FREE Data Science Statistical Modeling & Inference Questions and Answers

Question 1

A data scientist is building a linear regression model to predict housing prices.
After fitting the model, they find that the residuals exhibit a clear U-shaped pattern when plotted against the predicted values.
Which of the following assumptions of linear regression is most likely violated?

Accepted Answer

Linearity

Answer

Independence of errors

Answer

Homoscedasticity

Answer

Normality of residuals

Question 2

In the context of hypothesis testing, what is the primary purpose of calculating a p-value?

Accepted Answer

To quantify the probability of observing data as extreme as, or more extreme than, the sample data, assuming the null hypothesis is true.

Answer

To determine the sample size required for an experiment.

Answer

To establish the confidence interval for a population parameter.

Answer

To calculate the effect size of an observed phenomenon.

Question 3

Which of the following statements best describes the concept of multicollinearity in a multiple linear regression model?

Accepted Answer

Two or more independent variables in the model are highly correlated with each other.

Answer

The error terms are not normally distributed.

Answer

The variance of the residuals is not constant across all levels of the independent variables.

Answer

The relationship between the dependent and independent variables is non-linear.

Question 4

A researcher is comparing the mean scores of three different teaching methods on a standardized test. The scores are normally distributed, and the variances across groups are assumed to be equal. Which statistical test is most appropriate for this analysis?

Accepted Answer

One-way ANOVA (Analysis of Variance)

Answer

Paired t-test

Answer

Chi-squared test of independence

Answer

Pearson correlation coefficient

Question 5

When interpreting the coefficients of a logistic regression model, what does an odds ratio greater than 1 for a predictor variable signify?

Accepted Answer

An increase in the odds of the outcome for a one-unit increase in the predictor.

Answer

A decrease in the probability of the outcome for a one-unit increase in the predictor.

Answer

An increase in the probability of the outcome for a one-unit increase in the predictor.

Answer

That the predictor variable has no effect on the outcome.

Question 6

Consider a scenario where a data scientist is performing A/B testing for a new website feature. The null hypothesis states there is no difference in conversion rates between the old and new features. If the p-value obtained from the test is 0.005 and the chosen significance level (alpha) is 0.01, what is the appropriate conclusion?

Accepted Answer

Reject the null hypothesis, as the p-value is less than alpha.

Answer

Fail to reject the null hypothesis, as the p-value is less than alpha.

Answer

Fail to reject the null hypothesis, as the p-value is greater than alpha.

Answer

Reject the null hypothesis, as the p-value is greater than alpha.

A data scientist is building a linear regression model to predict housing prices.After fitting the model, they find that the residuals exhibit a clear U-shaped pattern when plotted against the predicted values.Which of the following assumptions of linear regression is most likely violated?

A data scientist is building a linear regression model to predict housing prices.
After fitting the model, they find that the residuals exhibit a clear U-shaped pattern when plotted against the predicted values.
Which of the following assumptions of linear regression is most likely violated?