I dont know if this is not your your complete data set (i hope not!!!), but there is nearly no variation in your independent variable, therefore, I would doubt the whole results, additionally the sample size is really, really small...

But to your question:

Your interpretation is basically right, for every working day sales decrease by 38 units (what casts even more doubts about your data...) and for the other model also, that working days increase sales by 387 unit. The negative intercept tells you how much unit woul be sold, id you have 0 work days. Seems like a bad estimate, but this could be due to your range restriction in your IV and/or you dont have a linear relationship but maybe a logistic function or something else.

Attached are results from SAS. They are of course the same as yours. But at first example please have a look to R-Square = 0.0033. It means working days are able to explain less then 1% (0.33%) of variability of sales. Also effect of working days in non-significant. At figure on the page 8 of the file RG_reg.pdf you could see that for number of working days = 20 sale varies from 1205 to 2440. Also for number of working days = 22 sale varies from 1212 to 2452 and similarly for number of working days = 21. Simply this is not an appropriate model for sales and other factors must be included.

Same is true for 2nd example even if R-Square is better 0.3437 (34.37% of variability of sales can be explaned by number of working days). An intercept is an explapolation to number of working days = 0. Obviously than you shoudl expect zero sales. Than you should force zero intercept into the model. File RG_reg_zero_intercept cointains these results. Then for number of working days = 0 sales are zero (both interpects are zero by definition) and sales increases by 88.4 in 1st example and 89.0 in 2nd example if zero intercept is used.

Best regards

Lada

I'd recommend plotting these two variables and assuming you believe the relationship is linear showing some measure of precision of the estimate (like the confidence region). Like Rainer Duesing , I am assuming you have more data and that there is some variability. I would stress the uncertainty in the estimate. So my interpretation would be that the association between the two variables is between about -500 sales to day to about +500 (the 95% CI is a bit larger). The interpretation also depends on a lot of design issues, so I'd be cautious giving much to any interpretation without more information (and more about the whole data set).

I should add, you state that you are trying to understand the impact of workdays on sales. Were these data from an experimental design? Otherwise I would be cautious about such a causal interpretation.

Maybe you should work with Sales per working day, then perform an ANOVA with the number of working days in a month as the factor. There should be some theory behind your investigation, e.g. if you are talking about groceries, customers have a budget per month, and will spend the budget regardless of the number of work days. Impulse purchases should depend on the number of working days. Another question is whether the number of working days in a month affects the pay packet of the workers, i.e. the amount of money available, or is it a question of the number of shopping days in month?

I agree with Sir Pecen.

By looking at the summary of your model, there is no linear relationship between SALES and WORK_DAYS. So, interpreting any thing with the help of this model is not correct. R_squared value is evidence that WORK_DAYS is not capable of explaining variability in your SALES data.

So instead of looking for interpretations from this model (which is not correct), try some other(Non-linear) model or increase your data(by adding more variables and observations) if possible.

You asked 3 questions

The first related to your first data set

1) Every work day decreases the sale by 38.05 ?

The answer is yes, but must be completed by an estimation of the precision of this estimation, e.g. by the function confint(model) which here gives :

2.5 % 97.5 %

(Intercept) -11093.5421 16381.1831

work_days -695.6689 619.5663

Then you can see that your estimation is blurred by a tremendous lack of precision. The variation of sales for every work day is (probably) between a decrease of 695 to an increase of 619 !

The second and the third questions are related to the second data set.

2) Every workday increases the sales by 387 ?

The answer is yes again, but with the same comment.

confint(model) gives :

2.5 % 97.5 %

(Intercept) -17367.8732 4927.8219

work_days -147.0915 920.2197

There you can see that your estimation might be as low as a decrease of 147 and as high as an increase of 920.

3) How about the negative intercept ?

Again your intercept is probably between -17367 and +4927.

Here two more comments :

- you have no evidence, with your data, that the relation between sale and work_days is linear till the origin and let me remind you that extrapolation is known to be a risky game.

- in general the intercept is just a convenient convention, the zero of the IV being often without any practical meaning. Here you may place the origin in the middle of your observations. This will narrow the CI for the intercept but will leave unchanged the CI of the slope.