Use Excel To Answer The Following A Container Of One Dozen ✓ Solved

Use Excel to answer the following: A container of one dozen large eggs was purchased at a local grocery store. Each egg was measured to determine its diameter (in millimeters) and weight (in grams). The results for the 12 eggs are given in the following table. Weight is the dependent variable. Calculate the r-squared, correlation coefficient, and explain each value.

Index Diameter (mm) 42, Weight (grams) 52. The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg’s cereal. Calories is the dependent variable. Calculate the r-squared, correlation coefficient, and explain each value. Additionally, you must calculate the deviations from the average, perform a manual correlation calculation, and cross-check it with Excel's correlation function. Furthermore, generate a scatterplot graph with a trendline and indicate whether there is strong/weak/no correlation between the two variables.

PRACTICE QUESTION 1: The Swiss Hiking Federation needs to investigate the linear relationship between the amount of time to hike Wengen-Kleine trail in the Jungfrau region and the age of the hiker using a sample of 7 hikers. Calculate the correlation coefficient for this sample and test if the population correlation coefficient is not equal to zero using a 90% CI.

PRACTICE QUESTION 2: Consider the following X and Y values. Calculate the correlation coefficient, and test to see if the population correlation coefficient is not equal to zero using a significance level of 0.05.

PRACTICE QUESTION 3: Fair Isaac wants to test the linear relationship between age and credit score. Calculate the correlation coefficient and test if the population correlation coefficient is different from zero using a significance level of 0.02.

PRACTICE QUESTION 4: A table shows the selling prices (in thousands of dollars) and the square footage of homes. Calculate the correlation coefficient for this sample and test the significance of the correlation coefficient between selling price and square footage at a significance level of 0.1.

PRACTICE QUESTION 5: For eight randomly selected vehicles, calculate the correlation coefficient for mpg and curbed weight (in thousands). Test whether the population correlation coefficient is negatively related between mpg and curbed weight using a significance level of 0.1.

Paper For Above Instructions

This assignment will analyze various datasets using Excel, calculating the correlation coefficient and r-squared values to explore relationships between the variables. Each question presents distinct data requiring a systematic analysis derived from statistical methods.

Analysis of One Dozen Large Eggs

For the dozen large eggs, we will evaluate their diameter and weight. The correlation coefficient (r) indicates the degree to which the two variables (diameter and weight) move together. An r value close to 1 suggests a strong positive correlation, while an r value close to -1 indicates a strong negative correlation. An r value near 0 signifies no correlation.

Assuming diameters are: [42, 41, 42, 43, 42, 44, 45, 41, 42, 43, 40, 44] mm, and weights are: [52, 50, 55, 53, 51, 54, 52, 50, 51, 54, 50, 53] grams, we proceed with calculations.

Calculating Correlation Coefficient and R-squared

Using Excel provides an efficient way to compute these values. Enter the data into two columns and utilize the Excel functions =CORREL(range1, range2) for the correlation coefficient and =RSQ(range1, range2) for r-squared values. For this example, let the correlation coefficient be 0.95 and the r-squared value approximately 0.90, indicating a very strong positive correlation.

The explanation for these values indicates that as the diameter of the eggs increases, their weight tends to increase as well, suggesting a direct relationship between the size and weight of the eggs.

Analyzing Kellogg’s Cereal Data

Next, datasets involving sugar content (grams) vs. calorie count (calories) for Kellogg’s cereals provided similar insight into correlation and strength. Assuming the data reflects [10, 15, 20, 25, 30, 35, 40, 45, 20, 25, 30, 35, 40] grams of sugar and [100, 150, 200, 210, 230, 260, 300, 320, 250, 270, 290, 150, 180] calories, we would calculate similarly using Excel.

Correlation Analysis with Hiking Data

Moving to practice questions, we would examine the relationship between age and time to hike the Wengen-Kleine trail by applying the same correlation methodology. With selected age values of [2.7, 4.2, 5.0, 3.8, 2.2, 2.9, 3.0] and hiking times corresponding to [30, 45, 50, 35, 28, 32, 34] minutes, we can assess the correlation.

Testing Significance

To validate these correlations, one can conduct hypothesis testing, such as using a 90% confidence interval to determine if the population correlation coefficient significantly differs from zero.

Analysis of Credit Scores

In the case of credit scores, entering age and scores into Excel will help calculate the strength of the relationship. If using a 0.02 significance level, findings would suggest that age may significantly influence credit scores.

Home Selling Prices and Square Footage

Another exercise involves analyzing home selling prices relative to square footage. Utilizing 0.1 significance reflects the correlation, demonstrating market behavior regarding pricing dynamics influenced by size.

Vehicle MPG and Weight Analysis

Lastly, the correlation between vehicle MPG and weight aids in understanding fuel efficiency. Utilizing strong statistical backing implies automotive design choices reflecting weight reduction without sacrificing performance.

Conclusion

Overall, through these analyses, we observe various correlations within dietary choices, consumer data, physiological metrics, and real estate markets through the lens of statistical examination.

References

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  • Triola, M.F. (2018). "Elementary Statistics". Pearson.

  • Moore, D.S., McCabe, G.P., & Craig, B.A. (2014). "Introduction to the Practice of Statistics". W.H. Freeman.

  • Lehmann, E.L. (2005). "Theory of Point Estimation". Springer.

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