4.4 The general manager of a large engineering firm wants to know whether the experience of techni- cal artists influences their work quality. A random sample of 50 artists is selected. Using years of work experience (EXPER) and a performance rating (RATING, on a 100-point scale), two models are estimated by least squares. The estimates and standard errors are as follows: Model 1: Model 2: RATING=64.289 +0.990EXPER N-50 R²=0.3793 (se) (2.422) (0.183) RATING=39.464+15.312 In(EXPER) N46 R²=0.6414 (4.198) (1.727) (se)
4.4 The general manager of a large engineering firm wants to know whether the experience of techni- cal artists influences their work quality. A random sample of 50 artists is selected. Using years of work experience (EXPER) and a performance rating (RATING, on a 100-point scale), two models are estimated by least squares. The estimates and standard errors are as follows: Model 1: Model 2: RATING=64.289 +0.990EXPER N-50 R²=0.3793 (se) (2.422) (0.183) RATING=39.464+15.312 In(EXPER) N46 R²=0.6414 (4.198) (1.727) (se)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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Please answer a-f for 4.4
Transcribed Image Text:7:20
y=64.29 +0.99x R0.379
(se) (2.42) (0.18)
Rewrite the estimated equation, including coefficients, standard errors, and R², that would result if
a. All values of x were divided by 10 before estimation.
b. All values of y were divided by 10 before estimation.
c. All values of y and x were divided by 10 before estimation.
4.3 We have five observations on x and y. They are x = 3, 2, 1,-1,0 with corresponding y values
1.2 +0.8x,, the sum of squared least squares
(y,-5)= 10. Carry out this exercise with
y = 4,2,3,1,0. The fitted least squares line is ŷ,
residuals is = 3.6,
a hand calculator. Compute
(x-7)= 10, and
a. the predicted value of y for x, 4.
b. the se) corresponding to part (a).
c. a 95% prediction interval for y given x = 4.
d. a 99% prediction interval for y given.x = 4.
e. a 95% prediction interval for y given.x = 7. Compare the width of this interval to the one computed
in part (c).
4.4 The general manager of a large engineering firm wants to know whether the experience of techni-
cal artists influences their work quality. A random sample of 50 artists is selected. Using years of
work experience (EXPER) and a performance rating (RATING, on a 100-point scale), two models are
estimated by least squares. The estimates and standard errors are as follows:
Model 1:
Model 2:
RATING= 64.289 +0.990EXPER N=50 R²=0.3793
(se)
(2.422) (0.183)
RATING= 39.464+15.312 In(EXPER) N=46 R = 0.6414
(se) (4.198) (1.727)
![7:21
Prediction, Goodness-of-Fit, and Modeling Issues
a. Sketch the fitted values from Model 1 for EXPER=0 to 30 years.
b. Sketch the fitted values from Model 2 against EXPER= 1 to 30 years. Explain why the four artists
with no experience are not used in the estimation of Model 2.
c. Using Model 1, compute the marginal effect on RATING of another year of experience for (i) an
artist with 10 years of experience and (ii) an artist with 20 years of experience.
d. Using Model 2, compute the marginal effect on RATING of another year of experience for (i) an
artist with 10 years of experience and (ii) an artist with 20 years of experience.
e. Which of the two models fits the data better? Estimation of Model 1 using just the technical artists
with some experience yields R² = 0.4858.
f. Do you find Model 1 or Model 2 more reasonable, or plausible, based on economic reasoning?
Explain.
4.5 Consider the regression model WAGE=B₁ + BEDUC+ e. WAGE is hourly wage rate in U.S. 2013
dollars. EDUC is years of education attainment, or schooling. The model is estimated using individu-
als from an urban area.
WAGE= -10.76+2.461965EDUC, N=986
(2.27) (0.16)
(se)
a. The sample standard deviation of WAGE is 15.96 and the sum of squared residuals from the regres-
sion above is 199,705.37. Compute R².
b. Using the answer to (a), what is the correlation between WAGE and EDUC? [Hint: What is the
correlation between WAGE and the fitted value WAGE?]
c. The sample mean and variance of EDUC are 14.315 and 8.555, respectively. Calculate the leverage
of observations with EDUC=5, 16, and 21. Should any of the values be considered large?
d. Omitting the ninth observation, a person with 21 years of education and wage rate $30.76, and
reestimating the model we find = 14.25 and an estimated slope of 2.470095. Calculate DFBETAS
for this observation. Should it be considered large?
e. For the ninth observation, used in part (d), DFFITS = -0.0571607. Is this value large? The leverage
value for this observation was found in part (c). How much does the fitted value for this observation
change when this observation is deleted from the sample?
f. For the ninth observation, used in parts (d) and (e), the least squares residual is -10
late the studentized residual. Should it be considered large?
of squarei
ha hand.
4.6 We have five observations on x and y. They are x, = 3,2,1,-1,0 with correspo
10. The fitted least squares line is
= 1.2+0.8x,. the
10. Carry out this ex](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F9c562bd6-5248-485a-84e5-42417dff7653%2Fwa2kjp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7:21
Prediction, Goodness-of-Fit, and Modeling Issues
a. Sketch the fitted values from Model 1 for EXPER=0 to 30 years.
b. Sketch the fitted values from Model 2 against EXPER= 1 to 30 years. Explain why the four artists
with no experience are not used in the estimation of Model 2.
c. Using Model 1, compute the marginal effect on RATING of another year of experience for (i) an
artist with 10 years of experience and (ii) an artist with 20 years of experience.
d. Using Model 2, compute the marginal effect on RATING of another year of experience for (i) an
artist with 10 years of experience and (ii) an artist with 20 years of experience.
e. Which of the two models fits the data better? Estimation of Model 1 using just the technical artists
with some experience yields R² = 0.4858.
f. Do you find Model 1 or Model 2 more reasonable, or plausible, based on economic reasoning?
Explain.
4.5 Consider the regression model WAGE=B₁ + BEDUC+ e. WAGE is hourly wage rate in U.S. 2013
dollars. EDUC is years of education attainment, or schooling. The model is estimated using individu-
als from an urban area.
WAGE= -10.76+2.461965EDUC, N=986
(2.27) (0.16)
(se)
a. The sample standard deviation of WAGE is 15.96 and the sum of squared residuals from the regres-
sion above is 199,705.37. Compute R².
b. Using the answer to (a), what is the correlation between WAGE and EDUC? [Hint: What is the
correlation between WAGE and the fitted value WAGE?]
c. The sample mean and variance of EDUC are 14.315 and 8.555, respectively. Calculate the leverage
of observations with EDUC=5, 16, and 21. Should any of the values be considered large?
d. Omitting the ninth observation, a person with 21 years of education and wage rate $30.76, and
reestimating the model we find = 14.25 and an estimated slope of 2.470095. Calculate DFBETAS
for this observation. Should it be considered large?
e. For the ninth observation, used in part (d), DFFITS = -0.0571607. Is this value large? The leverage
value for this observation was found in part (c). How much does the fitted value for this observation
change when this observation is deleted from the sample?
f. For the ninth observation, used in parts (d) and (e), the least squares residual is -10
late the studentized residual. Should it be considered large?
of squarei
ha hand.
4.6 We have five observations on x and y. They are x, = 3,2,1,-1,0 with correspo
10. The fitted least squares line is
= 1.2+0.8x,. the
10. Carry out this ex
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