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I was given a set of data and asked to perform a test for existence of regression, as well as to calculate a value for the coefficient of determination and interpret whether the linear model is useful in predicting my Y variable. When conducting the test for existence of regression, the result was to reject my null hypothesis of B1 = 0 and thus the linear regression model is useful in predicting my Y variable. However, when calculating my value for $R^2$ I got a small value which suggests that the linear model is not useful for predictions.

So i was just wondering whether it is possible for these two to conclusions to contradict one another, or is it likely that i have made an error in my calculations somewhere?

Walter
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user75188
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    It is possible to have a significant test for the linear model for a not so high $R^2$ value. Please provide more information about your calculations or even the dataset for us to help you mor effectively. – Walter May 03 '15 at 23:49
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    There are numerous discussions of the small-$R^2$-but-significant-regression-model issue on site, such as [here](http://stats.stackexchange.com/questions/58465/is-this-regression-significant) and [here](http://stats.stackexchange.com/questions/58366/why-does-random-looking-data-give-a-really-good-model) for example. – Glen_b May 04 '15 at 00:07

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