Q. 3 (14 marks) Consider the following data set where y is the response variable and...
Decide (with short explanations) whether the following statements are true or false. e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model with the following questions 9, 25 (gender: males as 0 and females coded as 1) as your predictor variables. You will have to use the data set Economic Gun Legislation Survey Regression Exercise posted for Week 9 on the webpage. Please do the following in exactly this order: a. Excel Output b. Model: write down model like in form y- b, b,X, -b.X. +...
a,b,c,d 3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS estimators βο and A using the non-matrix method. (b) Find the OLS estimators using the matrix method. (c) Find the coefficient of determination. (d) Find the standard error of 3. Suppose the following data has been obtained for the linear model Y Bo+ x 14 2 1 4 0 22 (a) Find the OLS...
Consider a linear regression model where y represents the response variable, x is a quantitative explanatory variable, and d is a dummy variable. The model is estimated as yˆy^ = 14.6 + 4.5x − 3.4d. a. Interpret the dummy variable coefficient. Intercept shifts down by 3.4 units as d changes from 0 to 1. Slope shifts down by 3.4 units as d changes from 0 to 1. Intercept shifts up by 3.4 units as d changes from 0 to 1. Slope shifts...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
Consider the following small data set Subject x y 1 14 30 2 15 21 3 15 25 4 3 19 5 6 31 Find the linear correlation coefficient. r =
Consider a linear regression model where y represents the response variable, x is a quantitative explanatory variable, and d is a dummy variable. The model is estimated as yˆy^ = 14.4 + 4.6x − 3.1d. a. Interpret the dummy variable coefficient. Intercept shifts down by 3.1 units as d changes from 0 to 1. Slope shifts down by 3.1 units as d changes from 0 to 1. Intercept shifts up by 3.1 units as d changes from 0 to 1. Slope shifts...
2. Consider a simple linear regression model for a response variable Yi, a single predictor variable ri, i-1,... , n, and having Gaussian (i.e. normally distributed) errors Ý,-BzitEj, Ejį.i.d. N(0, σ2) This model is often called "regression through the origin" since E(Yi) 0 if xi 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function. (Hint: The function...
(1 point) Consider the following small data set. Subject x y 1 10 28 2 14 19 3 7 30 4 14 30 5 16 26 Find the linear correlation coefficient.
The random vector Y = (Y1, ..., Yn)T is such that Y = Xβ + ε, where X is an n × p full-rank matrix of known constants, β is a p-length vector of unknown parameters, and ε is an n-length vector of random variables. A multiple linear regression model is fitted to the data. (a) Write down the multiple linear regression model assumptions in matrix format. (b) Derive the least squares estimator β^ of β. (c) Using the data:...