Part 1: Multiple Linear Regression using R

There are 1253 vehicles in the cars_19 dataset. I am simply running mlr using Tensorflow for demonstrative purposes as using lm() in R is more efficient and more precise for such a small dataset.

TensorFlow uses an algorithm that is dependent upon convergence whereas R computes the closed form estimates of beta. I will be using 11 features and an intercept so R will be inverting a 12 x 12 matrix which is not computationally expensive with today's technology.

The dataset below of 11 features contains 7 factor variables and 4 numeric variables.

```
str(cars_19)
'data.frame': 1253 obs. of 12 variables:
$ fuel_economy_combined: int 21 28 21 26 28 11 15 18 17 15 ...
$ eng_disp : num 3.5 1.8 4 2 2 8 6.2 6.2 6.2 6.2 ...
$ num_cyl : int 6 4 8 4 4 16 8 8 8 8 ...
$ transmission : Factor w/ 7 levels "A","AM","AMS",..: 3 2 6 3 6 3 6 6 6 5 ...
$ num_gears : int 9 6 8 7 8 7 8 8 8 7 ...
$ air_aspired_method : Factor w/ 5 levels "Naturally Aspirated",..: 4 4 4 4 4 4 3 1 3 3 ...
$ regen_brake : Factor w/ 3 levels "","Electrical Regen Brake",..: 2 1 1 1 1 1 1 1 1 1 ...
$ batt_capacity_ah : num 4.25 0 0 0 0 0 0 0 0 0 ...
$ drive : Factor w/ 5 levels "2-Wheel Drive, Front",..: 4 2 2 4 2 4 2 2 2 2 ...
$ fuel_type : Factor w/ 5 levels "Diesel, ultra low sulfur (15 ppm, maximum)",..: 4 3 3 5 3 4 4 4 4 4 ...
$ cyl_deactivate : Factor w/ 2 levels "N","Y": 1 1 1 1 1 2 1 2 2 1 ...
$ variable_valve : Factor w/ 2 levels "N","Y": 2 2 2 2 2 2 2 2 2 2 ...
```

The factors need to be transformed into a format TensorFlow can understand.

```
cols <- feature_columns(
column_numeric(colnames(cars_19[c(2, 3, 5, 8)])),
column_categorical_with_identity("transmission", num_buckets = 7),
column_categorical_with_identity("air_aspired_method", num_buckets = 5),
column_categorical_with_identity("regen_brake", num_buckets = 3),
column_categorical_with_identity("drive", num_buckets = 5),
column_categorical_with_identity("fuel_type", num_buckets = 5),
column_categorical_with_identity("cyl_deactivate", num_buckets = 2),
column_categorical_with_identity("variable_valve", num_buckets = 2)
)
```

Create an input function:

```
#input_fn for a given subset of data
cars_19_input_fn <- function(data, num_epochs = 1) {
input_fn(
data,
features = colnames(cars_19[c(2:12)]),
response = "fuel_economy_combined",
batch_size = 64,
num_epochs = num_epochs
)
}
```

Train, evaluate, predict:

```
model <- linear_regressor(feature_columns = cols)
set.seed(123)
indices <- sample(1:nrow(cars_19), size = 0.75 * nrow(cars_19))
train <- cars_19[indices, ]
test <- cars_19[-indices, ]
#train model
model %>% train(cars_19_input_fn(train, num_epochs = 1000))
#evaluate model
model %>% evaluate(cars_19_input_fn(test))
#predict
yhat <- model %>% predict(cars_19_input_fn(test))
```

Results are very close to the R closed form estimates:

```
postResample(yhat, y)
RMSE Rsquared MAE
2.5583185 0.7891934 1.9381757
```