What independence test should I use for this group of data? <-----------

[hapx]

Hey Guys! I am working on a math project and I am stumped. I'm not sure weather I should use the chi-squared test or another test with my set of data. I am testing weather there is a relationship between crime rates and the unemployment rate of cities. Could someone please help? I'm not testing for the "r" correlation coefficient, but for the independence. I've attached my data. View attachment 3781 .
Please help me, I would really appreciate it! :-)

 

[chisigma]

Welcome on MHB hapx!...

… we introduce a simple algorithm that will be very useful in the examination of the data collected. Suppose we have n + 1 data formed in n + 1 points $x_{k},\ k = 0,1, ..., n$. Typically this is the situation that occurs when trying to characterize a phenomenon 'experimental'.Suppose we want to approximate the function 'unknown' y (x) for which we know in n + 1 samples detected 'experimentally' [therefore subjectto 'experimental errors' ...] with a polynomial of degree m with m<n so that it is …$\displaystyle y(x) \sim a_{0} + a_{1}\ x + a_{2}\ x^{2} + … + a_{m}\ x^{m} =p(x)\ (1)$ An approach known as the 'method of least squares' evaluates the coefficients $a_{i},\ i = 0,1, ..., m$ imposing to be minimum the quantity …$\displaystyle S= \sum_{k=0}^{n} [y_{k} – p(x_{k})]^{2}\ (2)$A case particularly 'simple' to deal is when the 'polynomial least squares' p (x) has degree m = 1, that is a straight line which iscalled 'line of least squares'. Since it is $p(x) = a_{0} + a{1}\ ⋅x$, is to determine only two unknowns: $a_{0}$ and $a_{1}$.With the usual techniques of the analysis is that the values of the two unknowns that minimize the expression (2) are ... $\displaystyle a_{0}= \frac{s_{2}\ t_{0} – s_{1}\ t_{1}}{s_{0}\ s_{2} –s_{1}^{2}}$ $\displaystyle a_{1}= \frac{s_{0}\ t_{1} – s_{1}\ t_{0}}{s_{0}\ s_{2} –s_{1}^{2}}\ (3)$… being...$\displaystyle s_{i}= \sum_{k=0}^{n} (x_{k})^{i}$$\displaystyle t_{i}= \sum_{k=0}^{n} y_{k}\ (x_{k})^{i},\ i=0,1,2\ (4)$

In Your case is n = 19, so You have all the data You need ... once You have calculated the line of least squares to plot everything you can in the manner shown in the picture ...

In this case, the linear relationship between the data appears to be very good ...

Kind regards

$\chi$ $\sigma$