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Lecture Goals
You should be able to:
- understand and calculate the standard error of the estimate Chapter 7
We find a positive relationship between study time and exam scores. Now we want to predict how much time we need to study to earn an A. How predict exam score based on study time???
Student Study time Exam score A 8 88 B 4 75 C 8 85 D 5 78 E 10 94 F 12 100 G 6 82 H 3 71
Study Time Average Exam Score 3 71.5 4 75.5 5 75 What about 6 82.5 studying for 8 87.3 7 or 11 hrs.? 10 94.3 12 94.6
= use relationship between to variables for prediction
= given data can we predict dosages??
= based on Line of Best Fit idea
Line Of Best Fit Best representation = line that is closest to all coordinates
2) Use statistics to determine formula for line of
best fit
1) The line itself is made up of many (x,y) coordinates (graph)
2) Lines have a slopes (graph)
3) If we extend the line it will intersect the y-axis somewhere (graph)
Formula for lines MUST capture these defining characteristics: - slope - y-intercept
Y = y coordinate of (x, y) pair X = x coordinate of (x, y) pair
b = slope of the line a = y-intercept
= rate of climb or fall
change in X values
b = Y1-Y2
(graph)
= rate of climb or fall
change in X values
b = 8-10 = -2 = 1 = .10
= rate of climb or fall
change in X values
b = 8-9 = -1 = .10
= where line meets y-axis = y-value when x = 0
Least Squares Regression Line
= line closest to all points (least error)
= line that minimizes the sum of the squared errors to all points
(graph)
= used to predict # errors given # drinks Formula: Y' = bX + a
a = (mean of Y) - b(mean of X) Student IQ GPA 1 110 1.0 2 112 1.6 3 118 1.2 4 119 2.1 5 122 2.6 6 125 1.8 7 127 2.6 8 130 2.0 9 132 3.2 10 134 2.6 11 136 3.0 12 138 3.6
Q - Which is x and which is y?
If want to predict IQ then GPA=X IQ=Y
If want to predict GPA then GPA=Y IQ=X
In this case IQ = X and GPA = Y Formula: Y' = bX + a
a = (mean of Y) - b(mean of X) What do we need????
(symbols)
Student IQ GPA 1 110 1.0 2 112 1.6 3 118 1.2 4 119 2.1 5 122 2.6 6 |
