Homework Answers
Conclusion:
For the given regression model , there is no intercept term, or
beta o=0 Thus, there is only one normal equation, and is easily
solvable. But, an inner analysis shows that the regression line
passes through the origin, and because of its forcibly passing
through the origin leads to the non zero mean of the residuals,
which is inconsistent with the best fit model
The regression function is plotted on a graph papa, which will pass
from the origin and by the help of the fitted regression equation
so that the sum of the squares of the errors is minimum
so if beta o =0 there is no intercept in the model .
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2. Refer to regression model Y' = +AX, +6. Assume that X = 0 is within...
(1.2) Marks available: 5 Consider a regression model of the form y-Ao +AX, + U, where corr(X,,U) ...
(1.2) Marks available: 5 Consider a regression model of the form y-Ao +AX, + U, where corr(X,,U) O. Now, define Zi = cXi, where c is a non-zero constant. Is Zi a valid instrument for Xi? What is the general implication of this exercise?
(1.2) Marks available: 5 Consider a regression model of the form y-Ao +AX, + U, where corr(X,,U) O. Now, define Zi = cXi, where c is a non-zero constant. Is Zi a valid instrument for Xi?...
its 8.17 the one that is highlighted and I have also attached the models. Xi2: 0 1 0 a. Explain how each regression coefficient in model (8.33) is interpreted hene. b. Fit the regression model...
its 8.17 the one that is highlighted and I have also
attached the models.
Xi2: 0 1 0 a. Explain how each regression coefficient in model (8.33) is interpreted hene. b. Fit the regression model and state the estimated regression function. c. Test whether the X2 variable can be dropped from the regression model; use α 01 St ate the alternatives, decision rule, and conclusion. d. Obtain the residuals for regression model (8.33) and plot them against XiXz. Is there...
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume th...
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...
3.7 In a simple regression model, y-, + Ax + u , which of the following...
3.7 In a simple regression model, y-, + Ax + u , which of the following is NOT referring to y? (a) Dependent variable (b) Explained variable (c) Predicted variable (d) Regressant (e) All of the above refer to y 3.8 Which of the following statements is correct? (a) If X and Y are independent, then E[YIX]- E[Y (b) If Xand Y are independent, then ElYx] (c) If Xand Y are independent, then E[Y|X] is irrelevant from E[Y] (d) None...
Consider the following formulations of the 1 variable regression model: Y = β0 + β1x +...
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?...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
f and g 1. Consider the standard bivariate regression: Y = Bo + B,X, + a)...
f and g
1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is...
Question 2: Suppose that we wish to fit a regression model for which the true regression...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
Using multiple linear regression, estimate the value of a in the given regression model. Use 4 decimal places. MODEL: y=ax^b e^cx
Using multiple linear regression, estimate the value of a in the given regression model. Use 4 decimal places. MODEL: y=ax^b e^cx
(1.2) Marks available: 5 Consider a regression model of the form y-Ao +AX, + U, where corr(X,,U) O. Now, define Zi = cXi, where c is a non-zero constant. Is Zi a valid instrument for Xi? What is the general implication of this exercise?
(1.2) Marks available: 5 Consider a regression model of the form y-Ao +AX, + U, where corr(X,,U) O. Now, define Zi = cXi, where c is a non-zero constant. Is Zi a valid instrument for Xi?...
its 8.17 the one that is highlighted and I have also
attached the models.
Xi2: 0 1 0 a. Explain how each regression coefficient in model (8.33) is interpreted hene. b. Fit the regression model and state the estimated regression function. c. Test whether the X2 variable can be dropped from the regression model; use α 01 St ate the alternatives, decision rule, and conclusion. d. Obtain the residuals for regression model (8.33) and plot them against XiXz. Is there...
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...
3.7 In a simple regression model, y-, + Ax + u , which of the following is NOT referring to y? (a) Dependent variable (b) Explained variable (c) Predicted variable (d) Regressant (e) All of the above refer to y 3.8 Which of the following statements is correct? (a) If X and Y are independent, then E[YIX]- E[Y (b) If Xand Y are independent, then ElYx] (c) If Xand Y are independent, then E[Y|X] is irrelevant from E[Y] (d) None...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
f and g
1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
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