Multiple regression - low F-statistics and multiple R-squared. What should i do/conclude I have two independent variable and one dependent variable. This is my summary when I use lm(y~x_1+x_2):
Residuals:
    Min      1Q  Median      3Q     Max 
-22.265  -9.563  -1.916   6.405  39.319 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  23.0107    18.2849   1.258  0.21407   
x_1          23.6386     6.8479   3.452  0.00114 **
x_2          -0.7147     0.3014  -2.371  0.02163 * 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.84 on 50 degrees of freedom
Multiple R-squared:  0.2018,    Adjusted R-squared:  0.1699 
F-statistic: 6.321 on 2 and 50 DF,  p-value: 0.00357

I got stuck because neither the F value and R squared are very significant. However the p-value is less than 0.05. Does it mean that y depends on both variables? What should I do next in my regression analysis?
 A: $R^2$ is conventionally interpreted as the percentage of variation in the $y$-term captured or "accounted for" by the regression model. As pointed out in the comments, that value of 0.20 might be considered pretty favorable in some applications. I remember the example dataset we were given in our linear regression course where we modeled hospital cost data and getting to an $R^2$ of 0.15 was the best we could achieve.
The penultimate question would require that you remove one and then the other variable and examine the coefficients. You probably need to look at their joint distribution, possibly with graphical methods.
The value of the $F$-statistic in measuring the amount of variation captured by the regression versus the amount that remains in the unexplained variation in the residuals. It's highly significant, although the $R^2$ does suggest that further analysis would still have the potential to explain some of the rest of the variability. Got any other variables in that dataset? Modeling often proceeds by building on initial models and yours looks promising. Do you have any existing science or theory to guide the model construction process?
Depending on what y, x_1 and x_2 "in reality" are measuring, you might want to do some residual plots to see in there is a systematic departure from the expect Gaussian distribution of residuals around 0 across the range of x_1 and x_2 values respectively. Spline fits or polynomial fits may be considered if there are no other variables available to investigate.
