Page 482 - Algebra 1

Trend lines may vary. However, a trend line that shows the linear relationship of a scatter plot the most accurately is called the line of best fit. The equation of the line of best fit can be calculated on a graphing calculator. The line of best fit is also referred to as the regression line.
Calculating a Line of Best Fit
The table shows the averages for homework grades and test scores for nine students. Use a graphing calculator to find the equation of the line of best fit.
Homework Grades and Test Scores
SOLUTION
Step1: Enterthedataintoyourgraphingcalculatorbypressing
to EDIT the data. Enter the average homework grades into L1 and
the average test scores into L2. Then return to the home screen.
Step 2: Calculate the equation for the line of best fit by pressing
to access the CALC menu. Then press to choose LinReg (ax + b). Type in L1, L2 and press to calculate the values used for writing the equation.
Step3: Roundthevaluesforaandbtothenearestthousandthand write the equation for the line of best fit in slope-intercept form:
y = 0.558x + 39.792
Two sets of data may be related to each other. A correlation is a measure of the strength and direction of the association between data sets or variables. When the points tightly cluster in a linear pattern, then the correlation is strong.
Data can be positively correlated or negatively correlated. There is a positive correlation when the data values for both variables increase. There is a negative correlation when the data values for one variable increase while the data values for the other variable decrease.
Strong positive correlation Strong negative correlation No correlation between x and y between x and y between x and y
yyy
xxx
The direction of the association can be determined for scatter plots that have correlation. If the slope of the trend line is positive, then there is a positive correlation between the data values. If the slope of the trend line is negative, then there is a negative correlation between the data values.
Example
2
Graphing Calculator Tip
For help with calculating a line of best fit, see Graphing Calculator
Lab 7 on page 464.
Average Homework Grade
75
85
94
88
91
95
76
84
90
Average Test Scores
83
87
95
93
88
91
83
80
92
Hint
The calculator uses the variable a instead of m to represent the slope in the slope-intercept form of a line.
Lesson 71 467