Question

According to the model, what would be the time for the fastest 79-year-old? Round your answer to the nearest hundredth. You must find the quadratic regression equation first.

Answer 1

The quadratic regression equation for the data is : y = 38.87 - 0.79x + 0.01241x² and the time for the fastest 79 - year would be 53.93 minutes. The correct option is B

Using a graphing calculator, the quadratic regression model written in the form : y = ax² + bx + c would be :

• y = 38.87 - 0.79x + 0.01241x²

b.)

The time for a 79 year old runner

• x = age = 79

Inputting x = 79 into our regression equation:

y = 38.87 - 0.79(79) + 0.01241(79)²

y = 38.87 - 62.41 + 77.45081

y = 53.91081 ≈ 53.91

The most appropriate answer is 53.93 minutes . Option B is correct.

Answer 2

From the question given:

First let's set up a fitting equation.

y = a + bx + cx²

a = 38.867

b = -0.790

c = 0.012

R² = 0.970

Therefore, the quadratic regression equation is given by:

y = 38.867 - 0.790x + 0.012x²

when x = 79:

lets place the value of x in the quadratic regression equation,

y = 0.012(79)² - 0.790(79) + 38.867

y = 0.012(6241) - 62.41 + 38.867

y = 74.892 - 62.41 + 38.867

y = 51.349

y = 51.35 (to the nearest hundreth).