In the multiple regression model with two explanatory variables
Y_i= ?₀ + ?₁X₁_i + ?₂X₂_i + u_i
the OLS estimators for the three parameters are as follows (small letters refer to deviations from means as in z_i = Z_i -

\bar { Z }

\hat { \beta } _ { 0 } = \bar { Y } - \hat { \beta } _ { 1 } \bar { X } _ { 1 } - \hat { \beta } _ { 2 } \bar { X } _ { 2 }

\hat { \beta } _ { 1 } = \frac { \sum _ { i = 1 } ^ { n } y _ { i } x _ { 1 i } \sum _ { i = 1 } ^ { n } x _ { 2 i } ^ { 2 } - \sum _ { i = 1 } ^ { n } y _ { i } x _ { 2 i } \sum _ { i = 1 } ^ { n } x _ { 1 i } x _ { 2 i } } { \sum _ { i = 1 } ^ { n } x _ { 1 i } ^ { 2 } \sum _ { i = 1 } ^ { n } x _ { 2 i } ^ { 2 } - \left( \sum _ { i = 1 } ^ { n } x _ { 1 i } x _ { 2 i } \right) ^ { 2 } }

\hat { \beta } _ { 2 } = \frac { \sum _ { i = 1 } ^ { n } y _ { i } x _ { 1 i } \sum _ { i = 1 } ^ { n } x _ { 1 i } ^ { 2 } - \sum _ { i = 1 } ^ { n } y _ { i } x _ { 1 i } \sum _ { i = 1 } ^ { n } x _ { 1 i } x _ { 2 i } } { \sum _ { i = 1 } ^ { n } x _ { 1 i } ^ { 2 } \sum _ { i = 1 } ^ { n } x _ { 2 i } ^ { 2 } - \left( \sum _ { i = 1 } ^ { n } x _ { 1 i } x _ { 2 i } \right) ^ { 2 } }

You have collected data for 104 countries of the world from the Penn World Tables and want to estimate the effect of the population growth rate (X₁_i)and the saving rate (X₂_i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S.)in 1990. The various sums needed to calculate the OLS estimates are given below:

\sum _ { i = 1 } ^ { n } Y _ { i }

= 33.33;

\sum _ { i = 1 } ^ { n } X _ { 1 i }

= 2.025;

\sum _ { i = 1 } ^ { n } X _ { 2 i }

=17.313

\sum _ { i = 1 } ^ { n } y _ { i } ^ { 2 }

= 8.3103;

\sum _ { i = 1 } ^ { n } x _ { 1 i } ^ { 2 }

= .0122;

\sum _ { i = 1 } ^ { n } x _ { 2 i } ^ { 2 }

= 0.6422

\sum _ { i = 1 } ^ { n } y _ { i } x _ { 1 i }

= - 0.2304;

\sum _ { i = 1 } ^ { n } y _ { i } x _ { 2 i }

= 1.5676;

\sum _ { i = 1 } ^ { n } x _ { 1 \mathrm { i } } x _ { 2 i }

= -0.0520
The heteroskedasticity-robust standard errors of the two slope coefficients are 1.99 (for population growth)and 0.23 (for the saving rate). Calculate the 95% confidence interval for both coefficients. How many standard deviations are the coefficients away from zero?

The Overall Regression F-Statistic Tests the Null Hypothesis That

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