Workshop Statistics: Discovery with Data and Fathom

Topic 9: Correlation Coefficient

Activity 9-1: Properties of Correlation

(b)-(c)

	strongly positive		mildly positive		virtually none		mildly negative		strongly negative
letter:	B	F	I	E	C	H	A	G	D
r	.994	.889	.51	.235	-.081	-.244	-.45	-.721	-.907

(d) Answers will vary from student to student (largest = 1, smallest = -1)
(e) Correlations of 1 or -1 occur when the observations pairs form a straight line.
(f) A positive correlation indicates a positive association.  A negative correlation indicates a negative association
(g) Correlation values near + 1 are strong, while values near 0 are weak.
(h) There appears to be a strong association, with the average monthly temperature increasing during the first half of the year as the month number increases, then decreasing during the second half of the year (after month seven) as the month number increases.
(i) r = .257;  This value seems to indicate a relatively weak positive relationship.  This is not consistant with our answer for (h).  This happened because r measures the strength of the linear association. While these variables are clearly related, they are not linearly related.
(j) r = .507;  This indicates a moderate positive association, though one would not guess this from the scatterplot.
(k) r = -.505

        With public colleges, the majority of the more expensive schools were founded relatively recently, while the older school tended to be a bit cheaper.  However, with private colleges, the reverse appears to be true; tuition costs tend to decrease with later founding dates, making the newer schools cheaper and the older schools more expensive.
 

Activity 9-2: Monopoly Prices

(b) r = .994
(c)

Boardwalk price	400	400	400	400	100	1	1
Boardwalk rent	40	100	1	1000	40	40	100
actual correlation	.994	.794	.670	.490	.707	.538	-.019

(d) The correlation coefficient is not a resistant measure of association.  A single change in the data can have a drastic effect on r.
 

Activity 9-3: Cars' Fuel Efficiency (cont.)

(b) r = -.816
(c) Most of the cars with negative weight z-scores have positive city MPG z-scores.  A strong negative association means that most positive z-score values of one variable will correspond to negative z-score values of the other variable, and vice-versa.
(d) r = -.816; yes, this agrees with what we calculated in (b)
 

Activity 9-4: Televisions and Life Expectancy

(c) r = -.804
(d) Many factors affect life expectancy, e.g., wealth of the nation.  Most of them are most likely more influential than the number of people per TV.
(e) No, other factors could be influencing the apparent association.
(f) Answers will vary from student to student, but some possibilities are technological advancements of the country, wealth of the country, medicinal advancements of the country.
 

Activity 9-5: Guess the Correlation