What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.
A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is. For each tutoring session, she charges a one time fee of $25 plus $15 per hour of tutoring. Svetlana tutors to make extra money for college. (c) If m < 0, the line slopes downward to the right. (a) If m > 0, the line slopes upward to the right. Any line that is not vertical can be described by this equation.įigure 2 shows the three possible graphs of. The graph of a linear equation of the form is a straight line. The following examples are linear equations. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable. X is the independent variable, and y is the dependent variable. Linear regression for two variables is based on a linear equation with one independent variable. You will also study correlation which measures how strong the relationship is. This involves data that fits a line in two dimensions. In this chapter, you will be studying the simplest form of regression, “linear regression” with one independent variable ( x).
In reality, statisticians use multivariate data, meaning many variables. The type of data described in the examples is bivariate data – “bi” for two variables. These are all examples in which regression can be used. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee. In another example, your income may be determined by your education, your profession, your years of experience, and your ability. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is it and how strong is the relationship? Professionals often want to know how two or more numeric variables are related.
Linear Regression and Correlation Student Learning Outcomesīy the end of this chapter, the student should be able to: 12 Simple Linear Regression and Correlationīarbara Illowsky Susan Dean and Margo Bergman
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