Question

Time Series Regression (10 marks)
The table below presents the number of students attending Statistics lectures in weeks 1 to 10
Week Number of students
1 90
2 82
3 75
4 70
5 59
6 51
7 48
8 40
9 41
10 35
Required:
(a) Write down the estimated Linear Trend Regression equation. (5 marks )
(b) Use the estimated equation to forecast the number of students present in week 11.

QUESTION 1 Time Series Regression (10 marks) The table below presents the number of students attending Statistics lectures in weeks 1 to 10 Number of students Week 90 1 82 3 75 70 4 59 6 51 7 48 8 40 9 41 10 Required: (a) Write down the estimated Linear Trend Regression equation. (5 marks) (b) Use the estimated equation to forecast the number of students present in week 11. (5 marks) ca

Answer 1

a week (x-mx)2 cx-mx) cy-my. No. of students. су) go 82 75 70 59 51 48 40 41 - 35 20.25 12.25 6.25 2 .5 0.25 -139.05 - 80.15 - 39.75 - 16.35 0.05 -4.05 -16.65 -67.75 -63.35 - 108.45 Total: - 515.5 2.25 6.25 12.25 20.25 825 TO Sum of x = 55 Sum of Y = 591 Mean (*) - Mx = 5.5 Meancy) - My = 59.1 Sum of squares Cssx) = 82.5 Sum of products CSP) = -515.5 Regression equation y = bx +a b= SP SSX a= My - bmx - - 515.5 - - 6.24848 82.5 = sg.l-(-6.25 5.5) *. a = 93.46667.

y = - 6.24848 X + 93.46667 This is estimated linear trend regression eq? for cast of no. of Students present in week !! x=11 y = - 6.24 848 CID) + 9 3.46667 . = -68.73328 + 93.46667 û = 24.7339 .. the number of students present in week late 25