Mop and Broom Manufacturing has tracked the number of units sold of their most p
ID: 3300889 • Letter: M
Question
Mop and Broom Manufacturing has tracked the number of units sold of their most popular mop over the past twenty-four months. This is shown.
Month
Sales
Month
Sales
Month
Sales
8
298
16
355
24
418
Develop a linear trend line for the data. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Sales =
+
(month)
Compute a correlation coefficient for the data and evaluate the strength of the linear relationship. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Correlation coefficient is
. It indicates
linear relationship. (Use not rounded amounts to answer this question.)
Using the linear trend line equation, develop a forecast for the next period,month 25. (Round your answer to 2 decimal places, the tolerance is +/-0.01. Do not round intermediate results used to achieve this answer.)
Forecast for month 25 =
Month
Sales
Month
Sales
Month
Sales
1 239 9 305 17 377 2 250 10 333 18 384 3 249 11 350 19 358 4 266 12 347 20 375 5 263 13 359 21 400 6 278 14 373 22 400 7 392 15 375 23 4048
298
16
355
24
418
Explanation / Answer
Solution:
Required regression analysis for the given data for linear trend line is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.900360049
R Square
0.810648217
Adjusted R Square
0.802041318
Standard Error
25.04021982
Observations
24
ANOVA
df
SS
MS
F
Significance F
Regression
1
59055.72261
59055.7226
94.185861
2.0759E-09
Residual
22
13794.27739
627.012609
Total
23
72850
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
249.923913
10.55070879
23.687879
3.774E-17
228.0430823
271.8047437
Month
7.166086957
0.738395799
9.70494005
2.076E-09
5.634747803
8.69742611
Above regression model is statistically significant, so we can use this model for forecasting purpose.
Questions:
Develop a linear trend line for the data.
Answer:
Sales = 249.92 + 7.17*Month
Compute a correlation coefficient for the data and evaluate the strength of the linear relationship.
Answer:
Correlation coefficient for the given data is 0.900360049.
It indicates strong positive linear relationship.
Using the linear trend line equation, develop a forecast for the next period, month 25.
Answer:
Sales = 249.92 + 7.17*Month
Sales = 249.92 + 7.17*25
Sales = 429.17
Forecast for month 25 = 429.17
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.900360049
R Square
0.810648217
Adjusted R Square
0.802041318
Standard Error
25.04021982
Observations
24
ANOVA
df
SS
MS
F
Significance F
Regression
1
59055.72261
59055.7226
94.185861
2.0759E-09
Residual
22
13794.27739
627.012609
Total
23
72850
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
249.923913
10.55070879
23.687879
3.774E-17
228.0430823
271.8047437
Month
7.166086957
0.738395799
9.70494005
2.076E-09
5.634747803
8.69742611
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