The stock market is said to be a leading indicator for gdp growth. because the stock market prices the expectations of future earnings, a bullish market may predict future economic growth and vice versa. let yt be gdp growth and xt be sp500 returns. (both series collected at the quarterly frequency as in the previous exercise). run ols for the following models:

a. yt=î²0+î²1xt+î¼t (contemporaneous correlation)
b. yt=î²0+axt-1+î¼t (one-quarter leading indicator)
c. yt= î²o+î²1xt-1+î²2xt-2+ î²3xt-3+ î²4xt-4+î¼t(four quarter leading indicator)
d. yt= î²o+î²1xt-1+î²2xt-2+ î²3xt-3+ î²4xt-4+î²5yt-1 +î¼t (leading indicator with gdp inertia)

for each model, assess the r-squared and the adjusted r-squared. which model do vou prefer?