Use simulation to find the standard error and the critical values for 10 and 5% of the slope coefficient of the linear zero-intercept bivariate regression model (Yˆ = bX) for a sample size of 10. Assume X to be normally distributed, X ~ N(mean = 20, standard deviation = 4), and generate values of Y based on the generated values of X using the following equation:

Y x Z = b + s Y − r 1 1 2 where b1 is the population value of b1, Z the random normal variate, s Y the population standard deviation of Y, and ρ the population value of correlation between X and Y. Use ρ = 0.6, n = 10, mx = 20, s x = 4, b1 = 3, and s Y = 2.