Visualization is certainly a good idea if these findings are important to communicate. A narrative description of an interaction effect may be cumbersome to write and to absorb, and it is unlikely to make the same impact that a chart would.
I'd make a bubble chart. This is not entirely an SPSS solution, but if you use Excel or R it will work, especially for the continuous-continuous interaction and especially if you are not concerned about making the equivalent of partial plots, i.e., if you don't need to show how the dependent variable is a function of these independent variables while controlling for others.*
Start with a grid consisting of values of HDI on one axis and share of non-renewable electricity consumption on the other. Divide each predictor into some discrete regions (5? 10? 50? It depends on your judgment and your facility with SPSS recodes, or with SPSS's auto-recode commands). For each X-Y region, plot the bubble size as the mean of your dependent variable in that region, taking Yes to be 1 and No to be 0.
If you use R, instead of bubble size you have the option of varying the points using color or symbol.
The continuous-binary interaction could be done the same way; it'll just look a little simpler, perhaps a little simplistic.
*If you do want to incorporate such control, first regress Y on the control variables--those you're not interested in plotting. Then, instead of using the mean of Y as your plot variable, use the mean of the residuals from that regression. The tricky thing here will be what to express about the range of values for these residuals, since they won't be bounded by 0 and 1.
If I've left out some important step someone will correct me....
EDIT: you could make this entirely an SPSS operation if you discretized your Y variable and created a scatterplot of X1 with X2...a) using the "by" command to plot Y in multiple colors, or b) using the "by [Y] (identify) command to plot Y in multiple characters.
This does not seem like a Cox regression problem. The Cox model is used to examine influences of variables on the time is takes for an event to happen. The time variable in your data seems to be 1 for the choice that was made and 2 for the choices that weren't made in each presentation/trial. It's not clear to me how Cox analysis with such a "time" variable would accomplish your goal, although if you have some reference to how it does so I would be glad to learn from it.
What you have is a set of trials involving a forced choice of 1 among 3 objects. Typically this would be analyzed as a multinomial logistic regression, and SPSS does have tools for that type of analysis. This examines how the probability of making a particular choice depends on predictor variables (in your case, price, price range, their interaction, and size) at each trial.
Complicating matters in this design is that over the entire study there were multiple SKU involved but only 3 were available in each trial. So the probability of choosing an SKU that wasn't presented is 0. Evidently the size of each SKU was fixed but the price was varied among trials. This type of design gets a bit beyond my personal expertise, but I will propose one way to proceed.
To analyze this as a multinomial regression, which seems most appropriate, it seems that you will have to include an additional predictor variable that indicates whether or not the SKU was available in a particular trial. That way, at least formally, all the SKU are included in the model for each trial. Then you proceed as follows, with one data line for each trial:
The output variable for each presentation is the SKU that was chosen.
The price, price_range, some type of interaction term between them, and the size are included as predictor variables. It's not clear that including the Respondent ID will help much, as each Respondent only saw 2 of the 12 different types of presentation, but include that if you think it is important (it may be difficult to interpret, however).
A set of variables indicating whether a particular SKU was available for choice at that trial is added as predictors. The "stratum" per se is then no longer needed as a predictor.
You should not just ignore the range_price variable as a possible predictor. It's hard to interpret interaction terms without also knowing the main effects.
There are a few dangers here whose importance may be affected by the details of your design. One is that although you have prices in numbers you only have a limited set of prices and price ranges, so it might be difficult to interpret your data directly in terms of change of odds per change in price. This may be a particular issue with your interaction term. A second is that the particular combinations of sizes, prices, and price ranges you used might have some internal relations that then pose problems like those that arose when your price_range and strata ended up being just two ways of presenting the same variable.
If this answer doesn't help, you might want to pose a new question based more directly on your experimental design, such as "multinomial regression with different choices among trials." If possible, if you do pose a new question present the choices available in each of your 12 "strata".
Best Answer
When a model is fitted with only the significant main effects, $y=a+b$, this suggests that both $a$ and $b$ variable contributes to explaining the variability in $y$. And when put together, the simultaneous effect of both variable on $y$ may be either multiplicative or additive.
For example, effect of variable $a$ on $y$ alone may be $\alpha$ and effect of $b$ on $y$ alone is $\beta$. Having both variable $a$ and $b$ may produce a overall multiplicative effect $\alpha\beta$. This can be explain in a model $y=a+b+ab$. By doing so, the interpretation becomes a little tricky since the main effect cannot be interpreted alone anymore. Also, an interaction model without main effects would not make sense. The model $y=ab$ is not testing for interaction but rather has a different meaning, it will be just testing if a new variable created $p =a\times b$ is linearly associated with your $y$.
Say you have a model $y=\beta_0+\beta_1a+\beta_2b+\beta_3ab$ where $a$ is the binary variable {0,1} and $b$ is the continuous variable. The overall effect of $a$ on $y$ when $a=1$ is $\hat{\beta}_0+\hat{\beta}_1+\hat{\beta}_2b+\hat{\beta}_3b$ and when $a=0$ is $\hat{\beta}_0+\hat{\beta}_2b$. The $p$-value associated with $\hat{\beta}_3$ (for the interaction term) should be used to determined if interaction effect is significant or not.
So for your model, since the interaction effect is not significant, you should revert back to a model without interaction.