Question

Use the data shown in the table. Replace each x-value and y-value in the table with its logarithm. Find the equation of the regression line for the transformed data. Then construct a scatter plot of

left parenthesis log x comma log y right parenthesis(log x,logy)

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

x	1	2	3	4	5	6	7	8
y	828828	353353	174174	103103	121121	6464	6969	3232

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

log

yequals=nothing

log

xplus+nothing

(Round to three decimal places as needed.)

Answer 1

Let's used excel:

First enter the given dataset in excel column:

then using LN() this command to transfer the data in natural logarithmic form

Regression using Excel.

Step 1) Click on Data >>> Data Analysis >>>Regression >>>>OK

Step 3) Input Y Range: Select the data of column "log Y"

Input X Range: Select all the data from "log x " column.

Click on Lable

then Click on Ouput Range

Look the following Image

Then Click on OK, we get following result.

from the above output the regression line is:

loy y = 6.780 +  - 1.434 log x

Scatter plot:

Select the data of both columns as log x and log y

then click on Insert >>>Scatter>>>select first image

then we get the following output:

Now right click on any point on the scatter plot

then select Add Trendline...

Select Linear and choose "Display equation on chart"

Look the following image:

Then click on Close

So we get the following output:

From the scatter plot we conclude that the correlation between log x and log y is approximately linear and negative.