A collector of antique clocks sold at auction believes that the price received for the clocks may be modeled as a linear function of the age of the clocks and the number of bidders at the auction. After a preliminary study and collection of 32 observations, the collector came up with the following second-order model: y = BO+B₁x₁+B₂x₂ + 3x₁x2 +4x²+e, where y: price of a clock; x₁: age of a clock; x₂: the number of bidders. Considering the output below and by setting a = 0.05, answer the following questions. The regression equation is Price = 262 +2.26 Age + 14.2 Bidder + 1.13 AgeBid 4.20 Bid^2 Predictor Constant Age Bidder AgeBid Bid^2 S = 84.512 Coef SE Coef T P 404.4 -0.65 0.523 2.052 1.10 0.280 -261.7 2.260 14.21 60.83 0.23 0.817 5.17 0.000 0.219 1.344 -3.12 0.004 R-Sq- 96.08 R-Sq (adj) 1.1301 -4.196 Analysis of Variance Source Variable Age Bidder AgeBid Bid^2 Regression Residual Error 27 Total DF SS MS F 4 4606950 1151737 161.26 0.000 192840 7142 31 4799790 - 95.4% a. Is the model useful as a whole? Apply an appropriate F-test (state the hypothesis, critical F value, conclusion, etc.) and confirm your conclusion by stating the p-value. b. Is Bid^2 (i.e., x) a significant variable to predict y? Apply a t-test (state the hypothesis, critical t value, conclusion, etc.). c. By considering the p-values, state the statistically significant predictors and state which ones should be removed from the model, i.e., fill in the table below. Significant? (Yes or No) Remove? (Yes or No) Why? d. A 95% confidence interval for ₁ will be (circle the correct answer): i. 2.26±1 (84.512) iii. 2.26±1os (2.052) ii. 2.26± 10025 (0.219) iv. 2.26±tos (2.052)
A collector of antique clocks sold at auction believes that the price received for the clocks may be modeled as a linear function of the age of the clocks and the number of bidders at the auction. After a preliminary study and collection of 32 observations, the collector came up with the following second-order model: y = BO+B₁x₁+B₂x₂ + 3x₁x2 +4x²+e, where y: price of a clock; x₁: age of a clock; x₂: the number of bidders. Considering the output below and by setting a = 0.05, answer the following questions. The regression equation is Price = 262 +2.26 Age + 14.2 Bidder + 1.13 AgeBid 4.20 Bid^2 Predictor Constant Age Bidder AgeBid Bid^2 S = 84.512 Coef SE Coef T P 404.4 -0.65 0.523 2.052 1.10 0.280 -261.7 2.260 14.21 60.83 0.23 0.817 5.17 0.000 0.219 1.344 -3.12 0.004 R-Sq- 96.08 R-Sq (adj) 1.1301 -4.196 Analysis of Variance Source Variable Age Bidder AgeBid Bid^2 Regression Residual Error 27 Total DF SS MS F 4 4606950 1151737 161.26 0.000 192840 7142 31 4799790 - 95.4% a. Is the model useful as a whole? Apply an appropriate F-test (state the hypothesis, critical F value, conclusion, etc.) and confirm your conclusion by stating the p-value. b. Is Bid^2 (i.e., x) a significant variable to predict y? Apply a t-test (state the hypothesis, critical t value, conclusion, etc.). c. By considering the p-values, state the statistically significant predictors and state which ones should be removed from the model, i.e., fill in the table below. Significant? (Yes or No) Remove? (Yes or No) Why? d. A 95% confidence interval for ₁ will be (circle the correct answer): i. 2.26±1 (84.512) iii. 2.26±1os (2.052) ii. 2.26± 10025 (0.219) iv. 2.26±tos (2.052)
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
Transcribed Image Text:A collector of antique clocks sold at auction believes that the price received for the clocks may
be modeled as a linear function of the age of the clocks and the number of bidders at the auction.
After a preliminary study and collection of 32 observations, the collector came up with the
following second-order model:
y = BO+B₁x₁+B₂x₂ + ß3 x1x2 +B4x² +ɛ, where y: price of a clock; x₁: age of a clock; x2: the
number of bidders. Considering the output below and by setting a = 0.05, answer the following
questions.
The regression equation is
Price = 262 +2.26 Age + 14.2 Bidder + 1.13 AgeBid 4.20 Bid^2
Predictor
Constant -261.7
2.260
14.21
Age
Bidder
AgeBid
Bid^2
S = 84.512
Coef SE Coef
1.1301
-4.196
Analysis of Variance
Source
404.4
2.052
R-Sq= 96.0%
Variable
Age
Bidder
AgeBid
Bid^2
60.83 0.23
5.17 0.000
0.219
1.344 -3.12 0.004
R-Sq (adj)
DF
Regression
4
4606950
Residual Error 27 192840
Total
31 4799790
SS
T
P
-0.65 0.523
1.10 0.280
0.817
a. Is the model useful as a whole? Apply an appropriate F-test (state the hypothesis, critical F
value, conclusion, etc.) and confirm your conclusion by stating the p-value.
Significant?
(Yes or No)
95.4%
MS
F P
1151737 161.26 0.000
7142
b. Is Bid^2 (i.e., x2) a significant variable to predict y? Apply a t-test (state the hypothesis,
critical t value, conclusion, etc.).
c. By considering the p-values, state the statistically significant predictors and state which ones
should be removed from the model, i.e., fill in the table below.
Remove?
(Yes or No)
Why?
d. A 95% confidence interval for ₁ will be (circle the correct answer):
27
27
i. 2.26± 25 (84.512)
iii. 2.26± 1.025 (2.052)
30
ii. 2.26±1025 (0.219)
iv. 2.26±1.05 (2.052)
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