Linear Equations The most basic type of association is a linear association. This type of relationship can be defined algebraically by the equations used, numerically with actual or predicted data values, or graphically from a plotted curve. (Lines are classified…
This section of this chapter is here in recognition that what we are now asking requires much more than a quick calculation of a ratio or a square root. Indeed, the use of regression analysis was almost non- existent before…
One important value of an estimated regression equation is its ability to predict the effects on Y of a change in one or more values of the independent variables. The value of this is obvious. Careful policy cannot be made…
As we have seen, the coefficient of an equation estimated using OLS regression analysis provides an estimate of the slope of a straight line that is assumed be the relationship between the dependent variable and at least one independent variable.…
Regression analysis is a statistical technique that can test the hypothesis that a variable is dependent upon one or more other variables. Further, regression analysis can provide an estimate of the magnitude of the impact of a change in one…
Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form: y=a+bxy=a+bx where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Another way to think about this equation is…
The correlation coefficient, r, tells us about the strength and direction of the linear relationship between X1 and X2. The sample data are used to compute r, the correlation coefficient for the sample. If we had data for the entire population, we could…
As we begin this section we note that the type of data we will be working with has changed. Perhaps unnoticed, all the data we have been using is for a single variable. It may be from two samples, but…
Figure 13.1 Linear regression and correlation can help you determine if an auto mechanic’s salary is related to his work experience. (credit: modification of work “USPS commissions local repair-shop for some needed work on its older trucks” by Joshua Rothhaas/ Flickr, CC…
Test of Two Variances The F test for the equality of two variances rests heavily on the assumption of normal distributions. The test is unreliable if this assumption is not met. If both distributions are normal, then the ratio of the two…