Statistics

Statistics

*Most statistical analyses must have randomization. This is a very important concept when you are applying the information to a given population.

3.2 Regression Analysis

Regression analysis is use to determine how the dependent variable changes when the independent variable is altered. For example, how do student exam scores (dependent variable) change over the semester or time (independent variable)? From this example, we could compare early scores from the first exam taken at the start of the semester to those scores from exams taken at the end of the semester. We can use regression analysis to make a quantitative prediction. From our example, how do scores change over time? We may hypothesize, and hope, that scores will increase over time.

Formula and Calculations for Regression Analysis

The formula for regression analysis is written as:

= +

We have several components to this equation. Let us look at each.

• Both x and are always the variables. • is the slope of the line.

o Slope can be calculated with the following formula:

∑ − [(∑ )(∑ )] ∑ 2 − (∑ ) 2

=

is the intercept point of the line or slope at the y -axis. o The intercept can be calculated with the following formula:

•

∑ − (∑ )

=

= Number of values or observations

•

= First variable = Second variable

•

•

• ∑ = Sum of the product of first and second variable o Σ is the capital Greek letter, “Sigma”, in mathematics Σ is an operator meaning summation • ∑ = Sum of first variables • ∑ = Sum of second variables • ∑ 2 = Sum of square first variables

That is a lot of information. It is vital that you understand the components to the formulas and understand how to calculate each part.

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