I am completely new to data science and looking to narrow down the search and reduce the learning curve required to solve problems like the one given below
I have a data set with 7 columns , Column A(all positive decimal) is the data point I want to maximize. Column B and C are boolean values remaining columns are a combination of positive and negative decimal numbers. I want to find some relation and insights from all colums such that I can maximize the sum of column A.
In R you can run a linear regression. Consider this "academic" minimal example:
df = data.frame(c(3,5,2,7,5,3), c(1,0,1,0,1,0), c(0,1,1,0,1,0))
colnames(df) = c("A", "B", "C")
df
Take this data as an example:
A B C
1 3 1 0
2 5 0 1
3 2 1 1
4 7 0 0
5 5 1 1
6 3 0 0
Now we can see how B and C describe A in the best way.
reg = lm(A~B+C, data=df)
summary(reg)
Output:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.917 1.322 3.719 0.0338 *
factor(B)1 -1.750 1.774 -0.987 0.3966
factor(C)1 0.250 1.774 0.141 0.8968
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.048 on 3 degrees of freedom
Multiple R-squared: 0.2525, Adjusted R-squared: -0.2459
F-statistic: 0.5066 on 2 and 3 DF, p-value: 0.6463
This tells us that when B, C is 0, A=4.1917 if B=1 we would have A=4.917-1.750 and if C=1 we would have A=4.917+0.25.
So, we can also make predictions:
predict(reg, newdata=df)
Which would be in this case:
1 2 3 4 5 6
3.166667 5.166667 3.416667 4.916667 3.416667 4.916667
This is a simple form of ML (linear regression), where the sum of squared residuals is minimized in order to find the coefficients for the intercept as well as B and C which best describe A.
You would write this model like: $A = \beta_0 + \beta_1 B + \beta_2 C + u$, where $u$ is the statistical error term. You would solve this model by minimizing $\sum u^2$ (the sum of squared residuals).
In matrix algebra you could write $y=\beta X + u$, and you would solve this by $(X'X)^{-1}X'y = \hat{\beta}$.
So we do not "maximise" but minimize the statistical error $u$ in order to find the best "fit" for columns B, C given column A.
Have a look at the great book "Introduction to Statistical Learning" to get the main concepts sorted.
