colors <- bmw[bmw$Channel=="Colors" & bmw$Hour=20,] colors_test <- tail(colors, 89) colors_train <- head(colors, 810) colors_train_agg <- aggregate(colors_train$Impressions, list(colors_train$`Position of Ad in Break`), FUN=mean, na.rm=TRUE) colnames(colors_train_agg) <- c("ad_position", "avg_impressions") lm_colors <- lm(colors_train_agg$avg_impressions ~ poly(colors_train_agg$ad_position

I am trying to create a simple deep-learning based model to predict y=x**2 But looks like deep learning is not able to learn the general function outside the scope of its training set . Intuitively I can think that neural network might not be able to fit y=x**2 as there is no multiplication involved between the inputs. Please note I am not asking how to create a model to fit x**2 . I have already achieved that. I want to know the answers to following questions: Is my analysis correct? If the answer to 1 is yes, then isn't the prediction scope of deep learning very limited? Is there a better