This is example code to perform linear regression using keras.

import keras
from keras.models import Sequential
from keras.layers import Dense
from keras.optimizers import SGD

import numpy as np
from numpy.random import random

x = random((30, 2))
w = np.array([3., 2.])
b = 1.
y = np.dot(x, w) + b
print x
print y
model = Sequential()
# 30 observations. Each observation has 2 features.
model.add(Dense(1, input_shape=(2, )))
# MSE because we want linear regression.
model.compile(optimizer=SGD(lr=0.1), loss='mse')
model.fit(x, y, nb_epoch=60, batch_size=1)
print model.get_weights()

Output:

Using Theano backend.
Using gpu device 0: GeForce GTX 1080 (CNMeM is disabled, cuDNN 5105)
[[ 0.66716875  0.44536398]
 [ 0.58253148  0.45428442]
 [ 0.49094032  0.77897022]
 [ 0.16345683  0.27807741]
 [ 0.29913647  0.87666064]
 [ 0.41150342  0.4329423 ]
 [ 0.30724994  0.56194767]
 [ 0.1448368   0.61572276]
 [ 0.89288341  0.45568394]
 [ 0.20008006  0.1446671 ]
 [ 0.58501705  0.1407299 ]
 [ 0.8924096   0.58803216]
 [ 0.76954948  0.95146172]
 [ 0.17315788  0.03576668]
 [ 0.01515587  0.36599027]
 [ 0.77232613  0.35686848]
 [ 0.4897022   0.52092717]
 [ 0.50756237  0.20100097]
 [ 0.8372522   0.53871228]
 [ 0.2223611   0.5919245 ]
 [ 0.89898591  0.24163213]
 [ 0.571022    0.2140571 ]
 [ 0.55041835  0.00383233]
 [ 0.08253098  0.64526628]
 [ 0.3512973   0.53963146]
 [ 0.73578765  0.65469051]
 [ 0.91344962  0.40350727]
 [ 0.74023006  0.34414037]
 [ 0.41329666  0.22543498]
 [ 0.82787326  0.41838276]]
[ 3.8922342   3.65616327  4.03076141  2.0465253   3.6507307   3.10039487
  3.04564516  2.66595593  4.59001811  1.88957438  3.03651096  4.85329311
  5.21157187  1.591007    1.77744815  4.03071534  3.51096094  2.92468906
  4.58918115  2.8509323   4.18022197  3.14118018  2.65891972  2.53812548
  3.13315483  4.51674398  4.54736341  3.90897091  2.69075993  4.32038531]
Epoch 1/60
30/30 [==============================] - 0s - loss: 1.6538      
Epoch 2/60
30/30 [==============================] - 0s - loss: 0.1377     
Epoch 3/60
30/30 [==============================] - 0s - loss: 0.0793     
Epoch 4/60
30/30 [==============================] - 0s - loss: 0.0370     
Epoch 5/60
30/30 [==============================] - 0s - loss: 0.0265     
Epoch 6/60
30/30 [==============================] - 0s - loss: 0.0146     
Epoch 7/60
30/30 [==============================] - 0s - loss: 0.0096     
Epoch 8/60
30/30 [==============================] - 0s - loss: 0.0043     
Epoch 9/60
30/30 [==============================] - 0s - loss: 0.0030     
Epoch 10/60
30/30 [==============================] - 0s - loss: 0.0020     
Epoch 11/60
30/30 [==============================] - 0s - loss: 0.0012     
Epoch 12/60
30/30 [==============================] - 0s - loss: 6.9193e-04     
Epoch 13/60
30/30 [==============================] - 0s - loss: 3.6242e-04     
Epoch 14/60
30/30 [==============================] - 0s - loss: 2.2359e-04     
Epoch 15/60
30/30 [==============================] - 0s - loss: 1.1410e-04     
Epoch 16/60
30/30 [==============================] - 0s - loss: 7.5656e-05     
Epoch 17/60
30/30 [==============================] - 0s - loss: 4.6557e-05     
Epoch 18/60
30/30 [==============================] - 0s - loss: 2.9460e-05     
Epoch 19/60
30/30 [==============================] - 0s - loss: 1.6638e-05     
Epoch 20/60
30/30 [==============================] - 0s - loss: 1.0647e-05     
Epoch 21/60
30/30 [==============================] - 0s - loss: 6.4342e-06     
Epoch 22/60
30/30 [==============================] - 0s - loss: 3.5493e-06     
Epoch 23/60
30/30 [==============================] - 0s - loss: 1.8375e-06     
Epoch 24/60
30/30 [==============================] - 0s - loss: 1.3024e-06     
Epoch 25/60
30/30 [==============================] - 0s - loss: 8.3916e-07     
Epoch 26/60
30/30 [==============================] - 0s - loss: 5.3163e-07     
Epoch 27/60
30/30 [==============================] - 0s - loss: 2.8679e-07     
Epoch 28/60
30/30 [==============================] - 0s - loss: 1.5040e-07     
Epoch 29/60
30/30 [==============================] - 0s - loss: 1.1201e-07     
Epoch 30/60
30/30 [==============================] - 0s - loss: 6.0981e-08     
Epoch 31/60
30/30 [==============================] - 0s - loss: 4.7074e-08     
Epoch 32/60
30/30 [==============================] - 0s - loss: 2.9919e-08     
Epoch 33/60
30/30 [==============================] - 0s - loss: 1.6059e-08     
Epoch 34/60
30/30 [==============================] - 0s - loss: 9.3970e-09     
Epoch 35/60
30/30 [==============================] - 0s - loss: 5.7633e-09     
Epoch 36/60
30/30 [==============================] - 0s - loss: 3.3312e-09     
Epoch 37/60
30/30 [==============================] - 0s - loss: 2.1822e-09     
Epoch 38/60
30/30 [==============================] - 0s - loss: 1.2432e-09     
Epoch 39/60
30/30 [==============================] - 0s - loss: 6.8956e-10     
Epoch 40/60
30/30 [==============================] - 0s - loss: 4.4050e-10     
Epoch 41/60
30/30 [==============================] - 0s - loss: 2.5711e-10     
Epoch 42/60
30/30 [==============================] - 0s - loss: 1.5499e-10     
Epoch 43/60
30/30 [==============================] - 0s - loss: 8.9069e-11     
Epoch 44/60
30/30 [==============================] - 0s - loss: 4.6494e-11     
Epoch 45/60
30/30 [==============================] - 0s - loss: 3.0863e-11     
Epoch 46/60
30/30 [==============================] - 0s - loss: 1.5283e-11     
Epoch 47/60
30/30 [==============================] - 0s - loss: 8.9050e-12     
Epoch 48/60
30/30 [==============================] - 0s - loss: 4.8648e-12     
Epoch 49/60
30/30 [==============================] - 0s - loss: 3.5887e-12     
Epoch 50/60
30/30 [==============================] - 0s - loss: 2.0066e-12     
Epoch 51/60
30/30 [==============================] - 0s - loss: 1.1189e-12     
Epoch 52/60
30/30 [==============================] - 0s - loss: 6.5086e-13     
Epoch 53/60
30/30 [==============================] - 0s - loss: 3.3727e-13     
Epoch 54/60
30/30 [==============================] - 0s - loss: 1.7621e-13     
Epoch 55/60
30/30 [==============================] - 0s - loss: 9.8529e-14     
Epoch 56/60
30/30 [==============================] - 0s - loss: 5.6370e-14     
Epoch 57/60
30/30 [==============================] - 0s - loss: 5.3054e-14     
Epoch 58/60
30/30 [==============================] - 0s - loss: 4.9738e-14     
Epoch 59/60
30/30 [==============================] - 0s - loss: 3.9790e-14     
Epoch 60/60
30/30 [==============================] - 0s - loss: 4.4527e-14     
[array([[ 3.        ],
       [ 1.99999952]], dtype=float32), array([ 1.00000024], dtype=float32)]