In other words, we are estimating vector B from equation [1]:

X is matrix of size [N, M], where N stands for number of rows and M for number of columns

X holds number of clicks per keyword

B is searched vector that should provide us with estimated number of value per click per keyword

B is a vector of size [M]

U is scalar value presenting "residue" value

For illustration purposes, lets make assumptions for matrix X as:

date |
keyword1 |
keyword2 |
keyword3 |

2012-01-01 | 3 | 4 | 0 |

2012-01-02 | 3 | 4 | 5 |

2012-01-03 | 1 | 0 | 3 |

2012-01-04 | 0 | 2 | 1 |

2012-01-05 | 3 | 0 | 4 |

and vector Y as:

date |
revenue |

2012-01-01 | 12.56 |

2012-01-02 | 11 |

2012-01-03 | 5 |

2012-01-04 | 5 |

2012-01-05 | 6 |

# assigning matrix X

> X <- array(c(3,3,1,0,3, 4,4,0,2,0, 0,5,3,1,4), dim=c(5,3))

# assigning vector Y

> Y <- c(12.56, 11, 5, 5, 6)

# execute call to linear model function:

> lmr = lm(formula=Y ~ X)# let's review the results:

> summary(lmr)

Call:

```
lm(formula = Y ~ X)
Residuals:
1 2 3 4 5
0.23747 0.05937 0.89050 -0.59367 -0.59367
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.5584 1.3074 2.722 0.224
X1 1.3803 0.5343 2.583 0.235
X2 1.1558 0.3660 3.158 0.195
X3 -0.2764 0.3512 -0.787 0.576
Residual standard error: 1.248 on 1 degrees of freedom
Multiple R-squared: 0.9699, Adjusted R-squared: 0.8796
F-statistic: 10.74 on 3 and 1 DF, p-value: 0.2198
```

Fast and handy! Details on output and LR methodology can be found in [2] and [3].

[1] Wikipedia's entry on General Linear Regression

http://en.wikipedia.org/wiki/General_linear_model

[2] Using R for statistical analyses - Multiple Regression

http://www.gardenersown.co.uk/Education/Lectures/R/regression.htm#lr_models

[3] Overview of Multiple Linear Regression

http://online.stat.psu.edu/online/development/stat501/08multiple/07multiple_matrix.html

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