BNAD 276 exam 4
What does SSE stand for?
(sum of squared error) Each error term is squared and added up to get SSE
What does a correlation of -1 and +1 and 0 mean?
-1 : strong negative 0: no correlation 1: strong positive
What is the range of values for correlation?
-1 to 1
What is the range of values for R-squared?
0 - 1 0 = no predictive power 1 = perfect predictive power
What are the parameters in a regression model?
B_0 B_1
T stat < T crit
Explanatory not significant
What is the hypothesis for testing if there is significant (some) correlation?
H_a: P_xy not equal to 0 If we can reject H_o, so we can accept H_a that there is some correlation.
Go to rpsychologist.com/correlation . Move one observation to an extreme outlier position to understand how it affects correlation.
It complete changes the correlation.
What does a simple regression do, i.e. what is the purpose?
Makes predictions of a response variable given the input/value of 1 explanatory variable the b statistic estimates the B parameters the regression equation estimates the regression model
What does the observed amount look like visually in a scatterplot with regression line?
Observed amount: Y, at given x The distance a point is away from the regression line
What is the paramater (symbol) for population correlation?
P_xy
What does an error look like visually in a scatterplot with regression line?
Predicted amount: Y hat, at given x Observed amount: Y, at given x Error: (y - y hat) below regression line: negative above regression line: positive
Formula for R-squared
R^2 = SSR / SST SSR = Regression sum of squares SST = Total sum of squares SSE = Sum of squared errors SST = SSR + SSE The higher the SSR the more variation that the explanatory variable(s) accounts for.
How to Interpret R-squared
The amount of variation of y, explained by the variation of the explanatory variable.
How does sample size (n) affect the (Sample correlation) estimate for population correlation?
The more observations you have in your sample, the more stable This correlation is going to be, it's going to be more certain about the true population correlation.
What is a confounding variable?
The third variable that explains two very, very highly correlated variables.
Determine the confounding variable given the examples in lecture
Wealth and education
What symbol represents the explanatory variable in a regression?
X
What are the symbols for statistics in a regression equation?
Y = b_0 + b_1(X_1) X = explanatory Variable Y = Response variable Statistics: b_1 = slope b_0 = y intercept
What symbol represents the response variable in a regression?
Y or Y hat
A regression equation estimates Y = b_0 + b_1(X_1)
a regression model Y = B_0 + B_1(X_1) + E E = error term (noise) Parameters: B_0 B_1
how to get critical value using t table
look up your confidence level in the bottom row of the table; this tells you which column of the t-table you need. Intersect this column with the row for your df (degrees of freedom).
Why is the value "0" used in the hypothesis test?
no correlation H_o: P_xy = 0
Simple regression is just a straight line. Formula from algebra, just using different symbols
y = mx + b new: Y = b_0 + b_1(X_1) X = explanatory Variable Y = Response variable b_1 = slope b_0 = y intercept
What is the statistic (symbol) for sample correlation
r_xy
Share variance and correlation connection
shared variance = correlation^2 correlation = r shared variance = r^2
How to interpret the slope in a simple regression
slope = b_1 Interpretation: as "x" increases by one unit "y" increases by b_1 units. Slope can never be negative
How is a regression line determined, i.e. which is the best fitting line?
smallest sum of squared errors
What does correlation measure
strength of the relationship between two qualitative variables
How are correlation (r) and R-squared related?
the square root of R-squared is correlation
sample correlation estimates (r_xy)
population correlation (P_xy)
What does the "hat" mean over the response variable?
predicted value