Problem 2 (20 points) Let (x1,y1),(x2,y2),(x3,y3),,(xn,yn) represent n pairs of data points. The variable X is x1,x2,x3,,xn. The variable Y is y1,y2,y3,,yn. (A) Write down the two equations for the correlation coefficient between variable X and variable Y. Explain all symbols that you use in the two equations. (B) What is the range of the correlation coefficient? (C) If X and Y have a perfect linear correlation. What are the possible values of the correlation coefficient? (D) If the value of the correlation coefficient is zero, can we say that X and Y are uncorrelated? Explain why or why not. (E) Can we say that the larger the value of the correlation coefficient, the stronger the linear correlation between X and Y ? Explain why or why not. (F) What is the coefficient of determination? (G) Will the coefficient of determination change when the scale of either X or Y changes? Briefly explain why or why not. (H) Can we say that the larger the value of the coefficient of determination, the stronger the linear correlation between X and Y ? Explain why or why not. Problem 2 (20 points) Let (x1,y1),(x2,y2),(x3,y3),,(xn,yn) represent n pairs of data points. The variable X is x1,x2,x3,,xn. The variable Y is y1,y2,y3,,yn. (A) Write down the two equations for the correlation coefficient between variable X and variable Y. Explain all symbols that you use in the two equations. (B) What is the range of the correlation coefficient? (C) If X and Y have a perfect linear correlation. What are the possible values of the correlation coefficient? (D) If the value of the correlation coefficient is zero, can we say that X and Y are uncorrelated? Explain why or why not. (E) Can we say that the larger the value of the correlation coefficient, the stronger the linear correlation between X and Y ? Explain why or why not. (F) What is the coefficient of determination? (G) Will the coefficient of determination change when the scale of either X or Y changes? Briefly explain why or why not. (H) Can we say that the larger the value of the coefficient of determination, the stronger the linear correlation between X and Y ? Explain why or why not