Simple Linear Regression
What does the simple linear regression equation estimate?
the relationship between two variables
What is testing for significance?
hypothesis test to determine if B1=0
How is the coefficient of determination denoted?
R^2 (correlation coefficient squared)
What is the purpose of this method?
to use sample data to estimate the regression equation
When do you use a t-distribution? (4 stipulations)
1. small samples (n<30) 2. population standard deviation is unknown 3. data is approximately normal 4. sigma unknown
Which variable is predicted and which is the predictor?
Predicted= dependent variable, predictor= independent variable
What it is indicated about B1 and the relationship between x/y if Ho is rejected?
B1 does NOT = zero, there is a statistically significant relationship between x and y
What do 1, -1, and 0 represent in terms of a coefficient of determination?
1= perfect positive linear, -1= perfect negative linear, 0=no linear relationship
Why use the least squared method?
develop the estimated regression equation that minimizes the sum of squared residuals
What parameter is the t-distribution dependent on?
Degrees of freedom
How is simple linear regression approximated?
by a straight line
In linear regression, what does it mean if B1=0?
x and y do not correlate or have a linear relationship
how large the standard deviation is in relation to the mean
How do you reduce standard error?
double the size of the sample
what happens as degrees of freedom increase?
t-distribution approaches the standard normal distribution
E(y)=β0+β1x, what is this?
Regression Equation
What happens to r^2 as data deviates from the slope of the line?
correlation coefficient moves closer to 0
compare the means of 2 samples
𝑦 = 𝛽0 + 𝛽1𝑥 + 𝜖, what is this?
Regression Model
it can be either positive or negative