According to Irving Fishers theory of interest, the real rate of interest equals the nominal rate of intertest minus the expected rate of inflation; since the expected rate of inflation is likely to be highly correlated with the actual rater of inflation, the latter is often used as proxy for the former. To test this theory, the nominal rate of interest on three-month treasury bills (RTS) was regressed against the rate of change in the implicit price deflator (INF) using annual data for the period 1980-2015. The result of the regression is:

RTS = 1.658 + 0.785(INF)

(0.793) (0.161)

Where figures in parentheses are the corresponding estimated standard errors.

Use these results to test following hypothesis at 5% level of significance

1. The nominal rate of interest increases as the rate of inflation increases.
2. The nominal rate of interest increases by 1 percent for each 1 percent increase in the rate of inflation
3. The real rate of interest (i.e., the nominal rate of interest when INF = 0) is positive