Many deblurring and blur kernel estimation methods use a maximum a posteriori approach or deep learning-based classification techniques to sharpen an image and/or predict the blur kernel. We propose a regression approach using convolutional neural networks (CNNs) to predict parameters of linear motion blur kernels, the length and orientation of the blur. We analyze the relationship between length and angle of linear motion blur that can be represented as digital filter kernels. A large dataset of blurred images is generated using a suite of blur kernels and used to train a regression CNN for prediction of length and angle of the motion blur. The coefficients of determination for estimation of length and angle are found to be greater than or equal to 0.89, even under the presence of significant additive Gaussian noise, up to a variance of 10% (SNR of 10 dB). Using our estimated kernel in a nonblind image deblurring method, the sum of squared differences error ratio demonstrates higher cumulative histogram values than comparison methods, with most test images yielding an error ratio of less than or equal to 1.25.