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