# Correlation, Multiple Linear Regression, P Values in R

I am looking to find the correlation between activities performed by sales representatives such as calls, emails, and visits/meetings as the exploratory variables (discrete) and Sales Revenue as the dependent variable (continuous).

The other part is to find the correlation of the same exploratory variables with the dependent variable of (number of clients purchasing the product)

I've been advised to use Spearman method because of the following : small sample set, and the exploratory variables are discrete.

Is this correct?

cor(Emails/Messages,Revenue, method = c("spearman"))
[1] 0.4874122
> cor(Calls,Revenue, method = c("spearman"))
[1] 0
> cor(Visits,Revenue, method = c("spearman"))
[1] 0.4016772


After I've done this I want to confirm that Emails have the strongest correlation of all exploratory variables. I use multiple linear regression just to check (not predicting values)

Call:
lm(formula = Revenue ~ Emails/Messages + Calls + Visits)

Residuals:
1      2      3      4      5      6      7      8      9
-17925  -3080   9515   5664  -3463  -9089   5355  -8949  21972

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)       18111.430  12541.273   1.444    0.208
Emails/Messages    94.427    122.234   0.773    0.475
Calls                -4.719     87.557  -0.054    0.959
Visits               75.124    364.931   0.206    0.845

Residual standard error: 15100 on 5 degrees of freedom
Multiple R-squared:  0.1633,    Adjusted R-squared:  -0.3387
F-statistic: 0.3254 on 3 and 5 DF,  p-value: 0.8078


How would I interpret the P Values in this case. Can I state that emails/messages has a greater significance even though all variables are much greater than 0.05?

Regarding the correlation: Typically Spearman is used when the variables are ordinal, but it looks like your data are interval (e.g. number of calls, revenue generated), thus Pearson is more appropriate.

Regarding the regression: In order to compare the magnitude of the coefficients in the regression (i.e the values under "Estimate"), you must standardize your variables first. In R you do this using "scale", for example Calls_scaled <- scale(Calls). You should not state that emails/messages has a greater "significance", because all of the variables are insignificant. If you standardize the estimates, however, you will be able to compare the effect sizes (but you should still note that the effect sizes are not significant in your report, meaning the effects may not be generalizable).

You may already know this, but the slash in Emails/Messages computes Emails divided by Messages, which may not be a meaningful variable.

Good luck!

• To clairify, small sample size as there are only 9 observations (9 sales reps). So I would need to scale all the exploratory variables first and then use pearson correlation and then MLR?
– vw25
May 29, 2019 at 18:11
• My bad, I misread your degrees of freedom. Nine observations is certainly a small sample, so it is not surprising that the coefficients are not significant. Yes, you would scale the variables before running the regression, however, your regression has too few degrees of freedom to be reliable. May 29, 2019 at 18:31
• I've scaled my variables and still receive the same results in my MLR. Could I say that the data may be insufficient or incorrectly recorded (sales reps record their own activities some values are 0)
– vw25
May 29, 2019 at 18:37
• You could certainly say the data is insufficient. If you have monthly data (i.e. calls by month, revenue by month), you can aggregate that and increase your number of observations (since you do not seem to be interested in particular sales reps, but associations). May 29, 2019 at 18:46
• thanks for your help @unicoder. This is an attempt on analyzing the activities for promoting a product launch. The sales team doesn't contact clients as much in regards to the product after the launch. (Maybe this might be a change in order to get the data you're mentioning)
– vw25
May 29, 2019 at 19:16