Image Referencesįigure 9.1: Aaron Huber (2018). She records the following data: Figure 9.6: Amelia’s Points X (hours practicing jump shot)Ĭonstruct a scatter plot and state if what Amelia thinks appears to be true. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She wants to improve to play at the college level. The strength of a relationship is not always apparent in a scatterplot but we will see numerical measures of this in the future.Īmelia plays basketball for her high school. A stronger relationship has points clustered together closely while in a weaker one, points are more spread out. High values of one variable occurring with low values of the other variable.Īt this point we can think about the strength of a relationship as how tightly do the points on a scatterplot fit the linear pattern.High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable.On the other hand a negative (inverse) trend is seen when increasing x appears to cause y to decrease. If we do see a linear pattern, what sort of relationship is there? A positive trend is seen when increasing x also increases y. However, we only calculate a regression line if one of the variables helps to explain or predict the other variable. This line can will later be calculated through a process called linear regression. If we think that the points show a linear relationship, we would like to draw a line on the scatter plot. The linear relationship is strong if the points are close to a straight line, except in the case of a horizontal line where there is no relationship. Figure 9.2: Scatterplot ConfigurationsĪlthough we may see other shapes in a scatter plot, at this point we are only interested in applying these ideas when we see a linear pattern. The following scatterplot examples illustrate these concepts. When looking at a scatterplot you always want to note: You can determine the strength of the relationship by looking at the scatter plot and seeing how close the points are together. When you look at a scatterplot, you want to notice the overall pattern and any potential deviations from the pattern. A scatter plot shows a lot about the relationship between the variables. The most common and easiest way is a scatter plot. Consider a mathematical model (regression)īefore we take up the discussion of linear regression and correlation, we need to examine a way to display the relation between two variables x and y.Use numerical descriptions of the data and overall pattern (correlation, coefficient of determination).Look for an overall pattern and deviations from the pattern.When considering the relationship between two quantitative variables: An explanatory variable (also called x, independent variable, predictor variable) explains changes in the response variable. A response variable (also called y, dependent variable, predicted variable) measures or records an outcome of a study. When we are looking at bivariate data we first need to decide, if possible, does changing one variable seems to lead to a change in the other. This involves data that fits a line in two dimensions. Note that this does not imply that these ideas are “simple” but just that we are working with one independent variable ( x) and a linear relationship. In this chapter, you will be studying the “simple linear regression”. The type of data described in these examples is bivariate data - “bi” for two variables. 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 the relationship and how strong is it? Professionals often want to know how two (or more) numeric variables are related. Linear regression and correlation can help you determine if an auto mechanic’s salary is related to his work experience. Apply ideas of inference to linear regressionįigure 9.1: Auto Mechanic Salaries.Understand the impact of influential points and outliers in the context of linear regression.Predict future value using your regression line.Understand basic ideas of linear regression.Display and describe relationships in bivariate data.By the end of this chapter, the student should be able to:
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