Let X and Y be two random variables. They are such that any…

Let X and Y be two random variables. They are such that any set of joint observations of X and Y will lie along a straight line with slope -1. Let rho be the correlation coefficient between X and Y. Beta2 and R^2 come from the following regression using Y and X: Y = beta1 + beta2*X +U. Which of the following is true?

You believe that the time since an artist’s death has a larg…

You believe that the time since an artist’s death has a large impact on the price of their paintings. Using a random sample of oil painting sales (in thousands of dollars; sales) and time from the artist’s death to the sale of the painting (in years; Time) you generate the following regression output: oil painting sales = beta_0 + beta_1 * Time. (i) You want to test the hypothesis that an additional one year from the time of death to the sale of a painting will increase the price of the painting by $30,000 (30 units in the dependent variable). What is the null hypothesis? (ii) You want to test the hypothesis that an additional ten years from the time of death (10 units in Time) to the sale of a painting will increase the price of the painting by $100,000 (100 units in the dependent variable). What is the null hypothesis?