Question

The table contains real data for the first two decades of flu cases reporting

$\begin{array}{|lll|}\hline \text{Year}& \text{\# flu cases diagnosed}& \text{\# flu deaths}\\ \text{Pre-1981}& 91& 29\\ 1981& 319& 121\\ 1982& 1,170& 453\\ 1983& 3,076& 1,482\\ 1984& 6,240& 3,466\\ 1985& 11,776& 6,878\\ 1986& 19,032& 11,987\\ 1987& 28,564& 16,162\\ 1988& 35,447& 20,868\\ 1989& 42,674& 27,591\\ 1990& 48,634& 31,335\\ 1991& 59,660& 36,560\\ 1992& 78,530& 41,055\\ 1993& 78,834& 44,730\\ 1994& 71,874& 49,095\\ 1995& 68,505& 49,456\\ 1996& 59,347& 38,510\\ 1997& 47,149& 20,736\\ 1998& 38,393& 19,005\\ 1999& 25,174& 18,454\\ 2000& 25,522& 17,347\\ 2001& 25,643& 17,402\\ 2002& 26,464& 16,371\\ \text{Total}& 802,118& \mathbf{489}\mathbf{,}\mathbf{093}\\ \hline\end{array}$

Find the correlation coefficient.

$r=\_\_\_\_\_\_\_$

Short answer

The correlation coefficient$r=0.453$.

Step-by-step solution

Given information 

Given in the question that a table

$\begin{array}{|lll|}\hline \text{Year}& \text{\# flu cases diagnosed}& \text{\# flu deaths}\\ \text{Pre-1981}& 91& 29\\ 1981& 319& 121\\ 1982& 1,170& 453\\ 1983& 3,076& 1,482\\ 1984& 6,240& 3,466\\ 1985& 11,776& 6,878\\ 1986& 19,032& 11,987\\ 1987& 28,564& 16,162\\ 1988& 35,447& 20,868\\ 1989& 42,674& 27,591\\ 1990& 48,634& 31,335\\ 1991& 59,660& 36,560\\ 1992& 78,530& 41,055\\ 1993& 78,834& 44,730\\ 1994& 71,874& 49,095\\ 1995& 68,505& 49,456\\ 1996& 59,347& 38,510\\ 1997& 47,149& 20,736\\ 1998& 38,393& 19,005\\ 1999& 25,174& 18,454\\ 2000& 25,522& 17,347\\ 2001& 25,643& 17,402\\ 2002& 26,464& 16,371\\ \text{Total}& 802,118& \mathbf{489}\mathbf{,}\mathbf{093}\\ \hline\end{array}$

Solution

Correlation coefficients are indicators of the power of the linear connection between two separate variables, $x$and $y$. A linear correlation coefficient that is more significant than zero reveals a positive relationship.

To find the variables $r$

Perform correlation in Minitab by following the steps shown below:

1. Enter data in Minitab worksheet.
2. Go to Stat and click on Basic Statistics. Then choose correlation. The dialog box will appear.
3. In the dialog box, enter variables "number of AIDS cases diagnosed" and "year" in variables textbox.
4. Click Ok to get output as shown below:

Therefore the correlation$r$is$0.453$.