9. DS 0412-10 Operations Management Fall 2017 My Courses DS041210-F17R FORECASTI
ID: 375462 • Letter: 9
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9.
DS 0412-10 Operations Management Fall 2017
My CoursesDS041210-F17RFORECASTINGQ9
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What is the slope of the linear regression line for the following time series? (Two decimal places needed.)
Months Sales
1 106
2 108
3 105
4 113
5 115
6 121
7 118
8 127
9 130
10 138
ans:
Explanation / Answer
months x
Sales y
x^2
y^2
x*y
1
106
1
11236
106
2
108
4
11664
216
3
105
9
11025
315
4
113
16
12769
452
5
115
25
13225
575
6
121
36
14641
726
7
118
49
13924
826
8
127
64
16129
1016
9
130
81
16900
1170
10
138
100
19044
1380
Sum
55
1181
385
140557
6782
a=[(y)( x2) –( x)( xy)] / [n(x2)-( x)2]
a =[(1181)(385) –( 55)(6782)] / [10(385)-(55)2] = 81675/825 =99
b=[n*( xy) –( x)( y)]/ [n(x2)-( x)2]
b=[10*( 6782) –( 55)( 1181)]/ [10(385)-( 55)2] =3.47
so the linear equation is given as:-
y’=b+ax
y’=3.47+99x
so the slope is b=3.47
months x
Sales y
x^2
y^2
x*y
1
106
1
11236
106
2
108
4
11664
216
3
105
9
11025
315
4
113
16
12769
452
5
115
25
13225
575
6
121
36
14641
726
7
118
49
13924
826
8
127
64
16129
1016
9
130
81
16900
1170
10
138
100
19044
1380
Sum
55
1181
385
140557
6782
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