woodsAA#5a
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School
Trevecca Nazarene University *
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Course
6073
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
docx
Pages
5
Uploaded by GeneralMorningAnt104
CASE #1
The scatter plots allow us to see the following:
- There is a negative linear relationship between temperature and MPG, meaning that MPG falls
with temperature.
- There doesn't seem to be a clear linear relationship between humidity and MPG.
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Humidity Line Fit Plot
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Predicted Temp
Humidity
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We can use SSP's correlation option to create a correlation matrix for these variables once the scatter plots have been created. The strength and direction of the linear relationships between the variables will be displayed in the correlation matrix. The correlation matrix is as follows:
| | Temperature | Humidity | MPG |
|--------|-------------|----------|---------|
| Temperature | 1.00 | -0.24 | -0.89** |
| Humidity | -0.24 | 1.00 | 0.19 |
| MPG | -0.89** | 0.19 | 1.00 |
It is evident from these regression models that Humidity has a positive coefficient and Temperature has a negative coefficient. This validates the trends found in the correlation matrix
and scatter plots.
Part2:
The correlation matrix shows that there is a strong negative correlation (r = -0.89, p < 0.01) between temperature and MPG.
- There is a weak positive correlation between humidity and MPG (r = 0.19, p > 0.05).
- There is a weak negative correlation between temperature and humidity (r = -0.24, p > 0.05).
We can use an alpha = 0.05 significance level to test for statistical significance. We can determine that there is statistical significance in the relationship between Temperature and MPG because the p-value for this correlation is less than 0.05. However, there is no statistically significant correlation between humidity and MPG.
Regression analysis is the next step. With MPG as the dependent variable, we can run two different bi-variate regression models for temperature and humidity. The regression equations are as follows: MPG = 60.23 - 0.35(Temperature)
MPG = 26.02 + 0.03(Humidity)
We can look at the coefficient of determination (R-squared) value to see which bi-
variate regression model is stronger. With temperature serving as the independent variable in the regression model, the R-squared value is 0.79, meaning that temperature accounts for 79% of the variation in MPG. The model with humidity as the independent variable has an R-squared
value of 0.04, indicating that humidity does not account for a significant portion of the variation
in MPG.
From these results, we can infer that while humidity does not appear to have a significant impact, temperature is a significant predictor of fuel economy (MPG). We can advise our client to concentrate on managing temperature in order to increase fuel efficiency.
CASE#2
Step 1: Identification of Variables
Annual Sales are a Dependent Variable (DV).
Advertising Expenses and Territory Rating are the Independent Variables (IV).
Quantity of New Accounts Potential Market
Step 2: Screening Data
Verify the assumptions of normalcy, outliers, and missing values. Assume that the data have undergone screening and are suitable for analysis.
Step 3: Analysis of Correlations
Every IV has a positive correlation with annual sales, according to the correlation table. With the exception of Territory Rating, all IVs have a significant correlation (p-value less than 0.05) with Annual Sales.
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Step 4: Premises
Assume that the data satisfy the linearity, homoscedasticity, and residual normality assumptions of correlation analysis.
Step 5: Recap
It appears from the scatter plots and correlation analysis that all IVs, with the exception of Territory Rating, could contribute to the explanation of the variation in Annual Sales. To ascertain the significance of the relationships and the relative importance of each IV, additional regression analysis is necessary.
PART2
Step 1: Identification of Variables
Annual Sales are a Dependent Variable (DV).
Spending on advertising is one of the independent variables (IV).
Quantity of New Accounts Potential Market
Step 2: Screening Data
Assume that the data have undergone screening and are suitable for analysis.
Step 3: Regression analysis The findings demonstrate that 61% of the variance in annual sales is explained by the regression model, which is statistically significant (F(3, 46) = 25.40, p < 0.001). Annual Sales are significantly positively impacted by all three IVs: Market Potential (β = 0.12, p = 0.267), Number of New Accounts (β = 0.21, p = 0.041), and Advertising Expenditures (β = 0.75, p < 0.001).
Step 4: Recap
Regression analysis indicates that the most significant predictors of annual sales are the number of new accounts and advertising expenditures, followed by market potential. With 61%
of the variance in annual sales explained, the model is deemed to be moderately strong. It suggests that in order to increase annual sales, the sales manager should concentrate on raising
advertising costs and the number of new accounts.