TOPIC 7 - CORRELATION COEFFICIENT
7-1: Properties of Correlation
(a)
| Strong | Moderate | Least Strong | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Negative |
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| Positive |
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(b) largest: 1; smallest: -1
(c) The data would have to fall exactly on a straight line.
(d) The sign of the correlation (positive or negative) matches the direction
of the association.
(e) The stronger the association, the closer the correlation comes to ±1. The
weaker the association, the closer the association comes to 0.
(f) The data reveal a distinct curvilinear relationship.
(g) 0
(h) Yes, except for the person who scored very high on the first exam and
very low on the second.
(i) Yes, except for the person who scored very low on both exams.
(j) H: 0.037; I: 0.705
(k) H: 1.000; I: 0.130; These correlations have changed substantially.
(l) No, because it can be strongly affected by outliers.
(m) There are two distinct clusters, one with students doing poorly on both
exams and another with students doing well on both exams.
(n) .954
7-2: Televisions and Life Expectancy
(a) fewest: United States, 1.3; most: Haiti, 234
(b)
(c) -.804
(d) (Asks for interpretation)
(e) no
(f) (Asks for interpretation)
7-4: Cars' Fuel Efficiency ( cont. )
(a)
| Model | Weight | Weight z-score | MPG | MPG z-score | Product |
|---|---|---|---|---|---|
| BMW 3-Series | 3250 | 0.07 | 28 | 0.07 | 0.00 |
| BMW 5-Series | 3675 | 0.79 | 23 | -0.68 | -0.54 |
| Cadillac Eldorado | 3840 | 1.07 | 19 | -1.28 | -1.37 |
| Cadillac Seville | 3935 | 1.23 | 20 | -1.13 | -1.39 |
| Ford Aspire | 2140 | -1.81 | 43 | 2.30 | -4.17 |
| Ford Crown Victoria | 4010 | 1.36 | 22 | -0.83 | -1.13 |
| Ford Escort | 2565 | -1.09 | 34 | 0.96 | -1.05 |
| Ford Mustang | 3450 | 0.41 | 22 | -0.83 | -0.34 |
| Ford Probe | 2900 | -0.52 | 28 | 0.07 | -0.03 |
| Ford Taurus | 3345 | 0.23 | 25 | -0.38 | -0.09 |
| Ford Taurus SHO | 3545 | 0.57 | 24 | -0.53 | -0.30 |
| Honda Accord | 3050 | -0.27 | 31 | 0.51 | -0.14 |
| Honda Civic | 2540 | -1.13 | 34 | 0.96 | -1.09 |
| Honda Civic del Sol | 2410 | -1.35 | 36 | 1.26 | -1.70 |
| Honda Prelude | 2865 | -0.58 | 30 | 0.36 | -0.21 |
| Lincoln Mark VIII | 3810 | 1.02 | 22 | -0.83 | -0.83 |
(b) -.96
(c) The cars with negative wieght z-scores tend to have positive MPG
z-scores, and vice versa.
7-6 Properties of Correlation
(a)
| Student | Exam 1 | Exam 2 |
| 1 | 65 | 75 |
| 2 | 80 | 90 |
| 3 | 89 | 99 |
| 4 | 59 | 69 |
| 5 | 70 | 80 |
(b) The points in the scatterplot should fall on a line with positive slope.
(c) correlation is 1
(d) Points in scatterplot fall on a line and the correlation is 1.
(e) Points in scatterplot fall on a line and the correlation is 1.
(f) Points in scatterplot fall on a line and the correlation is 1.
(g) You should realize that the size of the slope has nothing to do with the correlation between the variables.
7-7 States' SAT Averages
(a) -.866
(b) Cannot conclude any cause and effect relationship.
7-11 Climatic Conditions
(b) Jan lo and Jan hi have the strongest association. The correlation is .965.
(c) Precipitation and Jan lo have the weakest association. The correlation is .002.
(d) The Jan lo temperature would be most useful in predicting annual snowfall; July hi would be the least useful predictor of annual snowfall.
(e) July lo would be the most useful variable in predicting average July high temp; Jan lo would be the least useful predictor of July high.
7-13 Marriage and Divorce Rates
(a) A weak positive relationship appears to exist between divorce rate and marriage rate. The points are squashed to the left due to the large divorce rate point at the right (Nevada).
(b) r=.556 means that there is a moderate positive association.
(d) The new value of r using the incorrect divorce value is .452. This value is so different from the value in (b) since the outlier (Nevada) had a large impact on the correlation value.
(e) The second scatterplot is preferable since one can better see the relationship between the divorce rate and the marriage rate.