Section 5 - Correlation/Regression Analysis: For the two variables of interest:

1.show a scatter plot with Percent Time Asleep as the independent variable and Longevity as the dependent variable . The plot must include an informative title, along with correct labels for both axes. Include a plot of the least-squares equation (see #5 below).

2.Calculate the correlation coefficient and the coefficient of determination.

3.Identify any data points on the scatter diagram that appear to be influential. Use Cook's Distance > as the criterion for an influential data point. If there are no influential points, say so.

4.Conduct a formal hypothesis test at to determine if there is evidence of linear correlation between the two variables. Present the results in four parts similar to those used for the hypothesis test in Section 4 (omit the distribution type):

a.Your null and alternate hypotheses in the proper format.

b.The P-value and its logical relationship to (or ).

c.Your decision regarding the null hypothesis: reject or fail to reject.

d.A statement regarding the sufficiency of the evidence for correlation.

5.Construct the least-squares equation (must be in algebraic format for full credit).

6.Determine if the equation you constructed in #5 above is a valid model. Justify your decision with a detailed analysis that includes an assessment of the coefficient of determination (#2 above), a discussion of the effect of the hypothesis test results (#4 above) on model validity, and an assessment of the residuals, to include a residual histogram, a Q-Q plot, and a plot of the residuals against Percent Time Asleep (with explanatory paragraphs for each graphic). DATA BELOW

Pct Time Asleep Longevity 22 35 9 37 49 49 1 46 23 63 83 39 23 46 15 56 9 63 81 65 12 56 15 65 37 70 24 63 26 65 17 70 14 77 14 81 6 86 25 70 18 70 26 77 24 77 29 81 27 77 18 40 6 37 19 44 7 47 16 47 13 47 35 68 2 47 35 54 6 61 15 71 14 75 18 89 50 58 25 59 10 62 33 79 43 96 35 58 17 62 27 70 22 72 16 75 20 96 37 75 23 46 4 42 20 65 42 46 9 58 32 42 66 48 28 58 10 50 4 80 12 63 17 65 12 70 23 70 40 72 18 97 10 46 38 56 7 70 23 70 36 72 9 76 21 90 62 76 36 92 23 21 62 40 28 44 18 54 10 36 28 40 22 56 29 60 15 48 73 53 10 60 5 60 13 65 27 68 20 60 21 81 12 81 49 48 17 48 22 56 71 68 17 75 10 81 24 48 18 68 34 16 6 19 4 19 22 32 28 33 31 33 16 30 27 42 8 42 32 33 20 26 35 30 12 40 14 54 17 34 29 34 31 47 6 47 30 42 27 47 40 54 19 54 8 56 8 60 15 44