Stat 200 Homework 4 Based On Chapter 4 To Calculate The Corr

Sta200homework 4based On Chapter 4 To Calculate The Correlation Fac

STA200 Homework 4: Based on Chapter 4. · To calculate the correlation factor (r), go to Excel, Formulas, Statistics, and select the CORREL function. · To calculate the Regression Equation and Coefficient of Determination: a. Select the x,y data b. Insert a scatter chart from that data c. Click the chart, go to Chart Design d. Go to Quick Layout e. Select Layout 9 f. Then you get the Regression Equation, and r square. 1) Exercise 23, page 159. Roadway congestion is a costly item, in both time wasted, and fuel wasted. Let X represent the average annual hours per person spent in traffic delays and let Y represent the average annual gallons of fuel wasted per person in traffic delays. a) Draw a scatter diagram for the data. b) Compute r (Coefficient of Correlation). c) Is there a correlation? X (hr) Y (gal) ) Exercise 7, page 172. Let X represent the total number of jobs in each neighborhood, and let Y represent the number of entry-level jobs in the same neighborhood. A sample of six neighborhoods gave the following information (units in hundreds of jobs). X Y a) Calculate the media of jobs. b) Calculate the media of entry-level jobs. c) Compute r (Coefficient of Correlation). d) Draw a scatter diagram for the data, showing the regression line. e) Calculate the Coefficient of Determination. f) Calculate the Regression Equation. g) Question: If a neighborhood with 40 jobs, how many are predicted to be entry-level jobs?

Paper For Above instruction

This paper provides a comprehensive analysis of the methods used to evaluate relationships between variables through correlation and regression techniques, as demonstrated in exercises based on Chapter 4 of a statistical textbook. The exercises involve calculating the correlation coefficient, constructing scatter diagrams, deriving regression equations, and interpreting the strength and significance of relationships between different data sets. Emphasizing the practical application of Excel functions and graphical tools, the analysis underscores the importance of these statistical tools in real-world decision-making scenarios, such as traffic management and urban planning.

The first exercise examines the relationship between average annual hours spent in traffic delays and fuel wasted per person, represented by variables X and Y, respectively. Using Excel’s CORREL function, the coefficient of correlation (r) quantifies the degree of linear relationship between these variables. A scatter diagram visually illustrates the data, providing insights into the pattern and strength of association. The calculation of r involves using paired data points to determine the degree of linearity, with values close to +1 or –1 indicating strong positive or negative correlations, respectively. The existence of a significant correlation suggests that as traffic delays increase, fuel wastage also tends to increase, highlighting the interconnectedness of traffic congestion and fuel consumption.

The second exercise explores the linkage between the total number of jobs in a neighborhood (X) and the number of entry-level jobs (Y). Initially, the median (likely meant as 'mean') number of jobs in each category is calculated to understand the central tendency. Subsequently, the correlation coefficient is computed to assess the strength of the linear relationship between total jobs and entry-level jobs across six neighborhoods. Graphical representation through scatter diagrams, along with the regression line, visually demonstrates the relationship. Calculating the coefficient of determination (r^2) reveals the proportion of variance in entry-level jobs that can be explained by the total number of jobs. The derived regression equation allows for prediction of entry-level jobs based on the total number of jobs, such as estimating the number of entry-level jobs in a neighborhood with 40 total jobs.

The integration of statistical theory with practical Excel applications underscores the importance of correlation and regression analyses in understanding and predicting real-world phenomena. The exercises highlight key concepts such as data visualization, measurement of association strength, and predictive modeling, which are fundamental in fields like urban planning, traffic management, and economic development. Mastery of these techniques enables analysts and decision-makers to draw meaningful insights from data, supporting effective planning and policy formulation.

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