Q1. Consider the following data on x and y: XV 15 225 325 4 45 a) Make a scaterrplot of y versus x. By hand, or by R. b) Draw a line on the scatterplot that constitutes your best guess for the t. c) Find the slope of the line in part b. Hint: pick two points on your line, and then nd rise over run. Now, let me tell you that the equation of the best t is y = -5 + 12 x. Don't change your answer to part c! Just check to see how close you were. d) If we use this best t, what is the predicted value of the y of someone whose x is 1.5. Show work. e) If we use this best t, what is the error when you predict the y of someone whose x is 1.0? Repeat for x = 2, 3, and 4. Show work. Hint: error is observed y - predicted y. f) Find the variance of the four errors you found in part e. By R, or by hand. g) Find the variance of the y's. By R, or by hand. h) What is the percentage of that reduction? Hint: percent change = (part f - part gi/(part g) * 100, and a negative value means reduction. i) Finally, we've been told that r"2 ( times 100) gives the percentage of the variability in y that is explained by x. I can tell you that the correlation between x and y is about 0.94869. Is your r"2 close to the absolute value of the answer in part h ? It should be