# How To Evaluate Variables On The Basis Of Dependent Variables In R

## Introduction

In this article, I am going to demonstrate how to evaluate variables as a function of two dependent variables from a dataset together in a model to verify which one of the following variables are dependent on other variables for creating a best fit model in R. Using a combination of function aggregate with certain variables and dataset, we evaluate variables as a function of two dependent variables in a model and evaluate dependency between variables from a dataset. Using the combination function, we can evaluate how a certain amount of change in one variable can affect another variable.

## Evaluating Variables as a Function

In order to evaluate variables as a function of two dependent variables from a dataset together in a model and evaluate dependency between multiple variables together to fit a model, we can use a combination function along with mathematical operators as to evaluate dependency between two or more variables together. For example, we can use a conditional operator to obtain a Boolean result depending on the variables and colon operator inside an aggregate function to evaluate how many variables are dependent on each other for the creation of the best fit model.

We can define a formula along with arithmetic and conditional operator in lots of functions in R. One of these functions is the aggregate() function, which we can evaluate variables as a function of two dependent variables from dataset together in a model and evaluate dependency between multiple variables together to fit a model and remove different irrelevant variables to create a model.

Now I will demonstrate how evaluate variables as a function of two dependent variables from dataset together in a model and evaluate dependency between multiple variables together to fit a model and to use cluster function to find dependency between several variables together. We will be using gscars dataset to demonstrate the use of an aggregate function.
1. > gscars
2.                      mg cyl  disp  hp drat    wt  qsec vs bn gr carb
3. Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
4. Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
5. Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
6. Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
7. Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
8. Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
9. Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
10. Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
11. Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
12. Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
13. Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
14. Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
15. Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
16. Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
17. Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
18. Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
19. Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
20. Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
21. Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
22. Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
23. Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
24. Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
25. AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
26. Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
27. Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
28. Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
29. Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
30. Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
31. Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
32. Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
33. Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
34. Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
35. >
We will be using the ~ operator inside aggregate function along with conditional operator to evaluate variables as a function of two dependent variables from the dataset together in a model and to find associativity among multiple variables in R. For example if there are three variables named x, y and z, then x ~ y | z means that aggregate function will create a model x as a function of two dependent variables y and z , after evaluating the dependency of variable y and z among each other.
1. > aggregate(mg ~ gr|bn, data = data, median)
2.   gr | bn  mg
3. 1      TRUE 19.2
In the above aggregate function, there are three arguments. The first argument in the formula indicates that aggregate function represents mg as a function of gr and bn variables calculating the median and the second argument is variable depicting the dataset. Using the above code, the aggregate function creates a model that evaluates the dependency between the gr and bn variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together. The formula is returning a true value depicting gr and bn variables are dependent on each other.
1. > aggregate(mg ~ disp|hp, data = data, median)
2.   disp | hp  mg
3. 1      TRUE 17.2
4. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that the aggregate function represents mg as a function of disp and hp variables calculating the median and the second argument is variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the disp and hp variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together. The formula is returning a true value depicting disp and hp variables are dependent on each other.
1. > aggregate(mg ~ disp * hp, data = data, median)
2.     disp  hp  mpg
3. 1   75.7  52 30.4
4. 2  146.7  62 24.4
5. 3   71.1  65 33.9
6. 4   78.7  66 32.4
7. 5   79.0  66 27.3
8. 6  120.3  91 26.0
9. 7  108.0  93 22.8
10. 8  140.8  95 22.8
11. 9  120.1  97 21.5
12. 10 225.0 105 18.1
13. 11 121.0 109 21.4
14. 12 160.0 110 21.0
15. 13 258.0 110 21.4
16. 14  95.1 113 30.4
17. 15 167.6 123 18.5
18. 16 304.0 150 15.2
19. 17 318.0 150 15.5
20. 18 145.0 175 19.7
21. 19 360.0 175 18.7
22. 20 400.0 175 19.2
23. 21 275.8 180 16.4
24. 22 472.0 205 10.4
25. 23 460.0 215 10.4
26. 24 440.0 230 14.7
27. 25 350.0 245 13.3
28. 26 360.0 245 14.3
29. 27 351.0 264 15.8
30. 28 301.0 335 15.0
31. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that aggregate function represents mg as a function of disp and hp variables calculating the median and the second argument is variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the gr and qsec variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together.
1. > aggregate(hp ~ mg|cyl, data = data, median)
2.   mpg | cyl  hp
3. 1      TRUE 123
4. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that the aggregate function represents hp as a function of mg and cyl variables calculating the median and the second argument is a variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the mg and cyl variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together. The formula is returning a true value depicting mg and cyl variables are dependent on each other.
1. > aggregate(hp ~ mg * cyl, data = data, median)
2.     mpg cyl    hp
3. 1  21.4   4 109.0
4. 2  21.5   4  97.0
5. 3  22.8   4  94.0
6. 4  24.4   4  62.0
7. 5  26.0   4  91.0
8. 6  27.3   4  66.0
9. 7  30.4   4  82.5
10. 8  32.4   4  66.0
11. 9  33.9   4  65.0
12. 10 17.8   6 123.0
13. 11 18.1   6 105.0
14. 12 19.2   6 123.0
15. 13 19.7   6 175.0
16. 14 21.0   6 110.0
17. 15 21.4   6 110.0
18. 16 10.4   8 210.0
19. 17 13.3   8 245.0
20. 18 14.3   8 245.0
21. 19 14.7   8 230.0
22. 20 15.0   8 335.0
23. 21 15.2   8 165.0
24. 22 15.5   8 150.0
25. 23 15.8   8 264.0
26. 24 16.4   8 180.0
27. 25 17.3   8 180.0
28. 26 18.7   8 175.0
29. 27 19.2   8 175.0
30. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that aggregate function represents hp as a function of mg and cyl variables calculating the median and the second argument is variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the gr and qsec variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together.
1. > aggregate(wt ~ gr|qsec, data = data, median)
2.   gear | qsec    wt
3. 1        TRUE 3.325
4. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that the aggregate function represents wt as a function of gr and qsec variables calculating the median and the second argument is variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the gr and qsec variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together. The formula is returning a true value depicting gr and qsec variables are dependent on each other.
1. > aggregate(wt ~ gr * qsec, data = data, median)
2.    gear  qsec     wt
3. 1     5 14.50 3.1700
4. 2     5 14.60 3.5700
5. 3     3 15.41 3.8400
6. 4     5 15.50 2.7700
7. 5     3 15.84 3.5700
8. 6     4 16.46 2.6200
9. 7     5 16.70 2.1400
10. 8     3 16.87 3.5200
11. 9     5 16.90 1.5130
12. 10    3 17.02 3.4400
13. 11    4 17.02 2.8750
14. 12    3 17.05 3.8450
15. 13    3 17.30 3.4350
16. 14    3 17.40 4.0700
17. 15    3 17.42 5.3450
18. 16    3 17.60 3.7300
19. 17    3 17.82 5.4240
20. 18    3 17.98 5.2500
21. 19    3 18.00 3.7800
22. 20    4 18.30 3.4400
23. 21    4 18.52 1.6150
24. 22    4 18.60 2.7800
25. 23    4 18.61 2.3200
26. 24    4 18.90 2.6875
27. 25    3 19.44 3.2150
28. 26    4 19.47 2.2000
29. 27    4 19.90 1.8350
30. 28    4 20.00 3.1900
31. 29    3 20.01 2.4650
32. 30    3 20.22 3.4600
33. 31    4 22.90 3.1500
34. >
In the above aggregate function, there are three arguments. The first argument in the formula indicates that the aggregate function represents wt as a function of gr and qsec variables calculating the median and the second argument is a variable depicting the dataset. Using the above code, the aggregate function creates a model in which the model is evaluating the dependency between the gr and qsec variables to verify whether any change in one variable affects another variable or not by mapping the dependency among these two variables and both variables and dependencies are added together.

## Summary

In this article, I demonstrated how to evaluate variables as a function of two variables from the dataset together in a model to verify which one of the following variables are dependent on other variables for creating the best fit model in R.