Problem 3 Researchers investigating the causes of stressrelated health problems, such as heart attacks, believe that these are correlated with economic conditions. As a crude test of their hypothesis, we can estimate the equation: heart attacks, = [30 + lunemploymenti + ui where heart attacksi is the number of heart attacks per 100,000 population in year i, unemployment,- is the unemployment rate in year i, and u,- is the error term. Data from 1968-1978 are given below: heart attack rate er 100 000 10.7 11.1 11.5 11.7 12.0 12.0 12.1 12.7 12.5 13.3 12.5 unem .10 .. ent rate #:4909999???\" surname-racemes a. Compute the Ordinary Least Squares estimate of the parameters 50 and 51 (put the data into an Excel spreadsheet or directly into R if you prefer and do the computations using the formulas we reviewed in class when learning about the ordinary least square estimator in the ease of a single regressor). b. How would these coefcients change if heart attack rates were reported per 1,000 population? c. Calculate the predicted heart attack rates for each year. Calculate the estimated error for each year. d. What is the average estimated error? Why? e. The unemployment rate was 5.8 in 1979. Based on your estimates, what heart attack rate would you have expected that year? f. Suppose that a linear regression produces 31 = 0. Demonstrate algebraically that R2 must be equal to zero in this case