stat-60_lect-06_April_09

# stat-60_lect-06_April_09 - STATS 60 Spring 2008 April 9...

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STATS 60, Spring 2008 April 9, Lecture 06 1 Slope and intercept Soon we will begin our discussion on regression, and in regression we will want to draw a straight line through a group of points. To get ready, let’s review the equation of a line. Our example data is listed in Table 1. A plot of the data is shown in Figure 1 You will recognize the equation for this conversion, of course. It is C = 5 9 ( F - 32) . Now, the classic equation for a line is y = mx + b , where the slope is m and the y -intercept is b . Are these two equations the same? To ﬁnd out, substitute the symbols y for C and x for F . Then we have y = 5 9 ( x - 32) . Next, multiply everything in the parenthesis by 5 9 . We get y = 0 . 56 x - 17 . 8 , or y = mx + b with m = 0 . 56 and b = - 17 . 8 . The slope is the "rise/run" or "(change in y )/(change in x )", so in this case for every degree increase in F there is an 0.56 degree increase in C . From the (positive) value of m (as well as from the ﬁgure) we know that as x increases, so does y . If the slope were negative, y would decrease as x increases. Notice that there is no statistics involved with the equation y = mx + b . If you know x exactly, you know y exactly. No probability comes into play. Not only is there no uncertainty involved, we have more data then we need. The equation for a line has two unknowns, m and b . To determine them we only need two data points. After reading Chapter 7 you should be comfortable with the following: locating points on a graph given an ( x, y ) coordinate ﬁnding a slope and intercept given two points determining if a second point is on a line given a slope and a point determining if a point is on a line given a slope and an intercept identifying a line with a positive, zero, and negative slope Deg F, ( x ) Deg C, ( y ) 100 37.8 64 17.8 71 21.7 Table 1. Conversion to degrees C from degrees F 1

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Figure 1. Conversion of degrees F to degrees C Scatter plots Now consider a problem where you collect a good amount of data for two variables, which may or may not
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stat-60_lect-06_April_09 - STATS 60 Spring 2008 April 9...

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