Correlation and Coefficient of Determination

Key Questions

• What is the relationship between the slope of the least squares regression line and the correlation coefficient?

  Actually there isn't much relation between the two, except for the direction of the slope

  Let's do a few examples:
  If you correlate Hours of couch-surfing with Weight you may find a regression line that slopes up from left to right. The correlation coëfficient can still be anywhere between 0 and 1, meaning couch surfing is less or more related to weight. This would be called positive correlation.

  If you do the same with Hours working out, you may find a line that slopes down. Again correlation coefficients can go anywhere, but it is called negative correlation (=the higher the one, the lower the other).

  There are rules for what correlation coefficients may be considered significant, depending on sample size and desired degree of significance.

  Warning: NEVER draw conclusions about cause and effect!
  In some town they had yearly records about the number of births and the number of stork nests kept for over 60 years.
  Guess what?
  0.9 correlation, which is extremely significant by any measure!

  MeneerNask · 1 · Dec 25 2014

• What is the relationship between the slope of the least squares regression line and the correlation coefficient?
• How can adjusted r squared be negative?
• How do you calculate r squared by hand?
• How does r squared related to standard deviation?
• What are the bounds of an R-Squared value?
• What is the adjusted R-Squared?
• What is the relationship between R-Squared and the correlation coefficient of a model?
• What is the difference between the R-Squared and adjusted R-Squared when running a regression analysis?
• What are the limitations to using R-Squared as a measure of the validity of a model?
• Can an R-Squared value be greater than 1?
• Why doesn't an R-Squared value indicate anything about causation?
• Is a model with a high R-Squared value always better than one with a low R-Squared value?
• What is a correlation?
• Does a correlation between two random variables necessarily imply a direct relationship?
• Does a correlation between two random variables necessarily imply a causal relationship?
• What does a negative correlation coefficient mean about a scatter plot of the data?
• How should a scatter plot of data look if there is a negative correlation?
• How should a scatter plot of data look if there is a positive correlation?
• What is the difference between correlation and association?
• What does a correlation coefficient indicate about data?
• What defines a strong or weak correlation?
• How do you construct confidence interval for a correlation coefficient?
• What does it mean if the correlation coefficient between two variables is negative?
• What is the relationship between the correlation of two variables and their covariance?
• If two variables have a negative correlation, can they have a positive covariance?
• What does an R-Squared value show?
• What is the generalized R-Squared?
• When do you use a generalized R-Squared?
• For what statistical analyses can you determine an R-Squared?
• Can you determine the coefficient of determination from the correlation coefficient?
• Can you determine the correlation coefficient from the coefficient of determination?
• How is an R-Squared value affected by the over inclusion of explanatory variables?
• What is the difference between r and r-squared?
• What can be determined from an R-Squared value?
• Does an R-Squared value indicate that there is sufficient data for a conclusion?
• What is the partitioning of a regression?
• What is the explained sum of squares?
• What is the total sum of squares?
• What is the residual sum of squares?
• What is explained variance?
• Why do R-Squared values increase with the number of explanatory variables?
• Why is it possible for a model with a higher R-Squared value to be less accurate?
• If a single stock tends to rise when the S&P is down, is it positively or negatively correlated with the general market?
• Which of the following are negatively correlated?
• If the coefficient of determination is a positive value, then what kind of slope must the regression equation have?
• What does the regression equation y = .514x + 3.880 tell us? How would interpret the coefficient of determination: .264?
• What does a correlation coefficient represent?
• Why does having a strong linear correlation not imply causality?
• What key difference do experiments have that correlation studies do not have?
• What does correlation mean in a graph?
• What is the definition for zero correlation?
• How do you find the correlation of a scatter plot?
• Question #e918e