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# How To Represent Variables As Function For Model In R

## Introduction

In this article I am going to demonstrate how to select and represent relevant variables as a function for a model in R. Using a combination of function aggregate with certain variables and dataset, we can define the relevant variables from a dataset which can be used to create models in R. Using combination function, we can combine several important variables to create a model and also how define how a particular model will perform its tasks.

## Appending variables into model

In order to append number of variables together, we can use a combination function along with mathematical operators so as to combine two or more than two variables together. For example, we can use addition operator inside aggregate function to insert a variable for the creation of a model. To create a model in R, we can use various mathematical operators to insert relevant variables and to remove unnecessary variables.

We can use statistics along with arithmetic operators in lots of functions in R. One such function is the aggregate() function in which we append different relevant variables to create a model. We can use statistical formulas along with arithmetic operators in lots of functions in R. one of such functions is the aggregate() function in which we append different relevant variables to create a model.

Now I will demonstrate the use of cluster function to incorporate several variables together. We will be using gscars dataset to demonstrate the use of aggregate function.
1. > gscars
2.                      mg cyl  disp  hp drat    wt  qsec vs am 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 ~ operator inside aggregate function. For example if there are two variables named a and b, then a ~ b means that aggregate function will create a model having a as a function of b.
1. > data = gscars
2. > aggregate(mg ~ gr, data = data, mean)
3.   gr      mg
4. 1    2 18.30667
5. 2    6 21.33333
6. 3    4 26.48700
In the above aggregate function, there are three arguments. First argument in the formula indicates that aggregate function represents mg as a function of gr and the second argument is the variable depicting dataset. Using above code, aggregate function creates a model in which mg variable is appended with gr variable. The mean is also calculated.
1. > aggregate(mg ~ disp, data = data, mean)
2.     disp  mg
3. 1   71.1 33.9
4. 2   75.7 30.4
5. 3   78.7 32.4
6. 4   79.0 27.3
7. 5   95.1 30.4
8. 6  108.0 22.8
9. 7  120.1 21.5
10. 8  120.3 26.0
11. 9  121.0 21.4
12. 10 140.8 22.8
13. 11 145.0 19.7
14. 12 146.7 24.4
15. 13 160.0 21.0
16. 14 167.6 18.5
17. 15 225.0 18.1
18. 16 258.0 21.4
19. 17 275.8 16.3
20. 18 301.0 15.0
21. 19 304.0 15.2
22. 20 318.0 15.5
23. 21 350.0 13.3
24. 22 351.0 15.8
25. 23 360.0 16.5
26. 24 400.0 19.2
27. 25 440.0 14.7
28. 26 460.0 10.4
29. 27 472.0 10.4
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 in the model and also calculates the mean. The second argument is the variable depicting dataset. Using above code, aggregate function creates a model in which mg variable is appended with disp variable.
1. > aggregate(mg ~ hp, data = data, mean)
2.     hp      mg
3. 1   52 30.40000
4. 2   62 24.40000
5. 3   65 33.90000
6. 4   66 29.85000
7. 5   91 26.00000
8. 6   93 22.80000
9. 7   95 22.80000
10. 8   97 21.50000
11. 9  105 18.10000
12. 10 109 21.40000
13. 11 110 21.13333
14. 12 113 30.40000
15. 13 123 18.50000
16. 14 150 15.35000
17. 15 175 19.20000
18. 16 180 16.30000
19. 17 205 10.40000
20. 18 215 10.40000
21. 19 230 14.70000
22. 20 245 13.80000
23. 21 264 15.80000
24. 22 335 15.00000
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 hp and the second argument is the variable depicting dataset. Using above code, aggregate function creates a model in which mg variable is appended with hp variable.
1. > aggregate(mg ~ cyl, data = data, mean)
2.   cyl      mg
3. 1   4 26.66364
4. 2   6 19.74286
5. 3   8 15.10000
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 cyl and the second argument is the variable depicting dataset. Using the above code, aggregate function creates a model in which mg variable is appended with cyl variable.
1. > aggregate(mg ~ wt, data = data, mean)
2.       wt      mg
3. 1  1.513 30.40000
4. 2  1.615 30.40000
5. 3  1.835 33.90000
6. 4  1.935 27.30000
7. 5  2.140 26.00000
8. 6  2.200 32.40000
9. 7  2.320 22.80000
10. 8  2.465 21.50000
11. 9  2.620 21.00000
12. 10 2.770 19.70000
13. 11 2.780 21.40000
14. 12 2.875 21.00000
15. 13 3.150 22.80000
16. 14 3.170 15.80000
17. 15 3.190 24.40000
18. 16 3.215 21.40000
19. 17 3.435 15.20000
20. 18 3.440 18.56667
21. 19 3.460 18.10000
22. 20 3.520 15.50000
23. 21 3.570 14.65000
24. 22 3.730 17.30000
25. 23 3.780 15.20000
26. 24 3.840 13.30000
27. 25 3.845 19.20000
28. 26 4.070 16.40000
29. 27 5.250 10.40000
30. 28 5.345 14.70000
31. 29 5.424 10.40000
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 wt and the second argument is the variable depicting dataset. Using above code, aggregate function creates a model in which mg variable is appended with wt variable.
1. > aggregate(mg ~ qsec, data = data, mean)
2.     qsec   mg
3. 1  14.50 15.80
4. 2  14.60 15.00
5. 3  15.41 13.30
6. 4  15.50 19.70
7. 5  15.84 14.30
8. 6  16.46 21.00
9. 7  16.70 26.00
10. 8  16.87 15.50
11. 9  16.90 30.40
12. 10 17.02 19.85
13. 11 17.05 19.20
14. 12 17.30 15.20
15. 13 17.40 16.40
16. 14 17.42 14.70
17. 15 17.60 17.30
18. 16 17.82 10.40
19. 17 17.98 10.40
20. 18 18.00 15.20
21. 19 18.30 19.20
22. 20 18.52 30.40
23. 21 18.60 21.40
24. 22 18.61 22.80
25. 23 18.90 22.55
26. 24 19.44 21.40
27. 25 19.47 32.40
28. 26 19.90 33.90
29. 27 20.00 24.40
30. 28 20.01 21.50
31. 29 20.22 18.10
32. 30 22.90 22.80
33. >
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 qsec calculating the mean and the second argument is the variable depicting dataset. Using above code, aggregate function creates a model in which mg variable is appended with qsec variable.

## Summary

In this article I demonstrated how to select and represent relevant variables as a function for a model in R. Using a combination of function aggregate with certain variables and dataset, we can define the relevant variables from a dataset which can be used to create models in R.

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