Module #7 Assignment

 1.

 # Define the data

x <- c(16, 17, 13, 18, 12, 14, 19, 11, 11, 10)

y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)

# Create a linear regression model

model <- lm(y ~ x)

# Summary of the model to get coefficients

summary(model)

1.1 

The relationship model is y = a + bx, where y is the dependent variable (response), x is the independent variable (predictor), a is the intercept, and b is the coefficient of x.

1.2 

intercept <- coef(model)[1]

slope <- coef(model)[2]

2. 

# Data

visit <- data.frame(

  discharge = c(3.600, 1.800, 3.333, 2.283, 4.533, 2.883),

  waiting = c(79, 54, 74, 62, 85, 55)

)

# Fit a simple linear regression model

model2 <- lm(discharge ~ waiting, data = visit)

2.1 

The relationship model is discharge = a + b * waiting

where a is the intercept, and b is the slope.

2.2 

intercept2 <- coef(model2)[1]

slope2 <- coef(model2)[2]

intercept2 # Value of a

slope2     # Value of b

2.3 

# Predict discharge when waiting time is 80 minutes

predicted_discharge <- predict(model2, newdata = data.frame(waiting = 80))

predicted_discharge

3. 

# Load the mtcars data and select the variables

input <- mtcars[, c("mpg", "disp", "hp", "wt")]

# Fit a multiple regression model

model3 <- lm(mpg ~ disp + hp + wt, data = input)

3.1 

The relationship model is mpg = a + b1 * disp + b2 * hp + b3 * wt, where a is the intercept, and b1, b2, and b3 are the coefficients for disp, hp, and wt respectively.

# Get coefficients

intercept3 <- coef(model3)[1]

coef_disp <- coef(model3)[2]

coef_hp <- coef(model3)[3]

coef_wt <- coef(model3)[4]

intercept3  # Value of a

coef_disp   # Coefficient for disp

coef_hp     # Coefficient for hp

coef_wt     # Coefficient for wt

4.

# Install and load the ISwR package if not already installed

if (!require(ISwR)) {

  install.packages("ISwR")

  library(ISwR)

}

# Load the rmr data

data(rmr)

# Plot metabolic rate versus body weight

plot(rmr$metabolic.rate ~ rmr$body.weight)

# Fit a linear regression model

model4 <- lm(metabolic.rate ~ body.weight, data = rmr)

# Predict metabolic rate for a body weight of 70 kg

predicted_metabolic_rate <- predict(model4, newdata = data.frame(body.weight = 70))

predicted_metabolic_rate