Question 1
(a) (1 point) What is wrong with this formulation of the regression model: Y = β0 +β1X? How would you express it instead?
(b) (1 point) What assumptions are made about the distribution of the explanatory variable in the simple linear regression model?
(a) In the given model, there is no error part. There will be problem in analysis if there is no error term.
y = β0 + β1 + e
Here y is dependent variable whereas x is independent or explanatory variable.
(b) The error e is independent and identically distributed random variable with mean zero and constant variance σ2 (homoscedastic). X is supposed to possess linear relationship. The variable y is normally distributed for any x.
Question 1 (a) (1 point) What is wrong with this formulation of the regression model: Y...
Consider the following formulations of the 1 variable regression model: Y = β0 + β1x + u and Y = α0 + α1(x − ¯x) + a a) would the estimates of β0 and α0 the same? Explicitly shows this by deriving the estimates. b) What about β1 and α1 ? c) In the regression Y = β0 +β1x+u suppose we multiply each X value by a constant, say, 2. Will it change the residuals and fitted values of Y?...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the...
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...
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...
10.1 Understanding a linear regression model. Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with μy = 2.8 + 0.8x and standard deviation σ = 3.2. The explanatory variable x is the number of servings of fruits and vegetables in a calorie-controlled diet. (a) What is the slope of the population regression line? (b) Explain clearly what this slope says about the change in the mean of y for a change in...
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...
1. What is Frisch-Waugh Theorem? Express it in algebraic terms in a multiple linear regression model y = β0 + β1x1 + β2 x2 + u
An economist estimates the following model: y = β0 + β1x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x+ = x – 2. A portion of the regression results is shown in the accompanying table. Regression Statistics R Square 0.42 Standard Error 3.86 Observations 12 Coefficients Standard Error t-stat p-value Lower 95% Upper...