Question

Create a sample dataset {((),())} of 1000 examples where and are approximately linearly dependent. you may pick the parameters , as you like. −( ) is normal distributed.?

Answer 1

To create a sample dataset with linear dependency and normally distributed errors, define a linear equation with chosen parameters. Generate 'x' values, calculate 'y' using the equation, and add normally distributed errors to 'y' to complete the dataset.

Step-by-step explanation:

To create a sample dataset of 1000 examples where variables are approximately linearly dependent with error terms normally distributed, first decide on the equation of the linear relationship, such as y = ax + b. Choose values for a (slope) and b (intercept) based on your preference. Then, generate 1000 values for x, which could be random or evenly spaced within a certain range.

Next, calculate the corresponding y values using the defined linear equation. After that, add normally distributed errors to these y values. If you assume ε ~ N(0, σ), with a mean of 0 and some standard deviation σ, use a random number generator to create an error term for each x and add it to the corresponding y to get the final dataset. Your dataset will then be a set of pairs (x, y).

The specific value for σ can be determined based on how much variation you want in the relationship between x and y. If using Python's NumPy library, for example, you could use numpy.random.normal(0, σ, 1000) to generate the errors.