“Line of Best Fit” “Linear Regression Line” “Least Squares Line”
Three terms that mean the same thing
In many real-world problems, you will find data that relate 2 variables such as time and distance or age and height. You can view the relationship between 2 variables with a scatter plot.
There is a correlation between 2 variables when there appears to be a line about which the data points cluster. The diagram below shows some possible correlations.
Finding the Least-Squares Line
A scatter plot can help you see patterns in data involving 2 variables. If you think there maybe a linear correlation between the variables, you can use a calculator to find a linear-regression line, also called a least-squares line, that best fits the data.
STAT (L1, L2)
STAT / CALC / LINREG
Correlation and Prediction
• The correlation coefficient, denoted by r, indicates how closely the data points cluster around the least-squares line.
• The correlation coefficient can vary from -1, which is a perfect fit for a negative correlation, to +1, which is a perfect fit for a positive correlation.
Each day last week, the manager of a movie theater recorded how many people attended a movie. He also recorded how many bags of popcorn were sold.
1) Is there is a correlation between these two sets of data?
Number of people
attending a movie
Number of bags of
popcorn sold
175 76
100 43
213 101
249 133
362 197
331 185
250 148
y = .62x – 23.46 r = .99
2) Use your regression model to predict the attendance at a movie during which 198 bags of popcorn were sold.