In recent years, interest in shale plays has grown substantially due to horizontal drilling and hydraulic fracturing techniques. Special interest is in shale plays previously exhausted with vertical wells that are believed to still have high potential if developed with horizontal wells. However, with drilling costs at an all time high, choosing the right locations for new wells is a crucial issue. Therefore, identifying so called "sweet spots" with high potential for oil and gas is of great importance for oil companies worldwide. Well log data from millions of wells drilled using conventional techniques since the industry's inception is available and generally not used. We propose a data analytical solution that 1) automatically extracts simple features from complex and high-dimensional well log curves arising from vertical wells using functional Principal Component Analysis (fPCA), and 2) builds models that predict sweet spots in shale plays by correlating extracted features with production data from horizontal wells. Our solution builds predictive models for production directly using previous production data and petrophysical well logs alone, thus circumventing time consuming and expensive geological analysis. Regression in conjunction with interpolation (Regression-Kriging) is a well-known approach that can be used to correlate well log curves with production data. However, this method is only applicable once the set of (one-dimensional) predictors and the corresponding regression model have been defined. Summary statistics such as means, maximum or minimum peak heights are obvious candidates but are too simple to capture all the relevant features from the well logs. Instead, we extract a set of one-dimensional features from each of the well log curves, facilitating simple 2D interpolations as opposed to more difficult 3D interpolations. This is particularly advantageous in situations where seismic data are not available and 3D interpolations are challenging. Finally, by regressing previous production data from horizontal wells on the extracted features we show that it is possible to predict production at new locations directly. We have implemented our method using the R statistical package. We tested it using well log data from 2020 vertical wells and production data from 702 horizontal wells in a single field. For gas we get an accuracy of 90% at predicting whether a given horizontal well has production above a given high-production threshold, while for oil, we get an accuracy of 71%. The main novelty of our method is the systematic extraction of one-dimensional predictors using a statistically robust method called functional Principal Components Analysis (fPCA). To the best of our knowledge this is the first time fPCA is applied to well log curves in the context of oil and gas exploration.