It is impossible to answer without having the data.

But it is obvious from scatterplots that in independent variable X11 is outlier value what can cause a big problem if linear model is fitted. 

Thank you Jochen, your explanations and hints were useful.

Here are some more details,

Y: A productivity measure for an automobile plant.

X1: A dummy variable which means if the plant was involved in launching a new product

X2: Number of days that plant was working in each year

X3: Number of products variation in a plant

X4: Flexible manufacturing index

X5: Number of models which is a ratio-scaled (doesn’t have zero)

Year: Year of observation (interval-scaled variable)

X6: car class segment

X7: Number of cars produced in a year

X8: Utilized production capability of a plant

X9: Out sousing activities measure

X10: Platform strategy measure

X11: Percentage of Hourly employee

All the independents variables have some impacts on the Y (based on the literature review and my knowledge).

Segment (MD) is another type of car segment and I considered as a categorical variable which definitely has some impact on the productivity measure

 Please let me know if you need additional information.

 @ Ladisval, that observation (for X11) isn’t an outlier. I checked that and found it was a typo while entering the data (the correct value is 86.06).

Good catch Jochen. Thanks.

I updated the explanations now. Basically, segment M.D. and X6 are two different car segments. 

Linearity is just an assumption, based on your data pattern you can assume it.

In general, all relationships are nonlinear, and linear model is an approximate expression of nonlinear model. From your scatterplots, X2,X4,X10 and X11 have no obvious relationships to Y,  X3 and X9 have positve relationships, and year, X7 and X8 have negative relationships. Only X7 and X8 seem to be nonlinear, other variables can be assumpted linear. For X7 and X8, you can use either log-transformed  values or original values in the multiple linear regression, and have a comparison. I think it should be better to use the log-transformed  values.

Thank you Wei. In fact, all the variables except X9 are meaningful at the significance level of 0.10 (even without any transformations and removing or down weighting the outlier). On the other hand, all the multiple linear assumptions (rather than model linearity) are met too. My only concerns are:

1.       Do all the variables are linear with respect to Y (because, I’m using the multiple linear regression)?

2.       What are the right transformations for each variable to increase the model prediction power?

3.       Is there any robust mathematical/statistical way to decide what type of transformation is appropriate for each specific variable?

Thank you.

Dear Amir, for your 3 questions, I give the following answers for reference:

Question 1: You can find if the variable is linear with respect to Y from the scatterplot. For example, year is likely a linear variable, but X7 is probablly a nonlinear variable.

Question 2: The common transformations are logarithmic and relative transformations, and the former is most commonly used. Which is right? It is related to you question 3.

Question 3: For Y=f(x) and Y=f(x') where x' is a transformation of x, if the R^2 of the 2nd equation is larger than that of the 1st one, then the type of transformation is appropriate.