Final answer:
The correct model form for a multiple logistic regression analysis using classification as the response variable and glucose and resistin as explanatory variables is Y = α + β1X1 + β2X2. The slope and intercept have specific interpretations in the context of the logistic regression, and to assess model fit, we evaluate R-squared values and residuals, and test for linear relationship significance.
Step-by-step explanation:
To fit a multiple logistic regression model using classification as the response variable Y, with glucose as explanatory variable X1, and resistin as explanatory variable X2, the correct model form would be Y = α + β1X1 + β2X2, where α is the intercept, and β1, β2 are the slopes of the regression for X1 and X2, respectively. This model describes the log-odds of being a cancer patient as a linear function of the glucose and resistin levels.
The slope of the regression line tells us the change in the log-odds of the outcome for a one unit change in the predictor. The y-intercept (α) indicates the log-odds of the outcome when all predictors are zero. To determine how well the regression line fits the data, we look at metrics like R-squared and analyze residuals. The largest residual indicates the point that is furthest from the predicted regression line; if it's an outlier or influential, it could disproportionately affect the regression model's parameters.
To evaluate the presence of a linear relationship between two variables, we would examine the correlation coefficient and perform hypothesis testing, such as the t-test for regression slopes, checking if it differs significantly from zero at a significance level of 0.05.