a Use the linear regression feature on your graphing calculator or computer.
B
b The correlation coefficient is r in the linear regression output on your graphing calculator.
C
c Is park attendance increasing or decreasing over time? What was park attendance in the first year of the given data?
A
aLine of Best Fit: y=-9.58788x+844.545
Graph:
B
bCorrelation Coefficient: r=-0.9636
Correlation: This is a strong, negative correlation.
C
cSlope: ≈-9.6
y-intercept: 844.545
Practice makes perfect
a Let's begin by entering the data into our calculator and using the linear regression analysis tools.
Substituting the values of a and b into the equation y=ax+b gives us the equation for the line of best fit.
y=-9.58788x+844.545
We can see how the line fits with the data by plotting the data points and graphing the line on the same coordinate plane.
r=-0.9636
This tells us that correlation is both negative and very strong. We know that it is strong because it is extremely close to -1. A correlation of -1 would be a direct correlation explained by a line that goes through all of the points.
c In Part A, we found the equation for the line of best fit.
y=-9.58788x+844.545
In this equation, the slope is -9.58788 and the y-intercept is 844.545.
The slope tells us that, on average, the attendance at the amusement park is decreasing by approximately 9.6 thousand people each year.
The y-interceptwould give us a prediction for the attendance numbers in 2005, where x=0. However, this information was already given in the data, so in this case, the y-intercept of the line of best fit does not provide much useful information.
