Local spatial autocorrelation investigates the relationships between each observation and its surroundings, rather than providing a numerical summary of these relationships across space. Lets start by creating a moran plot for every variable. This type of graph depicts the spatial data against its spatially lagged values, augmented by reporting the summary of influence measures for the linear relationship between the data and the lag.

Moran plot for every variable is depicted on the figure ??. The plot is divided into four quadrants. In the upper right corner there is the first quadrant, upper left corner corresponds to the second, bottom left to the third and bottom right to fourth. For the Price variable (first plot), we can observe that the vast majority of the observations are clustered in the third quadrant. The third quadrant corresponds to low values surrounded by low values. The interpretation can be that the polygons with lower land price tends to be neighboured by another polygons with (relatively) low prices. In the empirical analysis chapter, when investigating spatial distribution of land price on the figure ??, similar cluster of low land price areas was identified North of the city center. We can see that in the second quadrant that corresponds to the low values surrounded by high values and in the fourth quadrant that corresponds to the high values surrounded by low values there is not many observations. It can be concluded that the city does not have many mixed neighbourhoods with respect to socioeconomic status of its inhabitants. Similar clustering pattern with most observations in the third quadrant can be observed for nearest bus stop distances. However this time the dispersion is more apparent. There is way more observations in the first quadrant, meaning that there are many polygons with relatively high distance to nearest bus station neighbouring with similar characteristic polygons. The observations for nearest metro,tram and train station distances seems to follow similar pattern as they are all aligned in diagonal line between first and third quadrants. This arrangement implies that there are either well connected neighbourhoods with low distances to nearest tram/train/metro stops or areas with bad connectivity and nothing between as there are only few points in the second and fourth quadrant.

How are particular moran statistics for each component distributed across spaced is analysed in dedicated chapters with links listed below:

• Spatial distribution of moran statistics for price
• Spatial distribution of moran statistics for area
• Spatial distribution of moran statistics for nearest bus stop distance
• Spatial distribution of moran statistics for nearest metro station distance
• Spatial distribution of moran statistics for nearest tram stop distance
• Spatial distribution of moran statistics for nearest train station distance

To investigate whether the data does spatially cluster, the statistical model known as Moran’s Test is performed. The output of the model is Moran I test statistic, which is number between -1 and 1 where 1 determines perfect positive spatial autocorrelation (so the data are clustered), 0 implies that the data are randomly distributed and -1 corresponds to negative spatial autocorrelation, so dissimilar values tends to be next to each other. The table below shows Moran I test statistic and corresponding p value for each variable.

From the tests‘ outputs we can conclude that there is strong positive spatial autocorrelation for Price, Metro, Train and Tram distance variables and these data spatially cluster. Regarding the Area, the p value is above 0.05, so we can conclude that there is no significant spatial clustering of the data and as the test statistic is near zero, we can conclude that the data are most likely to be randomly distributed. For the Bus distance, the p value is below 0.05 so there is significant spatial pattern in the data however, as the test statistic is 0.514, the relationship is much weaker when comparing with other distance variables. It might suggests that there is some spatial pattern for local spots but not for the entire dataset.

In the empirical analysis it was concluded, that some variables tends to spatially cluster arround historical city center. To investigate, whether this clustering is statistically significant and how strong it is, spatial autocorrelation analysis is performed in this chapter.
Lets start with brief explanation of the spatial autocorrelation concept. Autocorrelation (whether spatial or not) is a measure of similarity (correlation) between nearby observations. A spatial autocorrelation measures how distance influences a particular variable. It quantifies the degree of which objects are similar to nearby objects. Variables are said to have a positive spatial autocorrelation when similar values tend to be nearer than dissimilar values. Spatial autocorrelation in a variable can be exogenous (it is caused by another spatially autocorrelated variable, e.g. rainfall) or endogenous (it is caused by the process at play, e.g. the spread of a disease) ¹. There are two types of spatial autocorrelation – global and local. If the data are globally autocorrelated, the test statistics can tell us whether values in our map cluster together (or disperse) overall, but it won’t inform us about where specific clusters (or outliers) are. Local spatial autocorrelation investigates the relationships between each observation and its surroundings, rather than providing a numerical summary of these relationships across space. Both statistical models were applied and results were analysed in dedicated chapters.

• Global Autocorrelation
• Local Autocorrelation