Example. Comments. Example Scatterplot. Correlation. Some Correlation Pictures 9/8/2017. Section 2.5 Correlation and Best Fitting Lines

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1 Standard One-Wa Fare 9/8/07 Eample Section. Correlation and Best Fitting Lines A sample of one-wa Grehound bus fares from Rochester, NY to cities less than 70 miles was taken b going to Grehound s website. The following table gives the destination cit, the distance and the onewa fare. Distance should be the ais and the Fare should be the ais. Destination Cit Distance Standard One-Wa Fare Alban, NY 0 9 Baltimore, MD 0 8 Buffalo, NY 9 7 Chicago, IL 07 9 Cleveland, OH 7 Montreal, QU New York Cit, NY 0 Ottawa, ON 7 8 Philadelphia, PA 7 Potsdam, NY 9 7 Sracuse, NY 9 0 Toronto, ON 78 Washington, DC 9 87 Eample Scatterplot $00 Grehound Bus Fares Vs. Distance $90 $80 $70 $0 $0 $0 $0 $0 $ Comments The aes need not intersect at (0,0). For each of the aes, the scale should be chosen so that the minimum and maimum values on the scale are convenient and the values to be plotted are between the two values. Notice that for this eample,. The ais (distance) runs from 0 to 0 miles where the data points are between 9 and 07.. The ais (fare) runs from $0 to $00 where the data points are between $7 and $9. Distance from Rochester, NY (miles) Brooks/Cole, a division of Thomson Correlation Positive Correlation - the values tend to increase as the values increase. Negative Correlation- the values tend to decrease as the values increase Brooks/Cole, a division of Thomson

2 9/8/ Brooks/Cole, a division of Thomson Brooks/Cole, a division of Thomson Brooks/Cole, a division of Thomson Brooks/Cole, a division of Thomson Brooks/Cole, a division of Thomson

3 9/8/07 Properties of r The value of r does not depend on the unit of measurement for each variable. The value of r does not depend on which of the two variables is labeled. The value of r is between and +. The correlation coefficient is a) onl when all the points lie on a downward-sloping line, and b) + onl when all the points lie on an upward-sloping line. The value of r is a measure of the etent to which and are linearl related. Section. Linear Inequalities in Two Variables 008 Brooks/Cole, a division of Thomson Graphing inequalities on the coordinate plane Graph > on the coordinate plane. Recall Graph n < on a number line Graph - on the coordinate plane. - Graph Boundar Line = - + m = - b = Test a point not on the line test (0,0) 0 -(0) + Not true! - + on the coordinate plane. -

4 9/8/07 Graph Instead of testing a point If in = m + b form... Solid line Dashed line Shade up - + on the coordinate plane. Shade down > < - Graph on the coordinate plane. - > > < - Boundar Line m = b = - - Section.7 Piecewise Functions A function that is defined b two or more equations over a specified domain is called a piecewise function. Man cellular phone plans can be represented with piecewise functions. See the piecewise function below: A cellular phone compan offers the following plan: $0 per month bus 0 minutes Additional time costs $0.0 per minute. Ct 0 if 0 t ( t 0) if t>0 Eample Ct 0 if 0 t ( t 0) if t>0 Eample Graph the following piecewise function. if - f 8 if Find and interpret each of the following. C C 0 C 90

5 9/8/07 Some piecewise functions are called step functions because their graphs form discontinuous steps. One such function is called the greatest integer function, smbolized b int( ) or [ ], where int( ) the greatest integer that is less than or equal to. For eample, int(), int(.), int(.), int(.9) int(), int(.), int(.), int(.9) Eample The USPS charges $. for letters oz. or less. For letters oz. or less the charge $.9, and oz. or less, the charge $.7. Graph this function and then find the following charges. a. The charge for a letter that weights. oz. b. The charge for a letter that weights. oz. $.00 $.0 Section.8 Absolute Value Functions Plot The Parent Function f ( ) A(,) B(,) C(,) D(0,0) verte G E (-,) A B C F F(-,) E D G(-,) The General Absolute Value Equation f( ) a h k (h,k) is the verte of the function a is a scale factor that controls the direction that it opens and the steepness If a > 0 it opens up from the verte If a < 0 it opens down from the verte Larger values of a create steeper functions general function f( ) a h k f ( )

6 9/8/07 general function f( ) a h k f ( ) general function f( ) a h k f ( ) general function f( ) a h k f ( ) general function f( ) a h k f ( ) general function f( ) a h k f ( ) general function f( ) a h k f ( )

7 9/8/07 general function f( ) a h k f ( )