代做STAT3600 LINEAR STATISTICAL ANALYSIS 2022代做留学生SQL语言程序

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE

STAT3600

LINEAR STATISTICAL ANALYSIS

May 23, 2022

1.     You are given the  following matrices computed  for a regression analysis

Y = β0 + β1X1 + β2X2 + ε having normal error with zero mean and variance σ2.

The elements of the matrices are properly ordered according to the regression function given above. The total sum of squares is equal to SST = 261.96 (rounded to 2 decimal  places).

(a) Find the least squares estimates of β = (β0, β 1, β2)T  [Give 4 significant figures].    [3 marks]

(b) An unbiased estimate of σ2 is given as  ^(σ)2 = SSE/(n-p-1), where SSE is the error sum of squares. Rewrite SSE using the matrices YTY, XTY and  β(̂), and hence compute  ^(σ)2  [Give 4 significant figures].            [4 marks]

(c) Construct  an ANOVA table  for the regression analysis.  Test whether there is  a regression between the dependent and the independent variables at the 5% level of significance.         [4 marks]

If you cannot obtain  ^(σ)2  in (b), you may take  ^(σ)2  =  1.238 as an estimate of σ2  for the following questions.

(d) Test at the 5% level of significance,

(i)     β 1 = 10 or not.

(ii)     β2 = 1 or not.                                                                                         [6 marks]

(e) Test at the 5% level of significance, for the hypothesis,

H0  : β1 = 10    and    β2 = 1      versus      H1  : H0            is not true,

[6 marks]

           (f)  Obtain  the joint  Bonferroni  interval  estimates  for β 1   and β2,  using  a  95% joint confidence coefficient. (Some values of tα,df are provided in the table shown below.)             [4 marks]

           (g) Compare and comment on the results you obtained in (d) – (f).                    [7 marks]

The values of tα,dfare given in the following table.

[Total: 34 marks]

2.      A psychologist conducted an experiment to study the effects of the type of training program (Factor A,  1: structured, 2: partially structured, 3: unstructured) and gender (Factor B,  1:  Male,  2:  Female)  of  12 ten-year-old  children with mental retardation syndrome on the time (Y) for completing a specific task. The data (in minutes) are given in the following table.

Consider a two-way classification model with interaction.

(a) Sketch the line plot of estimated treatment means against gender. (i.e. x-axis is gender). Does it appear that any factor effects are present? Explain your answer.    [6 marks]

(b) Part of the ANOVA table for fitting the two-way classification model is given below. Fill in the blanks marked by "?" in theANOVA table.                                  [4 marks]

(c) Test at the 5% level of significance whether or not there is a relationship between Y and the two factors.                    [5 marks]

(d) Test at the 5% level of significance for the interaction effects between the two factors, irrespective of the findings obtained in (c).                   [2 marks]

(e) Test whether or not factor A main effects are present, irrespective of the findings obtained in (c) and (d). Do something similar for factor B. In each case, use the 5% level of significance.          [4 marks]

(f)  Obtain a 95% prediction interval of the time for completing the specific task for a ten-year-old female child taking a structured training program.                   [5 marks]

(g) Construct a 95% prediction interval for the difference in the time for completing the specific task between two ten-year-old  children taking the unstructured training program, one being a male, while the other being a female. Is it reasonable to construct such an interval? Why or why not?                                                [7 marks]

[Total: 33 marks]