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Lecture2014Ch4Fa07

# Lecture2014Ch4Fa07 - Ch 4 Describing the Relation between...

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Ch 4 – Describing the Relation between Two Variables Definition : When the values of two variables are measured for each member of a population or sample, the resulting data is called bivariate . When both variables are quantitative, we may represent the data set as a set of ordered pairs of numbers, (x, y). The variable x is called the input (or independent) variable ; the variable y is called the response (or dependent) variable . We may examine the relationship between the two variables graphically using a scatter diagram, or scatterplot . Example : The following data set for a sample of 6 randomly middle-age to elderly patients consists of x = age of patient, and y = measured value of systolic blood pressure of patient. We expect that as people age, their blood pressure will increase. We will examine the relationship between the two variables. Age, x Systolic Blood Pressure, y 43 128 48 120 56 135 61 143 67 141 70 152 To construct a scatterplot of the data using the TI-83: 1) Choose STAT , EDIT . Name one column Age; name the other column SBP. 2) Enter the data into the two columns. 3) Choose WINDOW . Set Xmin to be slightly smaller than the smallest value of x. In this case, we set Xmin = 40. Set Xmax to be slightly larger than the largest value of x. In this case, we set Xmax = 72. Set Ymin to be slightly smaller than the smallest value of y; in this case, Ymin = 118. Set Ymax to be slightly larger than the largest value of y; in this case, Ymax = 155. Set Xscl = 1, and Yscl = 1. 4) Choose 2 nd , STAT PLOT . Turn Plot 1 On . For Type , choose the first type, scatterplot. For Xlist , enter the name of the x variable; for Ylist , enter the name of the y variable. 5) Hit the GRAPH key. In this example, we see an increasing, linear trend relationship between age and systolic blood pressure, as expected. If we want to see the coordinates of the data points, we use the TRACE key. Linear Correlation The purpose of linear correlation analysis is to measure the strength of the linear relationship between x and y. Note : If the relationship between the two does not appear to be linear, then linear correlation analysis should not be done.

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Types of relationships: 1) If there is an increasing linear trend relationship, so that larger values of x tend to be associated with larger values of y, then we say that there is a positive correlation between x and y. There may be a strong positive linear trend relationship, if the data points cluster closely around a straight line; or a weak positive linear trend relationship, if the data points are not all close to a straight line. 2) If there is a decreasing linear trend relationship, so that larger values of x tend to be associated with smaller values of y, then we say that there is a negative correlation between x and y. There may be a
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