Correlation & Regression Correlation does not specify which variable is the IV & which is the DV.  Simply states that two variables are correlated. Hr:There.

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Correlation & Regression Correlation does not specify which variable is the IV & which is the DV.  Simply states that two variables are correlated. Hr:There is a correlation between education and income. Regression specifies an IV & DV.  States that the IV influences an outcome on the DV. Hr:People with higher levels of education will earn higher levels of income.

Level of Measurement IV & DV are interval/Ratio or a scale  Exception: Dummy variables Examples: Education (measured in years) and income ($) Education & TV hours Income and number of children

Education and Income Hr:   0 Ho:   0  (rho) = correlation in the population Hr:There is an association between years of education and income. Ho:There is association between years of education and income. See Scatter plot on the board X axis = years of education Y axis = income in dollars

Pearson’s r tells us 2 things: 1. The direction of the relationship between the X & Y 2. The strength of the relationship between the X & Y

Direction:  Range: r can range from –1 to +1  -r = inverse (negative) relationship. As values of X increase, values of Y decrease (see example on board)  +r = positive (direct) relationship. As values of X increase, values of Y increase

 Strength:  -1 is perfect negative correlation.  +1 is perfect positive correlation.  0 indicates no correlation  Rule of thumb: r =.60 (+or-) and above is a strong correlation. r =.30 (+or-) is a moderate correlation. r =.10 (+or-) is a weak correlation.

Calculating Pearson’s r See formula on the board (example height & weight in children) r = SP (sum of the products) / (divided by) square root of SSx (sum of squares x) * SSy Like t and ANOVA, r determines the extent to which variation in Y can be explained by X.

Significance of r  SPSS will give the actual probability of error associated with r.  Calculated Pearson’s r Pearson’s r for height & weight example =.61 Table r Alpha.05 df N-2 (two variables) = 8 –2 = 6 Critical (table) r =.7067 Calculated r must be = to or larger than.7067