Question

In: Statistics and Probability

The number of cans of soft drinks sold in a machine each week is recorded below...

The number of cans of soft drinks sold in a machine each week is recorded below

WEEKLY PERIOD

1

2

3

4

5

6

7

8

SOFT DRINKS SOLD

122

85

92

98

110

108

115

102

WEEKLY PERIOD

9

10

11

12

13

14

15

16

SOFT DRINKS SOLD

95

98

105

125

85

106

140

84

WEEKLY PERIOD

17

18

19

20

21

22

23

24

SOFT DRINKS SOLD

92

85

78

105

111

152

140

108

A. USING EXCEL, develop forecasts for periods 1 to 24 using a trend line.

B. Calculate the MSE AND MAD

C. CALCULATE and R statistic and interpret it.

PLEASE SHOW WORK IN EXCEL-SNAPSHOT AND EXPLANATION OF METHOD.

THANK YOU!!

Solutions

Expert Solution


SOLUTION:

(a) The trend line equation is Y=a+bx

      Using Excel a=INTERCEPT(y values,x values)

                        b=SLOPE(Y values,X values)

              a=3.6714
              b=0.0833

The trend line equation is Y=3.6714+0.0833X

forecast values

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.225695094
R Square 0.050938276
Adjusted R Square 0.007799106
Standard Error 7.043439833
Observations 24
ANOVA
df SS MS F Significance F
Regression 1 58.57901687 58.57901687 1.18078944 0.288958336
Residual 22 1091.420983 49.61004469
Total 23 1150
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 3.671454219 8.250848476 0.44497899 0.660682239 -13.43975814 20.78266658 -13.4397581 20.78266658
X Variable 1 0.083386501 0.076737831 1.086641357 0.288958336 -0.075758019 0.242531021 -0.07575802 0.242531021
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 13.84460733 -12.84460733
2 10.75930679 -8.759306794
3 11.3430123 -8.3430123
4 11.84333131 -7.843331306
5 12.84396932 -7.843969316
6 12.67719631 -6.677196314
7 13.26090182 -6.260901821
8 12.17687731 -4.176877309
9 11.5931718 -2.593171803
10 11.84333131 -1.843331306
11 12.42703681 -1.427036812
12 14.09476683 -2.094766829
13 10.75930679 2.240693206
14 12.51042331 1.489576687
15 15.34556434 -0.345564343
16 10.67592029 5.324079707
17 11.3430123 5.6569877
18 10.75930679 7.240693206
19 10.17560129 8.824398712
20 12.42703681 7.572963188
21 12.92735582 8.072644183
22 16.34620235 5.653797647
23 15.34556434 7.654435657
24 12.67719631 11.32280369

(b) Calculate MSE and MAD in Excel

period soft drinks sold(At) Predicted Y(Ft) At-Ft (At-Ft)^2
1 122 13.84460733 108.1553927 11697.58896
2 85 10.75930679 74.24069321 5511.680528
3 92 11.3430123 80.6569877 6505.549665
4 98 11.84333131 86.15666869 7422.971561
5 110 12.84396932 97.15603068 9439.294298
6 108 12.67719631 95.32280369 9086.436902
7 115 13.26090182 101.7390982 10350.8441
8 102 12.17687731 89.82312269 8068.19337
9 95 11.5931718 83.4068282 6956.69899
10 98 11.84333131 86.15666869 7422.971561
11 105 12.42703681 92.57296319 8569.753513
12 125 14.09476683 110.9052332 12299.97074
13 85 10.75930679 74.24069321 5511.680528
14 106 12.51042331 93.48957669 8740.300949
15 140 15.34556434 124.6544357 15538.72833
16 84 10.67592029 73.32407971 5376.420665
17 92 11.3430123 80.6569877 6505.549665
18 85 10.75930679 74.24069321 5511.680528
19 78 10.17560129 67.82439871 4600.149061
20 105 12.42703681 92.57296319 8569.753513
21 111 12.92735582 98.07264418 9618.243537
22 152 16.34620235 135.6537976 18401.95282
23 140 15.34556434 124.6544357 15538.72833
24 108 12.67719631 95.32280369 9086.436902
total 2541 300 2241 216331.579

MSE=

      =216331.579/24
      =9013.8157

MAD=

       =2241/24
        =93.375

Therefore MSE is 9013.8157 and MAD is 93.375

(c) R=0.2256

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.225695094
R Square 0.050938276
Adjusted R Square 0.007799106
Standard Error 7.043439833
Observations 24

orchestra answered 1 year ago
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