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19 Cards in this Set
- Front
- Back
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The best way to interpret polynomial regression is to: |
plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X |
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In the model ln(Y_i)=Beta_0 +Beta_1X_i + U_i, the elasticity of E(Y|X) with respect to X is: |
Beta_1X |
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A standard "money demand" function used by macroeconomists has the form :
ln(m)=Beta_0 + Beta_1ln(GDP) + Beta_2R
Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of nominal interest rate measured in percent per year. Suppose that Beta_1 = 4.45 and Beta_2 = -.09
What is the expected change in m if GDP increases by 10%?
What is the expected change in m if the interest rate increases from 1% to 6%? |
the value of m is expected to increase by approximately 45%
The value of m is expected to decrease by approx 45% |
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in the log-log model, the slope coefficient indicates |
the elasticity of Y with respect to X |
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SEE QUESTION 5 FOR SOME REGRESSION SH!T |
:( |
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SEE QUESTION 6 FOR A LONG PROBLEM |
:( |
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The interpretation of the slope coefficient in the model ln(Y_i)=Beta_0 + Beta_1X_i + U_i is as follows: |
A change in X by one unit is associated with a 100% Beta_1 % change in Y |
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SEE QUESTION 8 FOR LONG QUESTION |
:( |
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An example of a quadratic regression model is |
Y_i= Beta_0 + Beta_1X + Beta_2X^2 + U_i |
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You have estimated a linear regression model relating Y to X. Your professor says "I think that the relationship between Y and X is nonlinear". How would you rest the adequacy of your linear regression?
2 things |
if adding a quadratic term, you could test the hypothesis that the estimated coefficient of the quadratic term is significantly different from zero.
Compare the fit between of linear regression to the non-linear regression model |
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Consider the following least squares specification between test scores and the student - teacher ratio:
Test Scores (hat) = 557.8 + 36.42ln(Income)
According to this equation, a 1% increase in income is associated with an increase in test scores of: |
.36 points. |
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To decide whether Y_i=Beta_0 + Beta_1X + _i or ln(Y_i)= Beta_0 + Beta_1X _ U_i fits the data better, you cannot consult the regression R^2 because: |
the TSS are not measured in the same units between the two models. Come on, you know this, get with the program!! |
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a nonlinear function: |
Is a function with a slope that is not constant |
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in the log-log model, the slope coefficient indicates |
the elasticity of Y with respect to X |
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In the model ln(Y_i)= Beta_0 + Beta_1X_i + U_i, the elasticity of E(Y|X) with respect to X is |
Beta_1X |
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The interpretation of the slope coefficient in the model ln(Y_i)=Beta_0 + Beta_1ln(X) + U_i is as follows: |
a 1% change in X is associated with a Beta_1 % change in Y |
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in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: |
Delta Y = F(X_1 + delta X_1, X_2,.....X_k) - F(X_1,X_2,...X_k) |
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assume that you had estimated the following quadratic regression model.
Testscore (hat) = 607.3 + 3.85 Income - .0423 Income^2 . If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores wold be |
2.96 |
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You have estimated the following equation:
Testscore (hat) = 607.3 + 3.85 Income - .0423Income ^2
Where testscore is the average of the reading and math scores on the blah blah blah administered to 420 CA school districts in 1998 and 1999. Income is the average annual per capita income in the school district, measured in thousands of 1998 dollars. The equation: (how do test scores and income interact in the sample) |
suggests a positive relationship between test scores and income for most of the sample. |
