Question

heather is training for a long - distance run. her data points listed below represent the days of week x and the number of miles run, y
(1, 2.5), (2, 4.2), (4, 6.0), (6, 7), (8, 8.1), (10, 11)
use the equation to interpolate the value and estimate the distance that she could have run on day 3. round to the nearest tenth of a mile.
day 3 =
miles

Explanation:

Step1: Find the regression equation

Using a calculator or software (e.g., TI - 84 Plus: STAT → EDIT to enter data, then STAT → CALC → LinReg(ax + b)), for the data points \((x_1,y_1)=(1,2.5),(x_2,y_2)=(2,4.2),(x_3,y_3)=(4,5.6),(x_4,y_4)=(6,7),(x_5,y_5)=(8,8.1),(x_6,y_6)=(10,11)\)
The linear regression equation is \(y = 0.89x+1.59\) (where \(a = 0.89\) and \(b = 1.59\) are the coefficients from the linear regression).

Step2: Substitute \(x = 3\) into the equation

Substitute \(x = 3\) into \(y=0.89x + 1.59\)

$$y=0.89\times3+1.59$$

$$y = 2.67+1.59$$

$$y=4.26$$

Answer:

\(4.3\) miles