Question

Complete the R code using Rstudio so that it calculates and returns the estimates of β, the intercept and regression weight of the logistic regression of approximate GPA on Rouder-Srinivasan preference.

## Data
Preference <- c(  0,   0,   0,   0,   0,   1,   1,   1,   1)  # 0: Rouder; 1: Srinivasan
GPA        <- c(2.0, 2.5, 3.0, 3.5, 4.0, 2.5, 3.0, 3.5, 4.0)
Count      <- c(  4,   5,  21,  22,   8,   2,   1,   4,   7)

# Define the deviance function
deviance <- function(beta) {
   ... complete this ...
}

## Test the function
deviance(c(0,1))

## Estimate
optim(c(0, 1), deviance)$par

Answer 1

The attach images details solution solved in R-studion software given below.

1.

2.

Conclusion:

Null Deviance:         12.37 

Residual Deviance: 2.558e-09 

Lower the value of AIC=6 better the model

Deviance is a measure of goodness of fit of a model. Higher numbers always indicates bad fit. The null deviance shows how well the response variable is predicted by a model that includes only the intercept (grand mean) where as residual with inclusion of independent variables