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Lab8 Answers (Correlation & Regression) March 17, 2009 Question 1 : The file Lab8Q1.sav contains data from measurements you made of the armspan, height, foot length and gender of individuals in the class. Using pairs of variables in the sample data (only the three variables at the ratio level of measurement don’t bother with gender or year), assess the linear correlation. What test should you use for each comparison? State the null and alternative hypotheses for each test. Which pair of variables results in the strongest correlation and which pair results in the weakest correlation? What conclusions can you make? Assuming that students in this class are representative of all students at Canadian universities, have all assumptions been met? Test whether there is a significant positive linear correlation between foot length and armspan (state the null and alternative hypotheses and conclusions) Answers: Test: Linear correlation using Pearson product–moment correlation H o : ρ = 0; H 1 : ρ 0 (for each of 3 comparisons) Analyze Æ Correlate Æ bivariate Select the 3 variables (height, armspan, footlength) Options Æ means and standard deviations Strongest correlation: Armspan and height r = 0.775 Weakest correlation: Height and foot length r = 0.678 1

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For all 3 tests reject H o and conclude there is a significant linear correlation. Report (r = value from table, P = value from table, d.f. = 60 (n-2)) Assessing assumptions: 1. Plot scatterplots (Graph Æ Scatterplot & do this 3 times for the various combinations of X- and Y-variables) Æ to show the form of the relationship is linear 2
2. Q-Q Plots (From Analyze Æ Descriptive Stats Æ Explore) to show the variables are each approximately Normally distributed 3

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Normality tests (from Analyze Æ Descriptive Stats Æ Explore): Kolmogorov- Smirnov test shows a significant departure from Normality for Foot length, but I think this is due to a large sample size being able to find minor departures to be statistically significant.
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