Question

Use the data shown in the table that shows the number of bacteria present after a certain number of hours. Replace each​ y-value in the table with its​ logarithm,

log y

.

Find the equation of the regression line for the transformed data. Then construct a scatterplot of

left parenthesis x comma log y right parenthesis

and sketch the regression line with it. What do you​ notice?

Number of hours comma x

1

2

3

4

5

6

7

Number of bacteria comma y

58

111

187

370

640

988

1687

Find the equation of the regression line of the transformed data.

log y equals nothing x plus nothing

​(Round to three decimal places as​ needed.)

Answer 1

The given data is inputted in EXCEL here as:

x	y	Ln(y)
1	58	4.06
2	111	4.71
3	187	5.23
4	370	5.91
5	640	6.46
6	988	6.90
7	1687	7.43

Using the SCATTERPLOT function we obtain the scatter plot and then the TRENDLINE function is used further to get the regression equation between X and Ln Y as:

Therefore the regression equation here is given as:

Ln Y = 3.570 + 0.561x

This is the required regression equation here.