 This lesson covers two methods for finding an equation for a line that roughly models a set of data.  The first way is to eyeball a possible line,

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Presentation transcript:

 This lesson covers two methods for finding an equation for a line that roughly models a set of data.  The first way is to eyeball a possible line, find two points on it, and determine the equation of the line through those points.  The second is to use our graphing calculators by inputting the data. (The graphing calculator will do all the work for you!) 3/14/

 This is what you do if you DO NOT HAVE A GRAPHING CALCULATOR YET!!!!!  Draw a Scatter plot.  Draw a rough line of best fit.  Find 2 points closest to the line.  Determine the slope between these two points.  Use one of the points to write the equation in point-slope form.  Convert the equation to slope-intercept form.  Unfortunately, this method does not give you the correlation coefficient. You will only get the correlation coefficient if you have a graphing calculator.

 2 nd StatPlot Turn Plot 1 On  Stat Enter  Input Data into L 1 and L 2.  Zoom 9 (ZoomStat) (To see the Scatter Plot)  Stat Calc (Calculate) 4:LinReg (ax+b)  Some of you will have to scroll down to Calculate…others of you will just have to hit enter, or enter twice.  y = ax+b  a = slope (you know it as m)  b = y-int  r = correlation coefficient (ignore r 2 ) 3/14/

 When using the regression feature of your calculator it should give you a value for “r”.  “r” is the correlation coefficient.  The correlation coefficient is a number from 1 to – 1.  The sign of “r” indicates the direction of the relation between the variables.  If “r” is positive, the slope of the line is positive.  If “r” is negative, the slope of the line is negative.  The absolute value of “r” represents the strength of the relationship.  If | r | = 1, there is a perfect linear relationship. This means that your line will pass through every single point.  If r = 0, there is no linear relationship.  The closer to 1 “r” is, the better the relationship. (The more points that your line will go through.)

3/14/ The following data give the number of Ice Cream Cones sold and the high temperature on 9 different summer days. Temp Sold a)Find an equation of the regression line. (Round to the nearest thousandths.) b) What does the slope in your equation mean in terms of this situation? c) Use your equation to predict the number of Ice Cream Cones that would be sold on a 90° day. d)What is the correlation coefficient?(Round to the nearest thousandths.) d)What does the correlation coefficient mean? y = x – Each increase of 1° results in a sale of 70 ice cream cones (90) – = About 2102 ice cream cones will be sold on a 90° day. r =.920 This situation has a strong linear relationship, since I.920 I (absolute value) =.920 and it is close to 1.

3/14/ /14/ The Transportation Department studied the length of time traffic was halted as a freight train traveled across a road. The data in the table below relate the speed s of a 100-car train to time T. a)Find an equation of the regression line. (Round to the nearest thousandths.) b) Use your equation to predict the time that traffic will be halted if the train is traveling 35 mph. c) What is the correlation coefficient?(Round to the nearest thousandths.) d)What does the correlation coefficient mean? T = –.17s –.17(35) = 6.65 Traffic will be halted for about 7 minutes. r = –.969 This situation has a strong linear relationship, since I –.969 I (absolute value) =.969 and it is close to 1.. s (mph) T (min)107543

 Worksheet 3-6 3/14/