Regarding a scatterplot matrix: a. Identify two of its uses. b. What property should the scatterplots of the response versus each predictor variable have in order to proceed to obtain the regression plane for the data?

Step 1
a)
Scatterplot matrix:
A scatterplot matrix is defined as an array of scatterplots of the response variable with every one of the predictor variables, when there are more than one predictor variables present in the data.
Step 2
It is very useful for the researchers to be able to visualize the relationship among the data points, as this helps to determine which analysis procedures would be suitable. In case the response variable depends on several predictors, plotting separate scatterplots will show the nature of the relationship between the response variable and that particular predictor. However, the overall relationship may not be clear.
Thus, one of the uses of a scatterplot matrix is to get an overall visual understanding of the relationship of the response variable with each predictor variable.
Moreover, knowing the relationship among the predictors beforehand also helps the researcher to predict the type of relationship the response variable is likely to have with one predictor, when its relationship with another predictor is already known.
Thus, another use of a scatterplot matrix is to understand the nature of overall relationship among all the predictor variables.
b)
It is useful to construct a regression plane for a response variable depending upon two predictors, only when a linear relationship is known to exist between. In absence of a linear relationship of the response variable with each predictor, it is useless to obtain a regression plane. A scatterplot matrix helps to determine beforehand, whether the required linear relationship exists.
Thus, the property that the scatterplots of the response versus each predictor variable should have in order to proceed to obtain the regression plane for the data is linearity.