4. (24 points) Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question we consider an equation where the monthly change in the number of new one-family houses sold in the U.S. depends on last month's change in the 30-year conventional mortgage rate. Let HOMES be the number of new houses sold (in thousands) and IRATE be the mortgage rate. Their monthly changes are denoted by DHOMESt HOMES HOMESt-1 and DIRATE = IRATE-IRATEt-1. We obtain the following least squares regression estimates: DHOMESt = -1.98 - 52.49DIRATEt-1, N = 240, (3.24) (17.15) a. (3 points) Interpret the estimate of the slope coefficient. b. (6 points) Conduct a t-test to check whether DIRATE-1 statistically sig- nificant at the 5% significance level. t = c. (10 points) Let t denote the residuals from the above equation. Use the following estimated equation to conduct LM test and t-test for first-order autoregressive errors at the 5% significance level. -0.1945 - 3.1250DIRATE-1 0.3304t-1, R = 0.1167, N = 240. (15.876) (0.0632) d. (5 points) If we simply regress DHOMES, on DIRATE-1 and conduct hypothesis testing accordingly, are the testing results reliable? For those who believe it is reliable, please explain why. For those who believe it is unreliable, please give possible remedies.