Question

5. A Pearson correlation statistic is only valid when the relationship between the two quantitative (continuous) variables is ____________.

1. Explain why it is true that the slope of a line is related to the Pearson correlation statistic, r.
   
2. Create a scatterplot to investigate the association between the amount of fluoride in domestic water (ppm) and the number of dental caries in permanent teeth per 100 children for 21 cities. The data are below.
   1. Create the scatterplot
   2. Describe the association you see in your scatterplot.
   3. The value of r is -0.86, -0.36, 0.36, or 0.86?

3. CityID	FLUORIDE (ppm)	CARIES
   1	1.9	236
   2	2.6	246
   3	1.8	252
   4	1.2	258
   5	1.2	281
   6	1.2	303
   7	1.3	323
   8	0.9	343
   9	0.6	412
   10	0.5	444
   11	0.4	556
   12	0.3	652
   13	0.0	673
   14	0.2	703
   15	0.1	706
   16	0.0	722
   17	0.2	733
   18	0.1	772
   19	0.0	810
   20	0.1	823
   21	0.1	1037

Answer 1

A Pearson correlation statistic is only valid when the relationship between the two quantitative (continuous) variables is linear.

The slope of the line is given as,

b = r Sy / Sx

where Sx and Sy are standard deviations of X and Y which are always positive.

So, if the slope of a line is positive, to the Pearson correlation statistic, r is positive. And, if the slope of a line is negative, to the Pearson correlation statistic, r is negative.

a.

b)

With the increase in Fluoride, there is decrease in Caries. Thus there is negative association between Fluoride and Caries.

c)

Let x be Fluoride and y be Caries

= -0.86