I am quite confused while working on a problem finding the line of best fit.
There is a table showing basketball players names. The next column is the number of points they have scored, and the next, the number of minutes they have played. It looks like this:
Kobe Bryant 1819 2689
Caron Butler 1195 2746
Chucky Atkins 1115 2903
Lamar Odom 975 2320
Chris Mihm 735 1870
Jumaine Jones 577 1830
I'm asked to find the line of best fit rounded to the nearest thousandth on all numbers. I find that to be y = .794x + 1544.201
Also, I'm asked to find the r value, which is .746. To me, .746 means that the data is not very accurate, or does not fit the trend line very well.
If I would go back in and plug one of the player's statistics in, for eg, the last one, y = .794(577) + 1544.201, this would equal 2002.339.
Since y is minutes (the second column), and x is points scored (the first column), and this player's actual points scored is 1830, is this an example of why the line of best fit is not that accurate?
Yes, you are on the right track. The line of best fit is an approximation of the relationship between the points scored and minutes played for the basketball players in the dataset. The equation y = 0.794x + 1544.201 represents this approximation.
When you plug in the points scored (x = 577) into the equation, you get y = 2002.339. However, the actual value for minutes played (y) for that player is 1830. This difference between the predicted value (2002.339) and the actual value (1830) is an example of why the line of best fit may not be very accurate.
The r value, also known as the correlation coefficient, is a measure of how well the line of best fit represents the relationship between the variables. The value of 0.746 suggests a moderately strong positive correlation between points scored and minutes played, but it also indicates that there is some variability in the data that the line of best fit does not capture.
It's important to keep in mind that the line of best fit is an approximation and may not perfectly represent all data points in the dataset. It provides a general trend and can be useful for making predictions or drawing conclusions, but individual data points may deviate from the line.