Question

Please set eval = FALSE in the codechunk of your RMarkdown, as the output for this question will be too lengthy. In R, use set.seed (35135) and then the rnorm) command to generate 80,000 standard normally distributed observations. Put those values into a matrix with 400 rows and 200 columns. Now fit a multiple linear regression where the tenth column of that matrix is the 'response' variable, and the remainder of the columns are considered predictors. Note: the syntax lm(Y ~ to tell R that the variable named Y in the dat.matrix should be modelled using the remainder of the variables in dat.matrix data-dat.matrix) is a shortcut Examine the summary output for the model you just fit. Manually count the number of statistically significant (α-0.05) predictor variables in this model. How many are there? What concept in class is this illustrating? How many statistically significant predictor variables would we expect to see for this simulation?

Answer 1

R-code:

As per output, R-Squre = 0.4598 = 45.98% of the variation in the 10 column is explained by the remaining columns.

Test Statistic F = 0.8553

Here P-value = 0.8647 which is greater than 0.05 so we conclude that there multiple regression equation is not best fit tot he given data.