Significance of regression test. We will simulate from two different models in R

Question

Significance of regression test. We will simulate from two different models in Rstudio

The “significant” model

The “non-significant” model

For both, we will consider a sample size of 25 (you may make your own data) and three possible levels of noise. That is, three values of ?.

n=25

??(1,5,10)??(1,5,10)

Use simulation to obtain an empirical distribution for each of the following values, for each of the three values of ?, for both models.

The F statistic for the significance of regression test

The p-value for the significance of regression test

R2

For each model-? combination use 2500 simulations. For each simulation, fit a regression model of the same form used to perform the simulation.

Discussions:

Do we know the true distribution of any of these values?

How do the empirical distributions from the simulations compare to the true distributions? (You could consider adding a curve for the true distributions if you know them.)

How are R2 and ? related? Is the relationship the same for the significant and non-significant models?

Organize the plots in a grid for easy comparison.

Explanation / Answer

Running the regression test in Rstudio with the function 'lm'

We have taken our own data as specified in the question. Now after running the test with 'lm' between dependent and independent variable, the star marks at the end of table (results) shows the significance . a three star shows most significat and a one star shows less significant.

Yes these follow the normal distribution as per the central limit theorem.

R2 tells the fitness of the function. Its value if near to 1 means our model( regression) is good. It tells the goodness of fit.

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