# Solutions to Algoritmo Lab’s Data Science Challenge – November 2021 on Linear Regression

**Q1. For a good model, R-squared takes a value close to 1.0**

Ans. True

**Q2. The n-1 dummy encoding needs to be performed in all-numeric predictor variables**

Ans. False

**Q3. If the p-value of the F-Statistic is less than the significance level**,

Ans. Data provide evidence that the regression model fits the data well

**Q4. When can R-Squared be negative?**

Ans. When regression model fit is worse than average line

**Q5. Build an intercept model with 7 numeric predictors & 1 numeric target variable. Build 2nd intercept model after z-score standardizing the predictors.**

Ans. Both Multiple & adj r-squared will be the same for models 1 & 2

**Q6. An intercept model is built with X as a predictor. Change X to Z where Z is 2021-X. Build the 2nd intercept model.**

Ans. If the coefficient of X in model 1 is 121, the coefficient of Z in model 2 is -121

**Q7. Is it necessary to standardize variables before using Lasso and Ridge Regression?**

Ans. Yes

**Q8. Errors from a linear regression model should be normally distributed with zero mean. If error terms are not normally distributed, it implies**

Ans. Confidence Intervals will be too wide or narrow

**Q9. The parameters of a linear regression model can be estimated using**

Ans. Both least squares and MLE procedure

**Q10. In linear regression, we can calculate the importance of variables by ranking predictors based on the**

Ans. Descending order of absolute value of the standardized coefficient.

**Q11. In the linear regression model, when an interaction is created from two variables that are not centered on 0,**

Ans. Some amount of collinearity will be induced

**Q12. In the linear regression model, is it helpful to standardize a variable when you include polynomial terms like X ^{2} or X^{3}**

Ans. Yes, Standardization helps remove collinearity

**Q13. Which of the following enforces sparsity in models?**

Ans. L1 Norm

**Q14. The more able a model is to ignore extreme values in the data, the more robust it is. Which of the following is correct?**

Ans. L1-norm is more robust than L2-norm

**Q15. A closed-form solution for a linear regression model is given by β=( X^{T}.X)^{-1}.X^{T}.Y. In case perfect multicollinearity exists, (X^{T}X)^{-1} may lead to**

Ans. Singular matrix error

**Q16. One-Hot encoding can lead to multi-collinearity and should be avoided in linear regression analysis**

Ans. True

**Q17. The Durbin Watson (DW) statistic is a test for autocorrelation in the residuals of a regression model. DW can take values between 0 and 4.**

Ans. A value of 2 indicates there is zero autocorrelation

**Q18. Ridge regression can reduce the coefficients to zero values**

Ans. False