A response variable is a variable that. An explanatory variable is a variable that.

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1 Name:!!!! Date: Scatterplots The most common way to display the relation between two quantitative variable is a scatterplot. Statistical studies often try to show through scatterplots, that changing one variable (the explanatory variable) causes changes in another variable (the response variable). A response variable is a variable that. An explanatory variable is a variable that. Interval between eruptions of Old Faithful against the duration of the previous eruption Life expectancy of people in many nations against each nation s gross domestic product per person 1

2 School grade point averages and IQ tests scores for 78 seventh-grade students Home consumption of natural gas versus outdoor temperature Interpreting Scatterplots To interpret a scatterplot, apply the usual strategies of data analysis. Describe the form by describing the shape: examples: 2

3 To describe the direction use the terms positive association and negative association. The strength of a relationship in a scatterplot is determined by how closely the points follow a clear form. Correlation A scatterplot displays the of the relationship between two variables. Straight-line relations are particularly important because a straight line is a simple pattern that is quite common. A straight-line relation is strong if the points lie close to a straight line and weak if they are widely scattered about a line. Correlation is. Positive r indicates positive association between the variables, and negative r indicates negative association. The correlation r always falls between 1 and 1. Values of r near 0 indicate a. Values close to 1 and 1 indicate that. Values of 1 and 1 only occur when. 3

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5 Correlation Moving one point reduces the correlation from r = to r =

6 Exercise: Enter these 3 lists of data into your graphing calculator and call them HOURS, SCORE, CUPS: Hours Test Scores Cups of Coffee To look at two variables at a time (let s look at hours of sleep and test scores first), set up Plot 1, as shown in the figure to the right, and then use ZOOMSTAT. Least Squares Regression Lines Let s say that we d like to use this data to some predicting:! What test score will I get, if I get only 4.5 hours of sleep?! If I get a test score of 100, how many hours of sleep will I have had? 6

7 In order to answer these questions, we need some kind of equation that best fits the data we ve been given. We re going to try to fit the best straight line possible through this data, the one that would capture as many of the data points as possible, or at least get as close to all them as possible. This line is known as the Least Squares Regression Line (LSRL), and claims to do as good a job as possible of showing the straight-line relationship between the explanatory and response variables. First, please make sure that diagnostics are ON:!!!!!! Then go to STAT CALC 4, and press ENTER.!!!!!! According to this Least Squares Regression Line, the line that will best fit this data is given by the equation, and its correlation coefficient is. Please make a note of the fact that this least squares regression line is meant to model the data ONLY for the original interval... it s not meant to model what would happen if you got only 1 hour of sleep nor 23 hours. Now use your equation (not your graph) to answer these questions: Hours of Sleep vs. Test Scores: 1.! 4.5 hours of sleep translates into a predicted test score of (show your work) 2.! hours of sleep translates into a predicted test score of 100. (show your work) 3.! How confident are you with these predictions? Justify your response. 7

8 Cups of Coffee vs. Test Scores:!! 4.! r =! LSRL equation: 5.! 4 cups of coffee translates into a predicted test score of 6.! cups of coffee translates into a predicted test score of ! How confident are you with these predictions? Justify your response. Hours of Sleep vs. Cups of Coffee: 8.! r =! LSRL equation: 9.! Does the LSRL seem reasonable? Why or why not? 8