Correlation Coefficient
-provides a measure of how two variables are linearly associated in a sample; providing us with a sense of strength and direction of the relationships between two numerical variables.
sample
R is a ___ statistic.
no, but suggests that no linear relationship exists
What does an R value of 0 zero tell us about two variables? Independent or unrelated?
one or more independent variables( continuous) and a single dependent variable
In a Simple Linear Regression, we have:
to establish a relationship between the variables
What is the goal of regression models?
tell you to the degree of how x influences y
A positive relationship tells you there is a correlation, but does not
e
-is the error of estimate
-how much variation there is in our estimate of the regression coefficient
OLS
-determines the best-fitting line
-this line minimizes the sum of segments drawn from the observed data points on the scatter plot to the fitted line.
a
Measures linear association between Y and X.
a) correlation coefficient
b) Coefficient of determination
b
Percent change in Y explained by X.
a) correlation coefficient
b) Coefficient of determination
as we increase the number of times we exercise per month, we increase our life expectancy by 3.45 months.
This is the equation for the line of best fit regarding the number of times exercised per month to increase in life expectancy. Interpret this data.
y= 3.45x + 76
linearity, homoscedasticity, independence, normality
What are the assumptions associated with a linear regression model?
homoscedasticity
-one assumes that the error in the relationship between X & Y is distributed equally.
normality
-any fixed value of XY is normally distributed
no linear relationship between two variables
What is the null hypothesis in simple linear regression tests?
constant
-when we have a confounding variable that may influence the outcome of one group over the other.
-we have to make that variable constant
ex: age & blood pressure + antihypertensive medication use
to predict a binary outcome variable
When do we use a logistic regression?
a
OR>1 indicates:
a) odds of having event increases as predictor increases
b) odds of having the event decreases as the predictor increases
b
OR < 1 indicates:
a) odds of having event increases as predictor increases
b) odds of having the event decreases as the predictor increases
Cox Regression
-outcome of interest consists of the occurrence and timing of an event
ex: cardiac event, mortality, relapse, the onset of disease
Cox Regression
What test do we use when we follow subjects over time from a well-defined time point?
smaller hazard in the treatment group that control group
HR < 1 indicates what?
Kaplan-Meier Curve
estimates survival curves for:
- a proportion of the sample (50%)
-probability up to and beyond a given time
-compares survival among groups
two curves are equivalent
What is the null hypothesis for Kaplan-Meier Curves?
HR=1
No relationship
HR>1
Greater hazard in the treatment group than in the control group
HR<1
Smaller hazard in the treatment group than in the control group