Question

when a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. the relationship between the time and area of the circles was analyzed and is shown in the computer output.
regression analysis: area versus time²
predictor coef se coef t p
constant 0.010 0.00017 58.8235 0.000
time² 3.141 0.00140 2120.73 0.000
s=0.035 r - sq=0.999 r - sq(adj)=0.999
what is the equation of the least - squares regression line?

• $widehat{\text{area}} = 3.141 + 0.010(\text{time}^2)$
• $widehat{\text{area}} = 0.010 + 3.141(\text{time}^2)$
• $widehat{\text{area}^2} = 3.141 + 0.010(\text{time})$
• $ln(widehat{\text{area}}) = 0.010 + 3.141(\text{time}^2)$

Explanation:

Step1: Identify regression variables

The output shows regression of Area vs Time².

Step2: Extract coefficients

Constant (intercept) Coef = 0.010; Time² Coef = 3.141.

Step3: Form regression equation

The form is $\widehat{\text{Area}} = \text{Constant} + (\text{Time}^2 \text{ Coef}) \times \text{Time}^2$.

Answer:

B. $\widehat{\text{Area}} = 0.010 + 3.141(\text{Time}^2)$