Question

Describe the each scatterplot's usefulness in terms.

(x and y has simple linear regression relationship.)

(Y~X)

1. scatter plot of x and y

2. scatter plot of x and residuals

3. scatter plot of order of the x and residuals

4. scatter plot of yhat and residuals

Answer 1

1.

Scatter plot of x and y-

Through scatter plot of two random variables X and Y we can observe whether there is any relation between them or not.

Observing the nature of plotted data we can approximate the probable relation as whether it is linear, non-liner, quadratic, logarithmic, exponential or of any other mathematical model. In fact, if the data are not at all related, then that can be also approximated using these scatter plots.

2.

Scatter plot of x and residuals-

Through this type of scatter plot we can compare the amount of residuals (i.e. values of y - predicted value of y ) with change of values of independent variable x.

3.

Scatter plot of order of the x and residuals-

Generally scatter plot is done according to some chronology or any particular order. Through this type of scatter plot we can study change of residuals over time or place (or the particular order which was used to collect data).

4.

Scatter plot of and residuals-

In our usual notation, represents predicted values of dependent variable y corresponding to values of independent variable x which is obtained using appropriate regression equations.

Through this type of scatter plot we can study the trend between predicted values of dependent variable y and residuals (i.e. values of y - predicted value of y ) obtained in prediction.