Advanced R Programming for Data Analytics in Business Week 5 Answers Nptel
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Advanced R Programming for Data Analytics in Business Week 5 Answers (July-Dec 2025)
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Question 1. In a simple linear regression model y = β₀ + β₁x + μ, which of the following best describes the nature of the variables?
a) Both y and x are random variables.
b) x is random and y is fixed (not-stochastic).
c) x is fixed (not-stochastic) and y is random.
d) Both y and x are fixed (not-stochastic).
Question 2. Why does the Ordinary Least Squares (OLS) method minimize the sum of squared residuals rather than just the sum of residuals?
a) Squared residuals always produce zero mean errors.
b) Squaring ensures that positive and negative errors do not cancel each other out.
c) Squared residuals are easier to interpret than absolute residuals.
d) OLS always provides the maximum likelihood estimate.
Question 3. Which of the following is correct regarding the OLS cost function?
a) It minimizes ∑|μᵢ| (summation of absolute errors) to optimize the estimated parameters.
b) It minimizes ∑(yᵢ – ŷᵢ)² which is the sum of squared residuals.
c) It maximizes ∑(yᵢ – ŷᵢ)² to obtain the best-fitting line.
d) It assumes all residuals are zero for model validity.
Question 4. You’re running a multiple regression model with high multicollinearity among independent variables. What is the most likely consequence in practice?
a) The R-squared becomes 0.
b) The model fails to converge.
c) Coefficients become statistically insignificant due to inflated standard errors.
d) OLS assumptions are automatically violated.
These are Advanced R Programming for Data Analytics in Business Week 5 Answers Nptel
Question 5. Which of the following scenarios would likely cause adjusted R² to decline while R² increases?
a) Adding a variable that significantly increases model fit.
b) Adding a variable that is highly correlated with the dependent variable.
c) Adding an irrelevant variable that adds minimal explanatory power.
d) Removing an important explanatory variable from the model.
Question 6. You use a log-log transformation on a regression model to estimate the relationship between sales and advertising budget. What does the coefficient of the transformed model represent?
a) Absolute change in sales for a one-unit increase in ad budget.
b) Percentage change in ad budget for a unit change in sales.
c) Percentage change in sales for a percentage change in ad budget.
d) Change in sales for one standard deviation change in ad budget.
Question 7. You’re testing whether a predictor X significantly affects Y. You compute a t-statistic for the coefficient of X and it lies in the critical region. Which of the following is a correct interpretation?
a) The null hypothesis is accepted.
b) The predictor has no effect.
c) The coefficient is significantly different from zero at the chosen significance level.
d) The adjusted R² must be high.
These are Advanced R Programming for Data Analytics in Business Week 5 Answers Nptel
Question 8. In the training phase, ABC returns were regressed on Nifty returns using the command lm(ABC ~ Nifty, data=train). The t-statistic for the coefficient of Nifty was 18.67. What does this signify?
a) The model overfits the training data.
b) Nifty returns have no impact on ABC.
c) The relationship is significant at 1% level.
d) There is autocorrelation in residuals.
Question 9. Which diagnostic plot would best help detect non-normality of residuals in your trained model?
a) Scatter plot of fitted vs actual values.
b) Histogram of ABC returns.
c) Q-Q plot of studentized residuals.
d) Boxplot of Nifty returns.
Question 10. After applying the dwtest(SLR) command in R, you get a DW statistic close to 2 and a high p-value. What does this imply about the residuals?
a) There is significant negative autocorrelation.
b) There is significant positive autocorrelation.
c) There is no significant autocorrelation.
d) Residuals are not normally distributed.
Question 11. You are assessing the predictive performance of your regression model of Nifty returns on a particular stock (XYZ) returns. The correlation between the actual and your model predicted values is 0.57. What additional measure in R would you use to compare predictive performance across models?
a) summary().
b) MSE(test$abc, predict).
c) qqplot(SLR).
d) acf(predict).
Question 12. You used the vif() function on your multiple regression model and found a VIF of 2.9 for the Nifty variable. What does this suggest and what threshold is typically used for concern?
a) Suggests low correlation threshold is 10.
b) Suggests severe multicollinearity threshold is 1.
c) Suggests moderate multicollinearity threshold is 5.
d) Suggests high autocorrelation threshold is 2.
These are Advanced R Programming for Data Analytics in Business Week 5 Answers Nptel