Question

The Classification variable in the cancer data gives the disease status of each individual ( 0 : healthy controls; 1 : cancer patients). Use glm to fit a multiple logistic regression model using Classification as the response variable Y, Glucose as the explanatory variable X1​ and Resistin as the explanatory variable X2​. That is,

logP(yi​=0∣x1i​,x2i​/ P(yi​=1∣x1i​,x2i​)​=β0​+β1​x1i​+β2​x2i​,
where yi​ is the value of Classification for the i th individual, x1i​ is the value of Glucose and x2​ is the value of Resistin for the i th individual.
Attach your code and report the estimates for β0​,β1​,β2​.

Answer 1

The slope and y-intercept of the regression line provide information about the relationship between the explanatory variables and the response variable.

Step-by-step explanation:

In multiple logistic regression, the slope and y-intercept of the regression line provide information about the relationship between the explanatory variables (x) and the response variable (y). In this case, the slope (β1) represents the change in the log-odds of being a cancer patient for every unit increase in Glucose, holding Resistin constant. The y-intercept (β0) represents the log-odds of being a cancer patient when both Glucose and Resistin are zero.

In terms of how well the regression line fits the data, we can assess this by looking at the coefficients of determination (R-squared). A high R-squared value indicates a good fit between the regression line and the data, meaning that the model explains a large proportion of the variation in the disease status.

A residual is the difference between the observed value of the response variable and the predicted value from the regression line. The point with the largest residual represents an outlier, meaning it deviates significantly from the overall pattern of the data. However, whether it is influential or not depends on its leverage, which is a measure of how much it affects the estimates of the regression coefficients.

The regression line's fit to the data can be assessed using the coefficient of determination. Residuals indicate the differences between observed and predicted values, and outliers may be influential depending on their leverage.