**Machine Learning Methods in the
Environmental Sciences**

**Neural Network and Kernels
**
## Exercise 1.4

From the given data file (Ex1_4_corr) in Matlab format or text
format, compare the Pearson correlation with the Spearman rank
correlation for the time series *x* and *y* (each with 40
observations). Repeat the comparison for the time series
*x*_{2} and *y*_{2} (from the same data file
as above), where *x*_{2} and *y*_{2} are the
same as *x* and *y*, except that the 5th data point in
*y* is replaced by an outlier in *y*_{2}. Repeat the
comparison for the time series *x*_{3} and
*y*_{3}, where *x*_{3} and
*y*_{3} are the same as *x* and *y*, except that
the 5th data point in *x* and *y* is replaced by an outlier in
*x*_{3} and *y*_{3}. Make scatterplots of the
data points in the *x*-*y* space, the
*x*_{2}-*y*_{2} space and the
*x*_{3}-*y*_{3} space. Also plot the linear
regression line in the scatterplots.

## Exercise 1.5

Using the given data file (Ex1_5_MLR) in Matlab
format or text format, perform multiple
linear regression with predictors *x*_{1},
*x*_{2} and *x*_{3}, and the response variable
*y*. Rank the importance of the predictors in their influence on
*y*.

William W. Hsieh

2009