Although we know that the trend line is the best fitting among the possible linear trend lines, we don't know how well this fits the actual data. The significance of the regression parameters is obtained by testing the null hypothesis, which states that the given parameter equals to zero. The F-test in the output pertains to the hypothesis that each regression parameter is zero. In a nutshell, it tests the significance of the regression in general. A p-value below 0.05 can be interpreted as "the regression line is significant." Otherwise, there is not much point in fitting the regression model at all.

However, even if you have a significant F-value, you cannot say too much about the fit of the regression line. We have seen that residuals characterize the error of the fit. The R-squared coefficient summarizes them into a single measure. R-squared is the proportion of the variance in the response variable explained by the regression. Mathematically,...