b You can find the value of the correlation coefficient on the screen with linear regression results.
C
c Note that the price is in thousands of dollars and the mileage is in thousands of miles.
D
d Substitute the mileage for x in the equation for the line of the best fit.
E
e Substitute the price for y in the equation for the line of the best fit.
A
a y=4.9x-37.7
B
b r=0.936
C
c See solution.
D
d $60 300
E
e 37.6 feet
Practice makes perfect
a To perform a linear regression, we first have to enter the values into lists. Push STAT, choose Edit, and then enter the values in the first two columns.
To do a linear regression we push STAT, scroll right to CALC, and then choose the fourth option in the list, LinReg.
Therefore the correlation coefficient is approximately r=0.936. This tells us that correlation is both positive 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 Since the data shows the cost in thousands of dollars and the length in feet, the slope of 4.9 means that for every 1 foot, a sailboat increases in value by $4 900. Meanwhile, the y-intercept has no interpretation because a sailboat cannot have the length of 0 feet.
d In order to estimate the cost of a sailboat that is 20 feet long, we have to substitute 20 for x in the equation for the line of the best fit.
