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.

> gscars
mg cyl disp hp drat wt qsec vs bn gr carb
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
>

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.

> aggregate(mg ~ gr|bn, data = data, median)
gr | bn mg
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.

> aggregate(mg ~ disp|hp, data = data, median)
disp | hp mg
1 TRUE 17.2
>

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.

> aggregate(mg ~ disp * hp, data = data, median)
disp hp mpg
1 75.7 52 30.4
2 146.7 62 24.4
3 71.1 65 33.9
4 78.7 66 32.4
5 79.0 66 27.3
6 120.3 91 26.0
7 108.0 93 22.8
8 140.8 95 22.8
9 120.1 97 21.5
10 225.0 105 18.1
11 121.0 109 21.4
12 160.0 110 21.0
13 258.0 110 21.4
14 95.1 113 30.4
15 167.6 123 18.5
16 304.0 150 15.2
17 318.0 150 15.5
18 145.0 175 19.7
19 360.0 175 18.7
20 400.0 175 19.2
21 275.8 180 16.4
22 472.0 205 10.4
23 460.0 215 10.4
24 440.0 230 14.7
25 350.0 245 13.3
26 360.0 245 14.3
27 351.0 264 15.8
28 301.0 335 15.0
>

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.

> aggregate(hp ~ mg|cyl, data = data, median)
mpg | cyl hp
1 TRUE 123
>

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.

> aggregate(hp ~ mg * cyl, data = data, median)
mpg cyl hp
1 21.4 4 109.0
2 21.5 4 97.0
3 22.8 4 94.0
4 24.4 4 62.0
5 26.0 4 91.0
6 27.3 4 66.0
7 30.4 4 82.5
8 32.4 4 66.0
9 33.9 4 65.0
10 17.8 6 123.0
11 18.1 6 105.0
12 19.2 6 123.0
13 19.7 6 175.0
14 21.0 6 110.0
15 21.4 6 110.0
16 10.4 8 210.0
17 13.3 8 245.0
18 14.3 8 245.0
19 14.7 8 230.0
20 15.0 8 335.0
21 15.2 8 165.0
22 15.5 8 150.0
23 15.8 8 264.0
24 16.4 8 180.0
25 17.3 8 180.0
26 18.7 8 175.0
27 19.2 8 175.0
>

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.

> aggregate(wt ~ gr|qsec, data = data, median)
gear | qsec wt
1 TRUE 3.325
>

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.

> aggregate(wt ~ gr * qsec, data = data, median)
gear qsec wt
1 5 14.50 3.1700
2 5 14.60 3.5700
3 3 15.41 3.8400
4 5 15.50 2.7700
5 3 15.84 3.5700
6 4 16.46 2.6200
7 5 16.70 2.1400
8 3 16.87 3.5200
9 5 16.90 1.5130
10 3 17.02 3.4400
11 4 17.02 2.8750
12 3 17.05 3.8450
13 3 17.30 3.4350
14 3 17.40 4.0700
15 3 17.42 5.3450
16 3 17.60 3.7300
17 3 17.82 5.4240
18 3 17.98 5.2500
19 3 18.00 3.7800
20 4 18.30 3.4400
21 4 18.52 1.6150
22 4 18.60 2.7800
23 4 18.61 2.3200
24 4 18.90 2.6875
25 3 19.44 3.2150
26 4 19.47 2.2000
27 4 19.90 1.8350
28 4 20.00 3.1900
29 3 20.01 2.4650
30 3 20.22 3.4600
31 4 22.90 3.1500
>

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.