chapter 3

• what are scatter diagrams?

  picture of the relationship between two variables; has regression line "line of best fit" as it helps summarize the scatter plot data.
• what is a correlation?

  whether two variables covary --> does Y get larger as X gets larger?
• what is a correlation coefficient?

  mathematical index that describes the direction and magnitude of a relationship.
• what is a positive correlation?

  Y score associated with high scores on X, and low scores on Y correspond to low scores on X
• what is a negative correlation?

  higher scores on Y are associated with lower scores on X, and low scores on Y are associated with higher scores on X. (e.g., as someone's smoking increases their health decreases)
• what is a regression?

  used to make predictions about scores on one variable from knowledge of scores on another variable. (predictions are obtained from the regression line).
• what is the regression coefficient?

  slope of the regression line, expressed as the ratio of the sum of squares for the covariance to the sum of squares.
• what is the principle of least squares?

  squaring of deviations --> why? --> to get rid of negative signs --> why? --> because if you add them up without squaring it adds up to 0.
• what is the point of least squares?

  the point of best prediction.
• what is the best fitting line?

  the regression line
• what is the coefficient of determination?

  the coefficient of determination is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s) "shared variance (things that are correlated share variance). e.g., r = .40 -> squared it becomes .16 -> translates to 16%
• what are residuals?

  the difference between observed and predicted score (Y - Y'). "how far off your prediction is."
• what is the standard error estimate?

  SD residuals (on average how bad do you predictions tend to be). the best fitting line keeps residuals to a minimum --> minimizes the deviation between observed and predicted Y scores. (residuals can be + and - and will cancel to 0 if averaged out).
• what is range restriction?

  limitation of range, don't have the entire range/population. e.g., only studying people from 19-25 (age range restriction) / only looking at height and weight of people on basketball team of Ithaca College.
• range restriction causes what?

  limited data that causes a correlation to go down; e.g., if everyone got question 4 on the exam wrong then the correlation is 0 because there is no range in response.
• what is factor analysis?

  used to study the interrelationships among a set of variables without reference to criterion.
• what are point biserial correlations?

  a statistical measure that quantifies the relationship between a continuous variable and a dichotomous variable.
• what's an example of a point biserial correlation?

  tests that measure ability can be dichotomous; questions are dichotomous (right or wrong answer); all items on test should be correlated with each other. the test itself is continuous.
• what is an example of a continuous varibale?

  height, weight, temperature
• every item on a test has its own what?

  point biserial because it is the correlation to the rest of the test; e.g., getting the first item right you are more likely to well on the rest of the test, the closer to 1.0 the stronger correlation and the closer to 0 the weaker the correlation. if it is a negative point (-0.25 etc.) people who get that wrong are doing best on the exam.