Discussion question - Research Paper Example

Hi Megersa, I completely agree with your response except one thing that you said about regression analysis “If the line passes exactly through every single point on the scatter plot, then it can be best fit line by  explaining all of the variation.” This is because a regression model is a probabilistic model, meaning that one variable is not determined completely by the other variable. Therefore, we need to estimate the population parameters y-intercept (β0) and slope (β1) using sample statistics b0 and b1.

In actual, we will not see that the line passes exactly through every single point on the scatter plot.I liked your second paragraph where you said how we can test if the regression line best represents the data using hypothesis test. Here, also I like to mention that it is possible that correlation (or regression) is significant; however, the value of R-squared is not close to one that is the regression line does not best represent the data. This is because as the sample size, n increases the critical value of r (or t) decreases.

For example: For a sample size of n = 5, the two-tailed critical values of r for α = 0.05 are ±0.878.For a sample size of n = 10, the two-tailed critical values of r for α = 0.05 are ±0.632.For a sample size of n = 30, the two-tailed critical values of r for α = 0.05 are ±0.361.For a sample size of n = 102, the two-tailed critical values of r for α = 0.05 are ±0.195.From above, it can be seen that for larger sample size, it may be possible that correlation or regression is significant; however, the regression line does not best represent the data.