MS5218 – Assignment 1
(Please refer to “A Second Course in Statistics: Regression Analysis” 7th edition, International Edition)
Chapter 3 (10 marks for each question)
Q68 Q80
Chapter 4 (10 marks for each question)
Q10 Q14 Q88
Chapter 5 (10 marks for each question)
Q 16
Question S1 – Lack of Fit Test & Polynomial Models
(20 marks)
To promote safe driving habits and to better protect its customers, an insurance company offers a discount of between 5% and 20% on renewal insurance premiums to customers who have completed a defensive driving course. The following table of data shows the number of customers who have applied for the discount at various discount levels, over a period of 12 months, where Y = number of renewing customers applying for discount (in 100); X = discount in %. In particular, n = 12, SSYY = 471.79. A quadratic regression model of Y on X is fitted to the data and the results are summarized in the following table.
Month
XY
5 4.85 10.25 10.56 10.20 11.49 11.00 18.00 18.05 17.25 22.25 23.25 26.50
a. Set up the appropriate hypotheses to test the overall significance of the quadratic model. Compute the F- value. Conduct a lack-of-fit test for the quadratic model.
b. Suppose that a straight line mode of Y on X is considered, set up the appropriate hypotheses to test the overall significance of the straight-line model. Compute the F-value. Conduct a lack-of-fit test for the straight-line model.
c. Calculate the total percent of variation explained by the straight-line model and the quadratic model.
d. Set up the appropriate hypotheses to test the significance of the X2 term in the quadratic model when the X
term is already included in the model.
e. Based on the above results, which one is the better model? Give details to support your reasoning.
1
2 5 3 5 4 10 5 10 6 10 7 15 8 15 9 15
10 20 11 20 12 20
Due Date:
Nov 17, 2020 (Tuesday)
Question S2 – Comparing nested models (20 marks)
Modeling results of 46 cases of observations of Y on X1, SSYY = 9642.11
X2, X3 and X4 are listed in the following table with
Parameter DF Estimated
Intercept
X1 1
X2 1
X3 1
X4 1
Standard Error
52.833 1.300 0.235 0.205 0.009
Variable
t value
1.96 -1.98 2.97 -3.50 3.19
P-value
0.0572 0.0545 0.0051 0.0012 0.0028
Type I SS
– 2804.505
2535.467 600.905 789.954
assignment score correctly.
• Late work will NOT be accepted
1 103.551 -2.578
0.699 -0.718 0.030
a. Set up the hypotheses to test whether the three variables X2, X3 and X4 are needed when the first variable X1 is already in the model. Compute the F-value.
b. Which of the independent variable(s) can be concluded to be significant in explaining the variation in Y? Give details of your work.
c. Based on the above results, can we test the significance of the model with
i. (X1, X2)
ii. (X2, X3)
iii. (X3, X4), when (X1, X2) are already included in the model,
iv. (X1, X2, X4)
in the model? Give reasons to support your answer in each of the above four cases.
Note:
• Write your answers in A4-size paper format and prepare your work in pdf format using your CityU student I.D. number as the file name. For example, if your student ID is 12345678, then the submit pdf file should be named as 12345678_A1.pdf where A1 stands for Assignment 1.
• Please submit the pdf file to the Convas course account before midnight of the scheduled due date.
• Please follow the above two instructions closely, otherwise, it will cause much inconvenience to record your
The End