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Economics
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13 Dec 2019

Which of the following is true of the t-statistic? It tells us how many standard errors the coefficient estimate is equal to zero. It is the value of the coefficient estimate divided by its standard error. It is the sum of the value of the coefficient estimate and its standard error. It measures the overall statistical validity of the regression equation. It is the coefficient’s standard error normalized to lie between 0 and 1.

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Related questions

. Suppose Y is related to R and S in the following nonlinear way:

Y= aRᵇSᶜ

a. How can this nonlinear equation be transformed into a linear form that can ve analyzed using multiple regression analysis.

Sixty-three observations are used to obtain the following regression results:

DEPENDENT VARIABLE: LNY

R-SQUARE

F-RATIO

P-VALUE ON F

OBSERVATION: 63

0.8151

132.22

0.0001

VARIABLE

PARAMETER ESTIMATE

STANDARD ERROR

T-RATIO

P-VALUE

INTERCEPT

-1.386

0.83

-1.67

0.1002

LNR

0.452

0.175

2.58

0.0123

LNS

0.30

0.098

3.06

0.0033

b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?

c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value of the F-statistic.

d. How well does this nonlinear model fit the data?

e. Using the estimated value of the intercept, compute an estimate of a.

f. If R = 200 and S = 1,500, compute the expected value of Y.

g. What is the estimated elasticity of R? Of S?

Econ 3050

7. When every member of the accessible population has an equal chance of being selected to participate in the study, the researcher is using:

a) Simple random sampling

b) Stratified random sampling

c) Convenience sampling

d) Purposive random sampling

8. A regression line has been found that has nearly all the points lying directly on the line, and only a few of them stray away from the line. Therefore, the standard error of the estimate is likely to be

Huge.

Small.

0.

Undefined.

9. Correlation coefficient ranges from _______ to ____________.

a) - 1 to 0.

b) 0 to 1.

c) -1 to 1.

d) None of the above.

10. The correlation coefficient of determination is the:

a) Ratio of the explained variation to the total deviation.

b) Ratio of the unexplained deviation to the explained deviation.

c) Ratio of the unexplained deviation to the total variation.

d) Ratio of the explained variation to the total variation.


11. If the correlation coefficient r = 0.5 then the coefficient of determination is:

a) 0.10

b) 0.25

c) 1.00

d) 2.50

12. Which one of the following is NOT appropriate for studying the relationship between two quantitative variables?

Scatterplot

Bar chart

Correlation

Regression

13. In regression, an independent variable is sometimes called a response variable.

True

False

14. The simple linear regression equation can be written y = b0 + b1x. In the simple linear regression equation, the symbol y represents:

The average or predicted response

Estimated intercept

Estimated slope

Explanatory variable

Refer to the example of the Cobb-Douglas production function discussed in class, where the GDP (Y), Total Employment (X2 ), and Stock of Fixed Capital (X3 ), are measured for the output, labor input and capital input, respectively. The following model is fitted and the R output is below. The data are yearly data from 1955 to 1974.

lnY = B1 +B2lnX2 + B3lnX3 + u

a. Interpret the coefficient estimate of B3 specific to this problem.

b. Find the rate of change of Y with respect to the change of X2 , at Y=218506.3 and X2=11152.6, and X3 = 340072.45.

c. Find the estimate of the return to scale parameter. (3 pts.)

d. Is there strong evidence that the GDP is inelastic relative to the stocks of fixed capital? Justify your answer at a=0.05.

e. Test if there is a positive (first order) autocorrelation in the error term using a=0.05 . Make sure to state the null and alternative hypotheses, to provide the values of the test statistic and the critical value(s), and to draw a conclusion. (6 pts.)

Regression output for Problem 3.

> fit<-lm(log(y) ~ log(x2) + log(x3))

> summary(fit)

Call:

lm(formula = log(y) ~ log(x2) + log(x3))

Residuals:

Min 1Q Median 3Q Max

-0.057142 -0.016250 -0.005793 0.023512 0.038739

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.65233 0.60619 -2.726 0.0144 *

log(x2) 0.33972 0.18569 1.830 0.0849 .

log(x3) 0.84600 0.09335 9.063 6.42e-08 ***

Signif. codes: 0 0.001  0.01 0.05  0.1  1

Residual standard error: 0.02829 on 17 degrees of freedom

Multiple R-squared: 0.9951, Adjusted R-squared: 0.9945

F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16

Durbin-Watson Statistic = 0.425618

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