Introduction to Curve Fitting: The Line of Best Fit

OBJ: To find the line of best fit for a set of data and find the correlation coefficient for a set of data

EX: Find an equation of the line of best fit for the data (1, 2), (2, 3), (3,

5), (4, 5).This is the keysequence on thecalculator: STAT, 1(for EDIT),1, ENTER, 2,ENTER, 3, ENTER, 4,ENTER, , 2, ENTER,3, ENTER, 5, ENTER,5, ENTER, STAT, , 4,ENTER.

In order to measure how closely points

tend to cluster about the line of best fit,

statisticians use a correlation

coefficient, denoted r. If the data fits

perfectly on a line with positive slope,

the correlation coefficient is said to be

+ 1. If the data fits perfectly on a line

with negative slope, the correlation

coefficient is said to – 1. If the points

tend not to lie on any line, then the

correlation coefficient is close to 0.

Find the correlation coefficient for the data. This is the key sequence on the calculator: VARS, 5, , , 7, ENTER.EX: For each pair ofvariables, tell whetheryou think thecorrelation is positive,negative, orapproximately zero. Briefly give yourreasons.

• Average dailytemperatureduring January andaverage heating cost in January.

• A person’s income and the value of his or her house.

• The amount of annual taxes a person pays and his or her height.

EX: The table shows statistics forfour NHL career scoring leaders.

• Find the correlation coefficient.

• Find an equation of the line of best fit.

• Bobby Hill played 1063 games. Use the equation of the line of the best fit to predict the number of goals he might have scored.

Games

Played x

Goals

Scored y

1767 801

1311 724

1282 717

696 593