Q5 (6 points) The following data represents the number of supervised workers (X) and the number of supervisors. Suppose it follows a linear model Y = a + ẞX + e. 1 2 4 5 6 7 8 10 11 12 13 14 ÷ 15 14 X Y 32 49 44 56 100 247 311 358 450 615 627 630 688 697 97 84 80 78 700 850 999 1021 1200 1250 106 128 109 97 180 112 (a) Plot these (X,Y) data points (You can take following area plot as an example). Do you feel this plot suggest a constant variance? Why? (b) Suppose var(e) = k²X². To remove heteroscedastic errors, appropriate transformation is made and the regression output is as follows. Predict the number of supervisors when the number of supervised workers are 300 and construct a 95% prediction interval of response for it. Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) 0.12002 0.01315 9.126 5.15e-07 *** 6.68428 0.907 0.381 1/X 6.05961 Signif. codes: 0*** 0.001 **** 0.01 *** 0.05 0.1'1 Residual standard error: 0.02347 on 13 degrees of freedom Multiple R-squared: 0.05946, Adjusted R-squared: -0.01289 F-statistic: 0.8218 on 1 and 13 DF, p-value: 0.3811 (c) Suppose var(€) = k²X². Derive the appropriate transformation to remove heteroscedastic errors and write down the explicit model after transformation.
Q5 (6 points) The following data represents the number of supervised workers (X) and the number of supervisors. Suppose it follows a linear model Y = a + ẞX + e. 1 2 4 5 6 7 8 10 11 12 13 14 ÷ 15 14 X Y 32 49 44 56 100 247 311 358 450 615 627 630 688 697 97 84 80 78 700 850 999 1021 1200 1250 106 128 109 97 180 112 (a) Plot these (X,Y) data points (You can take following area plot as an example). Do you feel this plot suggest a constant variance? Why? (b) Suppose var(e) = k²X². To remove heteroscedastic errors, appropriate transformation is made and the regression output is as follows. Predict the number of supervisors when the number of supervised workers are 300 and construct a 95% prediction interval of response for it. Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) 0.12002 0.01315 9.126 5.15e-07 *** 6.68428 0.907 0.381 1/X 6.05961 Signif. codes: 0*** 0.001 **** 0.01 *** 0.05 0.1'1 Residual standard error: 0.02347 on 13 degrees of freedom Multiple R-squared: 0.05946, Adjusted R-squared: -0.01289 F-statistic: 0.8218 on 1 and 13 DF, p-value: 0.3811 (c) Suppose var(€) = k²X². Derive the appropriate transformation to remove heteroscedastic errors and write down the explicit model after transformation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Q5 (6 points) The following data represents the number of supervised workers (X) and the number of
supervisors. Suppose it follows a linear model Y = a + ẞX + e.
1
2
4 5 6 7
8
10
11
12
13 14 ÷ 15
14
X
Y
32
49
44
56 100
247 311 358 450 615 627 630 688 697
97
84
80
78
700 850 999 1021 1200 1250
106
128
109
97
180
112
(a) Plot these (X,Y) data points (You can take following area plot as an example). Do you feel this plot
suggest a constant variance? Why?
Transcribed Image Text:(b) Suppose var(e) = k²X². To remove heteroscedastic errors, appropriate transformation is made and
the regression output is as follows. Predict the number of supervisors when the number of supervised
workers are 300 and construct a 95% prediction interval of response for it.
Coefficients:
Estimate Std. Error t value Pr(>Itl)
(Intercept) 0.12002 0.01315 9.126 5.15e-07 ***
6.68428 0.907 0.381
1/X
6.05961
Signif. codes: 0*** 0.001 **** 0.01 *** 0.05 0.1'1
Residual standard error: 0.02347 on 13 degrees of freedom
Multiple R-squared: 0.05946, Adjusted R-squared: -0.01289
F-statistic: 0.8218 on 1 and 13 DF, p-value: 0.3811
(c) Suppose var(€) = k²X². Derive the appropriate transformation to remove heteroscedastic errors and
write down the explicit model after transformation.
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