What is the range of the correlation coefficient? Give 5 values of correlation coefficients and interpret them. What does "in terms of variance explained" when interpreting correlation coefficients? What is the binomial distribution? Create a graph of Z-scores that illustrates a perfect positive correlation. Create a graph of Z-scores that approximates a positive correlation which is somewhere between .6 and .8. Does not have to be exact. What is the binomial effect size and what do you do to a correlation to get one? Do samples need to be large to have a trustworthy correlation coefficient? What are two problems with samples which make correlations misleading or untrustworthy? Some of the psychological instruments that have been assigned for class have multiple scales (e.g. The Minnesota Multiphasic Personality Inventory-Adolescents). How do test developers use correlation to develop scales within instruments? When a Z-score on test x and a Z-score on test y are both positive. Where would you graph that point using 4 quadrants
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1. State the null and alternative hypothesis when testing a claim about linear correlation 2. When testing a claim about linear correlation, if the p-value is 0.006, what is your decision on rejecting the null hypothesis and what do you conclude about linear correlation? 3. Suppose we are testing a claim about linear correlation among 30 ordered pairs and the scatterplot appears to show a possible straight-line pattern. If r = 0.512, does this set of points have linear correlation? Why or why not? 4. If all points lie on the line y =3 - 4x, what is the value of r? 5. In a study looking for a relationship between the weight and fuel consumption of vehicles, if the weights of the vehicles were converted from pounds to kilograms, would the value of r change? 6. State the regression line using the appropriate symbols for each situation: A. For a sample of points B. For a population of points
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Student Survey: Correlation Matrix A correlation matrix allows us to see lots of correlations at once, between many pairs of variables. A correlation matrix for several variables (Exercise, $T V,$ Height, Weight, and $G P A$ ) in the StudentSurvey dataset is given. For any pair of variables (indicated by the row and the column), we are given two values: the correlation as the top number and the p-value for a two-tail test of the corrclation right bencath it. (a) Which two variables are most strongly positively correlated? What is the correlation? What is the p-value? What does a positive correlation mean in this situation? (b) Which two variables are most strongly negatively correlated? What is the correlation? What is the p-value? What does a negative correlation mean in this situation? (c) At a $5 \%$ significance level, list any pairs of variables for which there is not convincing evidence of a linear association.
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