4. Suppose we run a multiple regression, and for observation 5 we get that Y5 =...
4. Suppose we run a multiple regression, and for observation 5 we get that Y5 = ‒4.73 and
Y5 = ‒4.28. What is the residual for observation 5?
Homework Answers
The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e).
Formula of residual is given as following types
Residual = Observed value - Predicted value.
e= y - ŷ
= -4.28 - ( -4.73)
= -4.28+4.73
= 0.45
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4. Suppose we run a multiple regression, and for observation 5
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which of the following procedures will yield the same estimate
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Y=0
+
1122+U
?
A. Run Y on
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1; run Y on
2, predict residual e2; run e1 on e2
B. Run X2 on X1 predict residual e; run e on Y
C.Run Y on X1 predict residual e1; run X2 on X predict residual
e2; run e1 on e2
E. none of the above
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Exercise 1 Suppose X is the initial matrix in a multiple regression problem. We then add an extra predictor z. So the regression matrix is now W = (X, z). Use the inverse of a partitioned matrix to show that the last diagonal element of (W'W)-1 is equal to +7,+, where z* is the residual vector from the regression of z on X.
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...
which of the following procedures will yield the same estimate
of
1 as in multiple regression
Y=0
+
1122+U
?
A. Run Y on
1, predict residual
1; run Y on
2, predict residual e2; run e1 on e2
B. Run X2 on X1 predict residual e; run e on Y
C.Run Y on X1 predict residual e1; run X2 on X predict residual
e2; run e1 on e2
E. none of the above
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