Regression/Multiple Regression Theory Objectives

What is a dependent variable?

The dependent variable is the variable that is measured, or a variable (y) whose value depends on another variable (x).

what is the equation for a simple linear equation model?

The equation for a simple linear equation model is Yi= B0 + B1 Xi +Ei

What is an independent variable?

factor in an experiment that is purposely changed.

Give an example of a regression model using two independent variables.

An example of a regression model using two independent variables could be cookie sales based on the price and advertising that was created/used and you would use this formula Sales = b0 + b1 (Price) + b2 (Advertising). You would fill in the formula based off of your Minitab output for the coefficient.

When is it appropriate to use multiple regression?

Is its most appropriate to use multiple regression when there are two or more independent variables that can have an affect on the dependent variable.

What is the purpose of correlation analysis?

The purpose of correlation analysis is the statistical tool used to study the closeness of the relationship between two or more variables.

What is the purpose of regression analysis?

The purpose of regression analysis is statistical modeling, regression analysis is a statistical process for estimating the relationships among variables

When looking at a graph of residuals, how can you tell if a model is appropriate for the data?

You tell that the model is appropriate for the data by a pattern being clearly shown, if there is no pattern then there is a better model that can be used.

How do you test the slope in multiple regressions?

You would use a T-Test to test the slope in a multiple regression.

Which test statistic do you use to test the overall model in multiple regression?

You would use the F-Test to test the overall model in multiple regression.

Explain, in your own words, the difference between interpolation and extrapolation. Which is more relevant?

a. Interpolation is an estimation of two values within the sequence of variables that you are working with. b. Extrapolation is the estimation of values that goes beyond the current data that you are working with. c. I would assume interpolation would be more relevant since you are working within the number that you have and can be more accurate that having numbers outside you working range.

Explain, in your own words, the following terms:

a. R= This tells you how strong the linear relationship, and is also the correlation coefficient. b. R^2= This show how closely related y is to all the independent variables. c. R^2 adjusted =This is r^2 but has been adjusted to the amount of predictors in the model. d. S= This describes the predicted values of y given x. e. Residuals= Used to evaluate the fit for a simple linear regression. If is a multiple regression with two independent variables you are using different plots to analyze the data. f. Slope Coefficient= this shows the amount change in y that happens do to a change in x.

Explain the meaning of the following abbreviations:

a. Yi = Dependent variable (sometimes referred to as the response variable) for observation i b. Xi = Independent variable (sometimes referred to as as the predictor, or explanatory variable) for observation I c. B0= Y intercept d. B1= Slope for the population e. Ei= Random error in Y observation i