5. (Q3.31 on textbook p.127) Show that the residuals from a linear regression model can be expressed as e = (I − H)ε
Hint: Use the expression of e on Lecture 2, p.18. (5 points)
5. (Q3.31 on textbook p.127) Show that the residuals from a linear regression model can be...
Consider the least-squares residuals ei-yi-yi, 1, 2, . . . , linear regression model. Find the variance of the residuals Var(e). Is the vari- ance of the residuals a constant? Discuss. n,from the simple
One of the residuals in a linear regression model is equal to 6.5. Other results from the model are MSE = 3.2, MSR = 4.5, SSE = 182, and SSR = 243. What is the value of the standardized residual?
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
When you use linear regression to fit a linear model, and create a scatterplot of actual vs. predicted values, you would ideally see: a. the points lie close to the diagonal line from bottom left to upper right b. the points form a random "cloud" C. the point lie close to a horizontal line (write a, b or c): (True/False) If you have many variables (features), you will tend to prefer non-parametric methods to parametric methods. The two plots below...
Question 4 Consider the linear regression model 1. For estimates βί, 「= 1,.. . , n, the residuals are given by Explain why. 2. Show the first order condition for 30 is Σηι ei = 0. 3. Show the first order conditions for B,... , Bk are respectively. (Hint: Consider your calculation from Question 1.)
Using the following completed regression model AR(1) with correlated residuals: Y. =-10+25x, in which p=.5 is the correlation coefficient between time ordered residuals. Given the following data: St 1 X 10 30 60 unknown 3 . Using the Hildreth Lu method , forecast the value of Yt for X=4.
3) Consider the following linear regression: y =a + Bx + Show that minimizing the sum of squared residuals ( - ) to obtain OLS estimators of the slope and the intercept results in the following algebraic properties a) b) Ex = 0 = 0 4) You run the following regression: TestScore = a + (Female) + where TestScore is measured on a scale from 400 to 1000, and female is an indicator for the gender of the student. You...
please help! Following is a simple linear regression model: y = a + A + & The following results were obtained from some statistical software. R2 = 0.523 Syx (regression standard error) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Interecpt Slope of X Parameter Estimate 0.519 -0.707 Std. Err. of Parameter Est 0.132 0.239 Note: For all the calculated numbers, keep three decimals. Write the fitted model (5 points) 2. Make a prediction...
5. Show that Var(Y)- Var(e in the simple linear regression model. (Yes, this should be that simple.) What did you assume?