woodsAA#5a

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Trevecca Nazarene University *

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6073

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Industrial Engineering

Date

Apr 3, 2024

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docx

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5

Uploaded by GeneralMorningAnt104

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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. 0 10 20 30 40 50 60 70 80 0.0 50.0 100.0 Humidity Line Fit Plot Temp Predicted Temp Humidity Temp 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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