Question

Can someone suggest an appropriate transformation to eliminate the problems encountered after seeing the results of fitting a straight line regression model with the following data set?

The newly fitted and transformed model will need to be checked for adequacy.

defects	weeks
13	4
16.1	5
14.5	6
17.8	7
22	8
27.4	9
16.8	10
34.2	11
65.6	12
49.2	13
66.2	14
81.2	15
87.4	16
114.5	17

Answer 1

Answer to the question)
the best and the quickest way to see which model fits it and to check its adequacy simultaneously one can make use of excel

enter data in excel

select the data

click on insert tab

In it click on other charts

In the drop down select all chart types

a new window appears

in this window select XY scatter plot

and click ok

.

A scatter plot appears on screen, this is linear plot by default

select the scatter point and right click

from the drop down menu select "add trendline"

A new window appears on screen

select the model you want: like linear

then tick mark the last two check boxes on this window ( to display the equation and value of R square]

.

Click ok to get the linear model equation along with its R square

repeat the same steps : select exponential model once, then select logarithmic model, quadratic model

you will get all the equations with their respective R square values on the graph itself as follows

.

Now one can compare the R square values for each of the models so obtained

the model with the highest value of R square is considered to be the most adequate model

R square for linear model = 0.8538

R square for exponential model = 0.7211

R square for quadratic model = 0.8954

R square for logarithmic model = 0.9137

Hence we conclude that the logarithmic model is the best fit for the given data