Question

bacteria growth was measured over a one - month period. the number of cells were counted for a certain number of days. a regression analysis was completed and is displayed in the computer output. regression analysis: ln(bacteria) versus time predictor coef se coef t p constant 2.077 0.03 69.233 0.000 time 0.142 0.001 122.524 0.000 s = 0.030 r - sq = 0.99 r - sq(adj) = 0.999 what is the equation of the least - squares regression line? \\(\bigcirc\\) bacteria = - 0.023 + 4.20 ln(time) \\(\bigcirc\\) ln(bacteria) = 0.142 + 2.077(time) \\(\bigcirc\\) ln(bacteria) = 2.077 + 0.142(time) \\(\bigcirc\\) ln(time) = 2.077 + 0.142(bacteria)

Explanation:

Step1: Identify Regression Form

The regression is \(\ln(\text{Bacteria})\) versus Time. So the response variable is \(\ln(\text{Bacteria})\), predictor is Time.

Step2: Recall Regression Equation

The least - squares regression equation for \(y\) (response) versus \(x\) (predictor) is \(y = b_0 + b_1x\), where \(b_0\) is the constant coefficient and \(b_1\) is the predictor coefficient.
Here, \(y=\ln(\text{Bacteria})\), \(b_0 = 2.077\) (constant coefficient), \(b_1=0.142\) (Time coefficient), and \(x = \text{Time}\).
So the equation is \(\ln(\text{Bacteria})=2.077 + 0.142(\text{Time})\)

Answer:

\(\ln(\text{Bacteria}) = 2.077+0.142(\text{Time})\) (corresponding to the option \(\ln(\text{Bacteria})=2.077 + 0.142(\text{Time})\))