Correlation Coefficient Homework http://www.mathportal.org/calculators/statistics-calculator/correlation-andregression-calculator.php (Don't forget to highlight the radio button for find the correlation coefficient) Identify the correlation coefficient for the following: 1. Look at the four categories below. Take a guess at which two variables will yield the highest correlation coefficient. 2. Transaction and Traffic 3. Transaction and OppVol 4. Transactions and Sales 5. Sales and Traffic Name I. McClean Z. Terrell A. Leaderis S. Teagle J. Brown P. Worlda V. Totalier L. Wheeler S. Miller M. Mayo C. McMillion J. Dixon M. Scott E. Browning M. Davis B. Wilson M. Merrill R. Haug L. Thompson D. Arias S. Reda M. Clarke T. Hags L. Endsoy J. Santiago Gender m f m f f f m m f f f f m f f m f f m m m f f m m Sales 1526 1382 1701 1573 2144 1357 2352 2113 2579 2533 2113 2441 2795 1699 2311 2255 1657 1756 1966 2211 1652 1095 1107 2552 1283 UPT - Units per transaction OppVol - Missed Sales based on volume Transactions Traffic 50 51 55 60 62 67 71 76 77 82 88 96 109 55 81 55 57 72 70 101 95 104 69 86 105 UPT 130 100 111 117 103 130 117 130 216 186 162 182 216 93 93 91 103 186 216 186 111 182 182 162 162 OppVol 5.82 6.22 6.02 5.56 5.64 6.22 5.56 5.64 6.02 5.69 5.8 6.03 5.64 6.52 6.28 7.03 6.33 6.81 6.28 6.33 6.62 6.51 6.71 6.43 7.03 618 25 784 456 31 159 874 32 951 30 173 1050 1316 34 52 64 102 132 147 257 258 259 357 861 895 Let's try a simple formula for finding sample size Sample size needs to be determined to ensure that our results will be statistically significant. The formula is 1.96 * E So let's try a problem now: We need to determine the sample size for an upcoming experiment. The is 23.5. The margin of error of E is 5. What is the sample size? a)7 b)11 c)4 d)9 The answer is D (9) Let's move on to Correlation Correlation Correlation describes the relationship between two variables. Positive Correlation Both variables are increasing at the same time Both variables are decreasing at the same time. Basically, both variables are changing in the same direction at the same time. Negative Correlation One variable is increasing while the other variable is decreasing. One variable is decreasing while the other variable is increasing. Basically, both variables are changing in the opposite directions at the same time. No Linear Correlation There is no relationship between the two variables. Correlation Correlation is defined by r. 0 weak 1 strong Weak or Strong The correlation between education and income is r = .86 Is this a weak or strong correlation? Of course, strong. As educational attainment increases, income increases or as educational attainment decreases, income decreases. Either way, we know both variables are going in the same direction. Participation Exercise 1. What is meant by the statement that correlation does not imply causality? (use your own words) 2. In a test of the Weight Watchers weight loss program, weights of 40 subjects are recorded before and after the program. Assume that the before/after weights result in r = 0.876. Is there sufficient evidence to support a claim of a linear correlation between the before/after weights? Does the value of r indicate that the program is effective in reducing weight? Why or why not