QM Test 2

• What is correlation?

  A statistical relationship between two variables which may or may not be causal
• What is a positive correlation?

  Both variables increase
• What is a negative correlation?

  Both variables decrease while the other increases
• What is a co-vary?

  When one variable increases or decreases as another variable increases or decreases
• What is covariance?

  Similar to the concept of variances, but is the product of deviation from the mean of two variables
• What is the correlation coefficient?

  The standard measure of the relationship between two variables
• What is the Pearson correlation coefficient? 


  Correlation coefficient (r) given by the description above, most common ranges for +1, perfect positive relationship to -1, perfect negative relationship points - falls on a line.
• What other definition does the PCC have?

  This is a linear estimator of the direction and strength of the relationship.
• What is the Spearman Rank Correlation (rho, p,rs)?

  Nonparmentic correlation based on ranks of values, used when nominates can be assumed or with ordinal data.
• What is the assumption of Pearson Correlation Coefficient?

  Continuous data 
• Pearson Correlation Coefficient is an estimator for what?

  Linear
• Significance test for correlation is what?

  t-distribution 
• A non-parametric correlation based on ranks of values, used when normality can’t be assumed, or with ordinal data, is know as

  Spearman Rank Correlation
• Strength levels of correlations - >0.8

  very strong
• Strength levels of correlations - 0.6-0.8

  Strong
• Strength levels of correlations - 0.4-0.6

  Moderate
• Strength levels of correlations - 0.2-0.4

  Weak
• Strength levels of correlations - <0.2

  Very weak
• Regression examines the relationship between a (Blank) variable, and (Blank) Variable(s)


  Dependent & Independent
• Ordinary Least Squares (OLS) that makes it "BLUE" is broken down into what

  1. Best
  2. Linear
  3. Unbiased
  4. Estimator
• In OLS "BLUE" The B stands for what

  B = it is the most efficient, regression line has the least sample to sample error variation of any estimator
• In OLS "BLUE" The L stands for what

  L = OLS estimates a straight line
• In OLS "BLUE" The U stands for what

  U = The mean of n sample estimates is equal to the true population parameter values
• In OLS "BLUE" The E stands for what

  E = It estimates populations values of Y given sample data for Y and X
• What is the formula for linear regression 


  ŷ = α + βx
• What do the different values in the linear regression formula stand for? ŷ = α + βx

  • ŷ = the predicted values of y
  • α = line intercept, the value of y when x is zero
  • β = the slope of the line (B = Change in y/Change in x)
  • x = is the observed value of x
• True or false - In linear regression assumptions, the residuals are dependent which means the value of one error is affected by the value of another.

  False the residuals are INDEPENDENT
• Residuals are the difference between the (Blank) values of y and the (Blank) values of y.


  Predicted & Observed
• Regression lines are not designed to exactly (Blank) every observed value of the (Blank) variable.


  Predict & Dependent
• True or false - Normality can be examined with a histogram and/or Shapiro-Wilk test.

  True
• Root Mean Square Error is the (Blank Blank)of the error term, and is the square root of the Mean Square Residual (or Error)

  Standard deviation
• What is linear regression?


  Fits a straight line through the data to describe the effect of x on y and how well it predicts x and y
• Can the linear regression equation accommodate a bivariate regression

  yes - one dependent and one independent variable
• What is an error in terms of linear regression

  prediction of y has error associated with every observed value of y - i.e difference between the predicted and observed value for every observation
• What is the difference between residuals vs fitted values plot

  shows the residuals of each observation on the y-axis against the predicted values of the dependent variable for each observation on the x-axis
• What are the degrees of freedom

  1. total = # of observation -1
  2. Model = # of predictions -1, the intercept counts
  3. Residual = total df - model df
• What is the coefficient of determination (r2 or R squared) 


  The proportion of variation in the dependent variable explained by the regression model
• What is collinearity?


  Correlation between independent variables such that they express a linear relationship in a regression model
• What are added assumptions in multicollinearity?

  No multicollinearity, multiple regression assumption that the independent variable are not highly corrected with each other.
• What is a dummy variable? 


  Binary variable (0/1) that are created to represent nominal categories in a regression model