7.4 Topic 4: Correlation and Regression 30. What does correlation do? Select the correct word to complete each sentence. (a) Correlation measures the strength of the relationship between two variables. (categorical/quantitative (b) Correlation measures strength (and/not) direction of the relationship. (linear/all) relationships. (increases/decreases/remains the same) when the units are converted (c) Correlation is appropriate for (d) Correlation from feet to inches. 31. A detailed study of the veined squid (Loligo forbesii) by Emam et al. showed several interesting linear relationships in body proportions. Consider the following related data sets. Data 1 Mantel Width: 2.5, 2.1, 2.6, 3, 3.5, 4, 4.4 Mantel Length: 0.4, 1.5, 3.7, 3.6, 4.3, 4.5, 4.9 Data 2 Mantel Width: 2.5, 2.1, 2.6, 3, 3.5, 4, 4.4 Fin Length: 2.3, 2.4, 3.2, 2.9, 3.8, 4.6, 4.3 (a) Find the correlation of each data set. (b) Is mantel length or fin length better for predicting mantel width? Explain. 32. Match the correlation with the plot in Figure 7.8. (a) -0.3796 (b) 0.3705 (d) -0.9564 (c) 0.9271 Figure 7.8: Matching Correlations Plot 2 Plot 1 10 2. 10 Plot 4 Plot 3 10 4. 8. -8 -2

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.