LSRL Chapter 4

Lines A line is made of infinite number of points Between two points only one line can pass A line needs the slope (steepness) and the y-intercept (location)

Math y = mx+b All the points are in the line For example y =3x + 2 will give us exactly

Math Given two points find A) the equation of the line y=mx+b B) Graph the line C) predict the value of y when x= -2

Line  Math  y = mx + b Given two points (1, 5) and (2, 8) A) find the equation of the line y=mx+b To Find the equation first you need to find the slope, then the y-intercept (0,b) To find slope use So slope m=3 Then you need to find the y-intercept (0,b)

Line  Math  y = mx + b Given two points (1, 5) and (2, 8) A) find the equation of the line y=mx+b To Find the equation first you need to find the slope, then the y-intercept (0,b) So slope m=3 Then you need to find the y-intercept (0,b) Y =mx+b replace the found slope Y= 3x +b now use one of the two points I chose (2,8) 8= 3 (2)+ b now solve for b  b= 2

Line  Math  y = mx + b Given two points (1, 5) and (2, 8) A) find the equation of the line y=mx+b To Find the equation first you need to find the slope, then the y-intercept (0,b) So slope m= 3 y-intercept is (0,2) so b = 2 Now write the equation y = 3x + 2

Math y = 3(-2) + 2 = -6 + 2 = -4 Given two points (1, 5) and (2, 8) A)Find the equation of the line B) Graph the line To graph the line use A table or the two given points C) predict the value of y when x = - 2 y = 3x + 2 y = 3(-2) + 2 = -6 + 2 = -4

Line  Stats  The Difference is that here we have too many scatter points and therefore we could make many lines. However to decide what is the best line, we use the Least Square Regression Line approach (LSRL) A line that minimize the distance from the observed y value in our data set to the y-predicted (that falls in the line)

Line  Stats  So to find Least Square Regression Line (LSRL) You need either a software or formulas that take into account all the scatter points in our data including the variability. Still the slope is The y-intercept (0, b0) or (0, a)

Line  Stats  So to find Least Square Regression Line (LSRL) You need either a software or formulas that take into account all the scatter points in our data including the variability. Still the slope is but now we use “r” which is the correlation coefficient that tell us the strength and the direction of the scatter points, We use Sy which tell us the variability in y (rise) we use Sx which tell us the variability in x (run) then fin the slope

Line  Stats  So to find Least Square Regression Line (LSRL) You need either a software or formulas that take into account all the scatter points in our data including the variability. To find the slope: To find y-intercept:

Here is the y-intercept Example 1 Find the LSRL correlation of nicotine and CO r = 0.863 Mean StDev Nicotine (x) 0.9414 0.3134 CO (y) 12.379 4.467 Here is the slope Here is the LSRL Least Square Regression Line Here is the y-intercept

Interpret of Slope and y-intercept in Stats CONTEXT is the most important part But the General form of interpretation is: Slope For every unit increase in x, y increases on average by the slope. Y-intercept When x = 0, then y equals “a”

Example 1 In Context Slope = 12.31 ppm (parts per million). For every one mg of nicotine increase, the ppm level in carbon monoxide increases on average by 12.31 ppm.   y-intercept =(0, 0.79) When the nicotine level is at o mg then the carbon monoxide level is at .79 ppm. In this context of the y intercept it does make sense because it is a positive number and you can have 0.79 ppm of CO.

Example 2 In Context Slope= 14.21 mg. For every one mg of nicotine increase, the tar level will increase on average by 14.21 mg. y-intercept = (0, -1.271 mg) When the nicotine level is at 0 mg, then the tar level equals to -1.271mg. In this context the y-intercept does not make sense because it is not possible to contain a negative amount of tar.