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Fit type and how to calculate increase?

BorislavP00

Hello,

I am trying to find out if there is a correlation between the marketing costs and sales done over the current year.

First, I am not sure what Fit type to use for the data I have.

Linear Fit - RSquare 0,255 (ANOVA p<alpha), Lack of Fit 0,1207

Polynomial Fit 2 - RSquare 0,263 (ANOVA p<alpha), Lack of Fit 0,1277

From what I understand the quadratic Polynomial fit gives a better explanation of the variance, but also a higher possibility of error? When I also plot the residuals, the normal quantile plot, is not normal to me, and it is the same with the linear fit and all kinds of polynomial fits.

Even after I apply the tests, I am not sure how to prove that with the increase in marketing costs, the sales also increase, and finally, I do not know how to calculate how much they increase.

I will also upload the file in case you need it.

Assignment trial.jmp

Accepted answers

peng_liu

If you meant the combination of Graph Builder and Local Data Filter gives you plausible results, and tried to see the statistics associated with the graph, here is where to find them. Look at the highlighted areas in the following screenshot, which shows you where to choose them, and where they are presented.

It pays to compare what I suggested to other comments in this thread. What I suggested is to fit models by subsets individually, subsets are defined by other variables. The other comments in this thread suggested building other variables directly into a model. Depending on the questions in your assignment and certain assumptions, those approaches might be preferred. The common point among responses to your original post is that you need to look at other variables in you data. And the interpretation of "a number" which you are looking for will depend on other variables and even the chosen approach.

All comments

peng_liu

Looks like this is a homework assignment. How about setting up Graph Builder with a Local Data Filter like in the following graph? Should that change your approach?

statman

First off, you can't prove anything. Increase your degree of confidence, yes, not prove. Seriously, dod you look at the data? Just because you can draw a line on the page doesn't make it useful. There are a few points that are influencing the quantitative analysis. Have you looked for any unusual data points or unusual clusters (related to Croatia)? If you do Multivariate Analysis>Multivariate with the 2 variables you have plotted, you will identify a number of outliers using Mahalanobis. If there were a time series, some simple MR charts would be useful as well.

BorislavP00

Thanks for the replies.

So as far as I understand, Graph Builder would do the work, as I would just have to explain what is seen on the graph.

However, is there any way to measure the correlation between the change in marketing costs and sales, so that I can come up with a number that shows how much are sales increased (decreased) with an increase in marketing costs?

txnelson

You may want to take a look at running a Fit Model on your current year sales, specifying marketing cost and country as the Effects. I come up with a .93 Rsquare. It may help explain the data more precisely.

dale_lehman

First of all, this seems like it is synthetic data. Exploring a few different models, it appears that the increase in sales is related to the marketing expenditures, the marketing strategy, and the East/West variable. The R-square of around .88 is not as high as txnelson got, but I prefer this model because having each country as a factor sort of begs the question as to why the countries differ. Given the small size of the data set, I think the East/West variable comes closer to a good explanation of the data. The reason I say the day is almost certainly synthetic, is that the data falls into almost perfectly distinct regions (by market strategy and East/West - and you might want to add an interaction term for those 2) with only a slight deviation from a linear relationship after accounting for those variables. This becomes clear looking at the leverage plots and residuals.

peng_liu

BorislavP00

Thank you all for your suggestions and ideas.

Also, I want to thank @peng_liu, because he also provided the equation for the slope, which I had a lot of trouble trying to find.