Week 3
MSE
Mean Square due to Error
MSR
Mean Square due to regression
F ratio
Ratio of amount of variation explained by all independent variables to the amount of variation remained unexplained
SSE
Remaining variation that cannot be explained by the model
In the graph of the simple linear regression equation, the parameter ß1 is the _____ of the true regression line.
slope
In a simple linear regression model, y = ß0 + ß1x + ε the parameter ß1 represents the
slope of the true regression line
If the null hypothesis (H0) is rejected
then at least one of the two variables is a significant factor
If the null hypothesis (H0) is not rejected,
then both variables (ie. units & labor) are not significant
In the graph of the simple linear regression equation, the parameter ß0 represents the _____ of the true regression line.
y-intercept
R squared
a relative measure of how much variation in Y that has been explained by X (SSR with x1) / SST Can never decrease Not a fair model selection criterion
Regression Analysis
a statistical procedure used to develop an equation showing how two variables are related.
multiple linear regression model
A linear regression model with two or more independent variables.
F ratio
A test statistic used in the analysis of variance; the ratio between the variability observed between treatment groups and the variability observed within treatment groups.
MSE
Average prediction error
The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are
B0 and B1
For a simple linear regression model (only one independent variable X), this is equivalent to testing
H0: B1 = 0 Ha: B1 not = 0
For a multiple linear regression model, the F-Ratio is used to test
H0: B1 = B2 = ... = Bk = 0 (the model is completely useless) Ha: at least one B does not = 0 (the model is not completely useless)
Small F ratio implies
None of the independent variables in the regression model help explain significant amount of the variation in Y
RSME
Root mean square error -Absolute measure of how big the prediction errors are -If values are small, prediction errors are small
MSE =
SSE / n-k-1
MSR =
SSR/k
A regression analysis involving one independent variable and one dependent variable is referred to as a
Simple Linear regression
Large F ratio implies
Variation in Y has largely been explained by all independent variables used in the regression model
t statistic =
least squares estimate / standard error
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.
residual
SSR
sum of squares due to regression Difference between SST and SSE SST - SSE = SSR
Estimated regression line
the graph of the estimated simple linear regression equation; b0 is the estimated y-intercept and b1 is the estimated slope.
SST
total variation in Y
In a linear regression model, the variable that is being predicted or explained is known as _____. It is denoted by y and is often referred to as the response variable.
dependent variable
In the simple linear regression model, the _____ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.
error term