In a simple regression of Y versus X, what is the relationship between the estimated slope, labeled b, and the correlation between Y and X, labeled r? Are they the same? Do they always have the same sign? Is it possible for r to be close to 1 and for b to be close to 0? Is it possible for r to be close to 0 and for b to be large? Explore this with simulation in the following way. Choose any values a and b for the intercept and slope of a linear relationship between X and Y and choose any value s for the standard error of estimate. Then generate a set of X values randomly. It doesn’t really matter how you do this, but for this problem, generate them from a normal distribution with mean 100 and standard deviation 10. Then generate each Y value from the equation Y = a + bX + e, where the error e is normally distributed with mean 0 and standard deviations. Given your generated data, calculate the estimated slope of the regression line with Excel’s SLOPE function and calculate the correlation between Y and X with Excel’s CORREL function. Once you have this setup, you can press the F9 key to get new results, or you can change your values of a, b, and s. Based on the simulated results, can you answer the original questions?