Logistic and Linear Regression

Suppose you have been given a fair coin and you want to find out the odds of getting heads. Which of the following option is true for such a case?

• odds will be 0

• odds will be 0.5

• odds will be 1

• None

Suppose, You applied a Logistic Regression model on a given data and got a training accuracy X and testing accuracy Y. Now, you want to add a few new features in the same data. Select the option(s) which is/are correct in such a case.

• Training accuracy increases

• Training accuracy increases or remains the same

• Testing accuracy decreases

• Testing accuracy increases or remains the same

Below are two different logistic models with different values for β0 and β1. Which of the following statement(s) is true about β0 and β1 values of two logistics models (Green, Black)?

Note: consider Y = β0 + β1*X. Here, β0 is intercept and β1 is coefficient.

• β1 for Green is greater than Black

• β1 for Green is lower than Black

• β1 for both models is same

• Can’t Say

Above are the three scatter plot(A,B,C left to right) and hand drawn decision boundaries for logistic regression. Which of the following above figure shows that the decision boundary is overfitting the training data?

• A

• B

• C

• None

What do you conclude after seeing this visualization?

• The training error in first plot is maximum as compare to second and third plot.

• The best model for this regression problem is the last (third) plot because it has minimum training error (zero).

• The second model is more robust than first and third because it will perform best on unseen data.

• The third model is overfitting more as compare to first and second.

• All will perform same because we have not seen the testing data.

The below figure shows AUC-ROC curves for three logistic regression models. Different colors show curves for different hyper parameters values. Which of the following AUC-ROC will give best result?

• Yellow

• Pink

• Black

• All are same

Suppose, Following graph is a cost function for logistic regression. How many local minimas are present in the graph?

• 1

• 2

• 3

• 4

Is Logistic regression a supervised machine learning algorithm?

• TRUE

• FALSE

Suppose that in our sample, following a logistic regression analysis, the odds for girls of having a positive attitude to school were 1.25. What proportion of girls would be expected to have a positive attitude?

• 25%

• 35%

• 45%

• 55%

Consider a following model for logistic regression: P (y =1|x, w)= g(w0 + w1x)

where g(z) is the logistic function.

In the above equation the P (y =1|x; w) , viewed as a function of x, that we can get by changing the parameters w.

What would be the range of p in such case?

• (0, inf)

• (-inf,inf)

• (0,1)

• (-inf,0)