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Accounting, Finance, SPSS

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# Statistical Data Analysis (Math Problem Sample)

Instructions:

The task involves conducting a detailed statistical data analysis for a project in statistical data analysis, specifically focusing on linear regression and cost function analysis. Part I requires a complete linear regression analysis on the relationship between major and minor axis lengths of dry beans, while Part II involves comparing two alternative cost functions for indirect manufacturing labor costs, using machine hours and direct manufacturing labor hours as independent variables. The final report should include all solution procedures, highlighted final answers, and justifications for the chosen models.
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Content:

Please read the following instructions very carefully before answering any questions:
* Please read all the questions very carefully.
* Please provide your answers in the boxes below each question, and do not change the text color.
* Your answer MUST show the solution procedure. There is no credit if you only state the final answer.
* Please highlight your final answer to each question.
* Please keep the naming conventions requested in this document and each question.
* Once you complete your tasks, rename your Word document file to the (CPAN123_FinalProject_FirstName_LastName). Replace FirstName and LastName with your first name and last name, respectively.
Part IComplete Linear Regression Model Analysis (60%)
A study in Computers and Electronics in Agriculture (Vol. 174, 2020) provides a method for obtaining uniform seed varieties from crop production. A computer vision system was developed to distinguish seven different registered varieties of dry beans with similar features in order to obtain uniform seed classification.
Images of 13,611 grains of the seven beans were taken with a high-resolution camera for the classification model. The images obtained using the computer vision system were subjected to segmentation and feature extraction stages, and a total of 16 features, 12 dimensions, and four shape forms were obtained from the grains.
Here, you are going to analyze the relationship between the major axis length (y) (in pixels) and the minor axis length (x) (in pixels) of the beans, in which y is the distance between the ends of the longest line that can be drawn from a bean and x is the longest line that can be drawn from the bean while stationed perpendicular to the main axis. The data are saved in a file named "BeanDataset.csv" accompanied by this project on the Blackboard.
You must conduct a complete, simple linear regression analysis of the data. Summarize your findings in a professional report. (Hint: See the Complete example in the slides.)
LINK Excel.SheetBinaryMacroEnabled.12 "C:\\Users\\BEEMARK\\Documents\\Part II.csv" "Regression !R1C1:R19C10" \a \f 4 \h \* MERGEFORMAT
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.826055
R Square
0.682367
Adjusted R Square
0.682343
Standard Error
48.29688
Observations
13610
ANOVA
df
SS
MS
F
Significance F
Regression
1
68190541
68190541
29233.85
0
Residual
13608
31741869
2332.589
Total
13609
99932410
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
1.764743
1.907595
0.925114
0.354923
-1.97441
5.503892
-1.97441
5.503892
173.8887
1.574039
0.009206
170.9791
0
1.555994
1.592084
1.555994
1.592084
Based on the provided regression output, the relationship between the major axis length (y) and the minor axis length (x) of the beans is highly significant, with an R-squared value of 0.6824, indicating that approximately 68.24% of the variance in the major axis length can be explained by the minor axis length. The F-statistic is very large (29233.85) with a significance level of virtually zero, providing strong evidence against the null hypothesis that there is no linear relationship between the two variables.
The coefficient for the minor axis length (x) is 173.8887 with a p-value of 0, which is statistically significant. This means that for each pixel increase in the minor axis length, the major axis length increases by about 174 on average.
In conclusion, the minor axis length is a highly reliable predictor of the major axis length in this bean variety classification model. The strong correlation and the high significance level suggest that the computer vision system's measurements of minor axis lengths are very effective in predicting the major axis lengths of the beans, contributing to a robust method for achieving uniform seed classification.
Part IICritical Analysis Challenge (40%)
Models of past cost behavior are called cost functions. Factors influencing costs are called cost drivers (Horngren, Datar, and Rajan, Cost Accounting, 2018). Assume the cost data shown below are from a rug manufacturer. Indirect manufacturing labor costs consist of machine maintenance costs and setup labor costs. Machine hours and direct manufacturing labor hours are cost drivers.
Week
Indirect
Manufacturing
Labor Costs
Machine-Hours
Direct
Manufacturing
Labor-Hours
1
$1,190
68
30
2
1,211
88
35
3
1,004
62
36
4
917
72
20
5
770
60
47
6
1,456
96
45
7
1,180
78
44
8
710
46
38
9
1,316
82
70
10
1,032
94
30
11
752
68
29
12
963
48
38
Your task is to estimate and compare two alternative cost functions for indirect manufacturing labor costs. In the first, machine hours are the independent variable; in the second, direct manufacturing labor i...

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