In this section, you learn how to:
Video Overview of the Section (Alternative .mp4 Version – 10:59 min)
- Interpret correlation coefficients by visualizing a scatterplot matrix
- Fit a plane to data using the method of least squares and calculus
- Predict an observation using a least squares fitted plane
Video Overview of the Section (Alternative .mp4 Version – 10:59 min)
Consider data sets where there are k explanatory variables and one dependent variable in a sample of size n. That is, the data consist of:
$$
left{
begin{eqnarray*}
x_{11},x_{12},ldots,x_{1k},y_1 \
x_{21},x_{22},ldots,x_{2k},y_2 \
vdots~~~~~~~~~~~~~~~~ \
x_{n1},x_{n2},ldots,x_{nk},y_n \
end{eqnarray*}
right} .
$$ The ith observation corresponds to the ith row, consisting of ( (x_{i1},x_{i2},ldots,x_{ik},y_i) ). For this general case, we take k+1 measurements on each entity.
To provide some context, the next page introduces an example that will be referenced throughout this chapter.