ISYE 6414: Regression Analysis Course Homework 1: Solutions | All Answers are Correct

6414: Regression Analysis Course Homework 1: Solutions I Multiple Choice: A True or False: 1 The simple linear regression model has three parameters that need to be estimated. (TRUE) 2 The only objective of linear regression is prediction. (FALSE) 3 In the regression model, the variable of interest for study is the explanatory variable. 4 In the regression model, the response variable is a random variable. (TRUE) 5 In the simple linear regression model, we loose only two degrees of freedom because of the estimation of the regression coefficients, β0 and β1. (TRUE) 6 Under the normality assumption, the estimator for β1 is a linear combination of normal distributed random variables. (TRUE) 7 The estimator σˆ 2 is a random variable. (TRUE) 8 A negative value of β1 is consistent with a direct relationship between x and Y . (FALSE) 9 Statistical significance of β0 means that the intercept of the regression is significantly different from zero. (TRUE) 10 βˆ 1 is the estimated expected value of the response variable when the predicting variable is equal to zero. (FALSE) 11 βˆ 1 is an unbiased estimator for β0. (FALSE) 12 The sampling distribution of βˆ 1 is a t-distribution for any distribution of the data. (FALSE) 13 If the confidence interval for β0 contains the value zero we interpret that β0 is definitely equal to zero. (FALSE) 14 The prediction interval