Problem 21 Graph the following on the axis provided Describe the relationship between X and Y If we had theoretical reasons to believe the relationship is a straight line, what could account for the variability (error). X – ScaleY – Scale 12 23 22 35 45 57 65 86 97 108
Pearson Correlation Coefficient We need a way to quantify how correlated two variables are. Pearson invented the correlation coefficient Ranges from -1 to +1 Perfect Positive Correlation = +1 Perfect Negative Correlation = -1
Testing the Significance of Pearson’s r The null hypothesis is usually that the correlation between X and Y is zero (no relationship, nothing is happening). You have to know the degrees of freedom then the computer can look up the probability that the correlation is zero (could result from chance alone). If that probability is less than your chosen alpha, you reject the null hypothesis.
Correlation Matrix Correlation matrix for five variables Variable12345 11.00.29.68.05.17 2.291.00.44.22.03 3.68.441.00.39.12 4.05.22.391.00.41 5.17.03.12.411.00
Factor Analysis Correlations between Variable V1 through V5 Showing Two Underlying Factors V1V2V3V4V5 V11.00 V2.801.00 V3.90.881.00 V220.127.116.11.00 V5.10.05.10.901.00 V1, V2, and V3 are highly correlated with each other and nearly uncorrelated with V4 and V5 V4 and v5 are highly correlated with each other and nearly uncorrelated with V1 – V3. Factor Analysis is a technique that identifies this sort of pattern in correlation a correlation matrix.