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Regression analysis

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I am attaching a word doc which contains and 2 questions and data. I need step by step answer for the questions in MS_WORD.

Step by step answer will help me understand the concept. Thank you. Please see attached file for full problem description.

A random sample of 85 utility stocks was taken to compare the amount of their annual dividends to the annualized yields of the dividends. The data are given in following Table.

a. Find the correlation coefficient.

b. Can we conclude that the variables are positively associated within the population
of all utilities? Use α = .05

c. Determine the regression equation and write about equation in brief.

Beginning in 1991, the nation's Department of Education began taking corrective and punitive actions against colleges and universities with high student-loan default rates. Those schools with default rates above 60% face suspension from the government's massive student-loan program, whereas schools with default rates between 40% and 60% are mandated to reduce their default rates by 5% a year or face a similar penalty (Tampa Tribune, June 21, 1989). A list of 66 colleges and universities in Florida with their student-loan default rate is provided in the table.

An SPSS printout giving descriptive statistics for the data set is shown below

a. Locate the mean and median default rates on the printout.

b. Locate the variance and standard deviation of the default rates on the printout.

c. What proportions of measurements would you expect to find within two standard deviations of the mean?

d. Determine the proportion of measurements (default rates) that actually fall within the interval of part c. Compare this result with your answer to part c.

e. Suppose the college with the highest default rate (Florida College of Business - 76.2%) was omitted from the analysis. Would you expect the mean to increase or decrease? Would you expect the standard deviation to increase or decrease?

f. Calculate the mean and standard deviation for the data set with Florida College of Business excluded. Compare these results with your answer to part e.

g. Answer parts c and d using the recalculated mean and standard deviation. This problem illustrates the dramatic effect a single observation can have on the analysis.

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Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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