Dahee - 

Just use the raw, estimated residual on the y-axis, and the predicted-y on the x-axis. 

There is a naturally occurring heteroscedasticity which is the result of members of the population being of different sizes (https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity).  But this is modified by other concerns (https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity). 

You can go further than the usual graphical residual analysis noted first above, and estimate the coefficient of heteroscedasticity from your data:

 https://www.researchgate.net/publication/263809034_Alternative_to_the_Iterated_Reweighted_Least_Squares_Method_-_Apparent_Heteroscedasticity_and_Linear_Regression_Model_Sampling

There are other ways to do this.  Consider the following: 

 https://www.researchgate.net/publication/263032446_Weighting_in_Regression_for_Use_in_Survey_Methodology

I am not clear on your application, but perhaps some of the above might help. 

Cheers - Jim

As far as I can see, there is no pattern of heteroscedasticity of residuals in your graphs.

HETEROSCEDASTICITY should be tested and verified.

We cannot make an empirical assertion by visual inspection of

of scatter plots. Such visual inspection may give us an impression,

but does not carry empirical weight. See below for testing for

heteroscedasticity.

TEST FOR HETROSCEDASTICITY IN REGRESSION

-Levene's test

-Goldfeld–Quandt test

-Park test

-Glejser test

-Brown–Forsythe test

-Harrison–McCabe test

-Breusch–Pagan test

-White test

-Cook–Weisberg test

TEST FOR HETROSCEDASTICITY IN GROUP DATA

-F-test of equality of variances

-Cochran's C test

-Hartley's test

LINKS:

White, Halbert (1980). "A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity". Econometrica. 48 (4): 817–838. doi:10.2307/1912934. JSTOR 1912934.

https://www.jstor.org/stable/1912934?seq=1#page_scan_tab_contents

R. E. Park (1966). "Estimation with Heteroscedastic Error Terms". Econometrica. 34 (4): 888. doi:10.2307/1910108. JSTOR 1910108.

https://www.jstor.org/stable/1910108?seq=1#page_scan_tab_contents

Glejser, H. (1969). "A new test for heteroscedasticity". Journal of the American Statistical Association. 64 (325): 316–323. doi:10.1080/01621459.1969.10500976.

https://www.tandfonline.com/doi/abs/10.1080/01621459.1969.10500976

Machado, José A. F.; Silva, J. M. C. Santos (2000). "Glejser's test revisited". Journal of Econometrics. 97 (1): 189–202. doi:10.1016/S0304-4076(00)00016-6.

https://www.sciencedirect.com/science/article/pii/S0304407600000166?via%3Dihub

I do not recommend hypothesis tests for heteroscedasticity, as a matter of practicality. An hypothesis test would concentrate on some aspect and you would have to have some way of determining a reasonable threshold for a p-value, based on sample size and some idea of an effect size.  That would be liable to end by being rather arbitrary.   Heteroscedasticity is a matter of degree.  One may estimate the coefficient of heteroscedasticity from the data.   In my response above, I gave two links to the nature of heteroscedasticity for population statistics, and two links to ways to estimate the coefficient of heteroscedasticity. 

It is true that heteroscedasticity may not always be readily apparent from a y vs x, or in multiple regression, a y vs y* graph, where y* is predicted y, when the estimated variance of the prediction error is relatively small.  However, you can still do graphical residual analyses, and that leads to my links above on estimating the coefficient of heteroscedasticity, especially the following one which I repeat here:

 https://www.researchgate.net/publication/263809034_Alternative_to_the_Iterated_Reweighted_Least_Squares_Method_-_Apparent_Heteroscedasticity_and_Linear_Regression_Model_Sampling

But often you really can see this in a y vs x plot such as shown in a Sage Publications encyclopedia here:

 https://www.researchgate.net/publication/262972023_HETEROSCEDASTICITY_AND_HOMOSCEDASTICITY

(Note that estimated residuals are measured vertically from the predicted values.)  

By looking at the scatter plot, your residuals seem fine. Nevertheless, it is hard to judge just by looking. Especially so because your dependent variable is ordinal. Perform some tests to be sure...

Explanation:

The sum of the std. residual and the std. fitted value is close to the standardized value of your dependent variable, for each point on the plot. This is what creates sets of points that look like they "outline" 12 downward sloping parallel linear lines, where each line corresponds to a value of the dependent variable (say upper line corresponds to value 2.2 and the lowest to -2.2).

Each line's length "represents" the variance of the residuals corresponding to a specific value of the dependent variable (from 2.2 to -2.2). If the downward sloping lines length's change systematically this implies that the variance of the residuals changes systematically with the value of the dependent variable (& the fitted value), which would imply heteroscedasticity. On your plot the downward sloping lines seem to be of equal length. This implies absence of heteroscedasticity.

See the two appended scatter plots. On the first one the residuals are homoscedastic. On the second one the variance of the residuals increases with the value of the dependent variable. Note how on the second plot the downward sloping lines are short at first and increase in length when the fitted value increases (or the true value..).

Best,v