A proof of concept (PoC) analysis utilizing tensorflow in RStudio for a linear regression modeling, including a comparison with lm basic function for linear regression in R.

right click for the Github project

# function to add some noise to data
noise <- function(x, decibel = 1) {
  set.seed(123)
  n <- length(x)
  noise <- runif(n, min(x)*decibel, max(x)*decibel)
}
# Create 100 x, y data points, y = x * 0.14 + 0.65
x_data <- runif(100, min=0, max=1)
y_data <- x_data * 0.14 + 0.65

# Adding some noise to data
y_data <- y_data + noise(y_data, 5*sd(y_data))

# Try to find values for W and b that compute y_data = W * x_data + b
# (We know that W should be 0.14 and b 0.65, but TensorFlow will
# figure that out for us.)
W <- tf$Variable(tf$random_uniform(shape(1L), -1.0, 1.0), name = 'W')
b <- tf$Variable(tf$zeros(shape(1L)), name = 'b')
y <- W * x_data + b

# Minimize the mean squared errors.
loss <- tf$reduce_mean((y - y_data) ^ 2)
optimizer <- tf$train$GradientDescentOptimizer(0.5)
train <- optimizer$minimize(loss)

# Launch the graph and initialize the variables.
sess = tf$Session()
sess$run(tf$global_variables_initializer())

Fit the line and print tf model parameters \(W\): Weights and \(b\): bias

# Fit the line (Learns best fit is W: 0.14, b: 0.65)
for (step in 1:206) {
  sess$run(train)
  if (step %% 20 == 0)
    cat(step, " - W:", sess$run(W),  " - b:", sess$run(b), "\n")
  Wfinal <- sess$run(W)
  bfinal <- sess$run(b)
}

## 20  - W: 0.3208395  - b: 0.7015385 
## 40  - W: 0.1844955  - b: 0.7759401 
## 60  - W: 0.1518018  - b: 0.7937807 
## 80  - W: 0.1439622  - b: 0.7980587 
## 100  - W: 0.1420823  - b: 0.7990845 
## 120  - W: 0.1416316  - b: 0.7993305 
## 140  - W: 0.1415235  - b: 0.7993894 
## 160  - W: 0.1414976  - b: 0.7994036 
## 180  - W: 0.1414914  - b: 0.7994069 
## 200  - W: 0.1414899  - b: 0.7994078

# Print Tensorflow Model parameters W: weights and b: bias
cat("Weights: ", round(Wfinal, 7), " - bias: ", round(bfinal, 7))

## Weights:  0.1414897  - bias:  0.7994079

data <- tibble(x = x_data, y = y_data)
datam <- tibble(x = x_data, y = x_data * Wfinal + bfinal)
g <- ggplot(data = data, aes(x, y)) + geom_point(colour = 'blue') + 
  geom_line(data = datam, colour = "red", size = 1.8) + 
  geom_smooth(method = "lm", colour = "green")
g

Regression diagnostics plots An important part of creating regression models is evaluating how well they fit the data. We can use the package ggfortify to let ggplot2 interpret lm objects and create diagnostic plots.

linearModel <- lm(formula = y ~ x, data = data)

# Print Linear Model $lm$ parameters $W: weights$ and $b: bias$ 
cat("Weights: ", round(linearModel$coefficients[2], 7), 
    " - bias: ", round(linearModel$coefficients[1], 7))

## Weights:  0.1414894  - bias:  0.799408

autoplot(linearModel, label.size = 3)

Comments:

• We observe on the Residuals vs Fitted plot a random pattern in the distribution of residuals, suggesting that a linear regression is valid to represent this relationship with the dependent variable.

• Linear regression therefore works the best in this case where a linear relationship between the dependent and non-dependent variables exists.