How can I predict memory usage and time based on historical values

Question

A maths problem really I think... I have some historical data for some spreadsheet outputs along with the number of rows and columns.

What I\'d like to do is use this da

Answer 1

You could fit a linear regression model.

Since this is a programming site, here is some R code:

> d <- read.table("data.tsv", sep="\t", header=T)
> summary(lm(log(Bytes.RAM) ~ log(Rows) + log(Columns), d))

Call:
lm(formula = log(Bytes.RAM) ~ log(Rows) + log(Columns), data = d)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.4800 -0.2409 -0.1618  0.1729  0.6827 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  12.42118    0.61820  20.093 8.72e-09 ***
log(Rows)     0.51032    0.09083   5.618 0.000327 ***
log(Columns)  0.58200    0.07821   7.441 3.93e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4052 on 9 degrees of freedom
Multiple R-squared: 0.9062, Adjusted R-squared: 0.8853 
F-statistic: 43.47 on 2 and 9 DF,  p-value: 2.372e-05 

This model explains the data pretty well (the R² is 0.89) and suggests the following relationship between the size of the spreadsheet and memory usage:

Bytes.RAM = exp(12.42 + 0.51 * log(Rows) + 0.58 * log(Columns))

A similar model can be used to predict the execution time (the Seconds column). There, the R² is 0.998.