You are studying Rio Tinto Limited (RIO) stock performance during last years. Since RIO is listed in Sydney Security Exchange, you believe that the returns of RIO is correlated with ASX200 index returns. As Rio Tinto is a multinational and the world's second largest metals and mining corporations, you also assume RIO returns are associated with S&P 500 index returns. You model the RIO returns (r_RIO) as below:

r_(RIO,t)=a_0+a_1*r_(SP500,t)+a_2*r_(ASX,t)+ u_t

and r_(ASX,t) are returns for S&P 500 index and ASX index, respectively, u_t is the error term.After obtaining historical data, you run a regression and get the following output:

ANOVA

df SS MS

Regression 2.000 0.441 0.220

Residual 212.000 1.048 0.005

Total 214.000 1.489

Coefficients Standard Error t Stat

Intercept 0.008 0.005 1.686

S&P 500 -0.094 0.171 -0.550

ASX 200 1.322 0.195 6.768

Test if the first slope coefficient estimate of a_1 is significant at the 1% level?

Construct and interpret the 95% confidence interval for the second slope coefficient estimate of a_2.

Determine if the two independent variables are jointly statistically related to r_RIOat the 0.05 significance level.