Two possible predictors, $X_1$ and $X_2$, are being considered when modelling a response variable $Y$. The following two models are proposed;
$$\text{Model 1}: Y_i = 0 + 1X_{1i} + i$$
$$\text{Model 2}: Y_i = 0 + 1X_{1i} + 2X_{2i} + i$$
When fitted to sample data, the following summary statistics are produced:
Model 1: $R2=0.887$ and adjusted $R2=0.884$
Model 2: $R2=0.888$ and adjusted $R2=0.882$
What can you say about the predictive power of $X_1$ and $X_2$?
Give a reason for your answer.
When examining the predictive power of your model, you want to look at whether your coefficients are statistically significant, among many other things.
Given the information you are providing, it seems like you may want to to test whether $X_2$ adds any explanatory power to your model. This could be done with an F-test.
The F-statistic is:
$F=\dfrac{(R_U^2-R_R^2)/q}{(1-R_U^2)(n-k-1)}$
where $R_U^2$ is the coefficient of determination for the unrestricted regression, $R_R^2$ for the unrestricted. $q$ is the number of restrictions you have. $n$, sample size, and $k$ the number of regressors in the unrestricted regression.
So for your case:
$F=\dfrac{(.888-.887)/1}{(1-.888)(n-2-1)}$
Solve for this value of $F$ and then using an F table find the critical value based upon the level of significance you desire.