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# How does correlation analysis differ from regression analysis?

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1. (a) How does correlation analysis differ from regression analysis? (b) What does a correlation coefficient reveal? (c) State the quick rule for a significant correlation and explain its limitations. (d) What sums are needed to calculate a correlation coefficient? (e) What are the two ways of testing a correlation coefficient for significance?

12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at &#945; = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

12.50 In the following regression, X = total assets (\$ billions), Y = total revenue (\$ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two- tailed test for zero slope, and use Appendix D to find the critical value at &#945; = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression

13.30 A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors: LifeExp (life expectancy in years), InfMort (infant mortality rate), Density (population density per square kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.

13.32 An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.

14.16 (a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992-2003 only. Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your choice to the 1992-2003 data. (f) Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set?

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## Correlation and regression analysis :MAT 300

Regression:
Using the height and weight of five people as listed below.
Height (inches) 67 66 66 62 63
Weight 148 173 131 123 115
Step 1: Calculate correlation coefficient (r) between height and weight.
Step 2: Determine if a significant linear correlation exists between height and weight.
Step 3: Find predicted value (weight) for a person that is 5 feet and 11 inches:
a. If significant linear correlation exists, use regression equation
b. If no significant linear correlation exists, use the sample mean
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Problem 2:
Historical Data Set in 1908, "Student" (William Gosset) published the article "The Probable Error of a Mean" (Biometrika, Vol.6, No. 1). He included the data listed below for two different types of straw seed (regular and kiln dried) that were used on adjacent plots of land. The listed values are the yields of straw in cwt per acre.
a. Using a 0.05 significance level, test the claim that there is no difference between the yields from the two types of seed.
b. Construct a 95% confidence interval estimate of the mean difference between the yields from the two types of seed.
c. Does it appear that either type of seed is better?
Regular 19.25 22.75 23 23 22.5 19.75 24.5 15.5 18 14.25 17
Kiln Dried 25 24 24 28 22.5 19.5 22.25 16 17.25 15.75 17.25

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