It sounds like your dependent variable meets the criterion of being interval level, but it appears that your independent variable is based on a subjective ranking. Can you say more about your independent variable?

Thank you David.

I have several independent variable

x1 = 1, 2, 3, .. etc this measures number of segment in each street

x2 = ranges between 0 and 0.16 .. continuously

x3 = ranges between 0 and 48.1 .. continuously

x4 = ranges between 0 and 1 .. continuously

I don't think there will be any violation with x2,3 and 4. I was worried about the dependent variable since number the value are rounded/bucketed.

I've checked my data I believe since I have a great number of observations nearly 7500 observations this will be maybe not accurate but meaningful.

It is not uncommon to have your variables scored in "buckets." For example, variables such as age, education, and income are often scored as the median for each of a series of ranges.

"Would it be appropriate to execute linear regression analysis ... ?"

The answer depends on what you are trying to do, what you are trying to estimate and how much model-development you are prepared to do in the search for meaning and "optimal estimates".

In the present context what you could do is to do a simple linear estimation by least squares, but ignore the usual summary statistics that produce "error-bars" for estimates. Keep only only a single statistic. If you had only a single independent variable this could be just the regression coefficient. For multiple independent variables (as you later mention) you could use the reduction in the sum-of-squares from the regression. Then, to get a test for whether there is a real statistical association between your observed values, you could apply the principle of permutation testing whereby you evaluate the same summary statistic from exactly the same algorithm when applied to randomised versions of the original dataset. Here the randomisation provides a representation of the case of "no statistical association". The randomisation can be applied by doing a random permutation of the column of data for the dependent variable.

The principle here is that you can construct any measure of association you like and obtain a valid statistical inference by a first-principles argument involving randomisation. You mention "multiple cities". Notionally, it is just a matter of constructing an overall measure of association to summarize across all cities and then doing the randomisation separately for each city (but within the same step).

Note that the above centres on the question "to see if there is a correlation between these two variable". If you really want some sort of predictive model, or are extremely concerned about extracting as much information as possible from the data, then you would need to develop a full statistical model and this would take you well away from a simple least squares analysis.