# Correlation and Regression Analysis

See attached files for full problem description.

31. The following cross tabulation shows household income by education level of the head of household.

Household Income (1000s)

Under 25.0- 50.0- 75.0- 100 or

Education level 25 49.9 74.9 99.9 more total

Not HS Grad 9285 4093 1589 541 354 15862

HS Graduate 10150 9821 6050 2737 2028 30786

Some College 6011 8221 5813 3215 3120 26380

Bachelorâ??s Deg. 2138 3985 3952 2698 4748 17521

Beyond Bach. Deg. 813 1497 1815 1589 3765 9479

TOTAL 28397 27617 19219 10780 14015 100028

a. Compute the row percentages and identify the percent frequency distribution of income for households in which the head of household is a high school graduate and in which the head of household holds a bachelorâ??s degree.

b. What percentage of households headed by high school graduates earn $75,000 or more? What percentage of households headed by bachelorâ??s degree recipients earn $75,000 or more?

c. Construct percent frequency histograms of income for households headed by persons with a high school degree and for those headed by persons with a bachelorâ??s degree. Is any relationship evident between household income and education level?

37. See excel file NFL

The National Football League rates prospects by position on a scale that ranges from 5 to 9. The ratings are interpreted as follows: 8-9 should start the first year; 7.0 â?" 7.9 should start; 6.0-6.9 will make the team as a backup; and 5.0-5.9 can make the club and contribute. Table 2.15 Excel File NFL shows the position, weight, speed (seconds for 40 yards), and ratings for 40 NFL prospects.

a. Prepare a crosstabulation of the data on Position (rows) and Speed (columns). Use classes of 4.00-4.49, 4.50-4.99, 5.00-5.99 for speed.

b. Comment on the relationship between Position and Speed based upon the crosstabulation developed in part (a)

c. Develop a scatter diagram of the data on Speed and Rating. Use the vertical axis for Rating.

d. Comment on the relationship, if any, between Speed and Rating.

45. Drug Store News provided data on annual pharmacy sales for the leading pharmacy retailers in the United States. The following data are annual sales in millions.

Retailer Sales Retailer Sales

Ahold USA 1700 Medicine Shoppe 1757

CVS 12700 Rite-Aid 8637

Eckerd 7739 Safeway 2150

Kmart 1863 Walgreens 11660

Kroger 3400 Wal-Mart 7250

a. Show a stem-and-leaf display

b. Identify the annual sales levels for the smallest, median, and largest drug retailers.

c. What are the two largest drug retailers?

47. See excel file HighLow

a. Develop a scatter diagram to show the relationship between the two variables, high temperature and low temperature.

b. Comment on the relationship between high and low temperatures.

5. â??â?See Excel Fileâ?â? named boats

a. Develop a scatter diagram for these data with baggage capacity rating as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between baggage capacity and price?

c. Draw a straight line through the data to approximate a linear relationship between baggage capacity and price?

d. Use the least squares method to develop the estimated regression equation

e. Provide an interpretation for the slope of the estimated regression equation.

f. Predict the price for a boar with a baggage capacity rating of 3.

7. Would you expect more reliable cars to cost more? Consumer Reports rated 15 upscale sedans. Reliability was rated on a 5-point scale: poor (1), fair (2), good (3), very good (4), and excellent (5). The price and reliability rating for each of the 15 cars are show. Please see excel file named CARS

a. Develop a scatter diagram for these data with the reliability rating as the independent variable.

b. Develop the least squares estimated regression equation.

c. Based upon your analysis, do you think more reliable cars cost more? Explain

d. Estimate the price for an upscale sedan that has a good reliability rating..

9. â?? Please see excel file Sales

A sales manager collected the following data on annual sales and years of experience.

a. Develop a scatter diagram for these data with years of experience as the independent variable.

b. Develop an estimated regression equation that can be used to predict annual sales given the years of experience.

c. Use the estimated regression equation to predict annual sales for a salesperson with nine years of experience.

17. x 2 6 9 13 20

i

y 7 18 9 26 23

i

^

These estimated regression equation for these data is y = 7.6 + .9x. What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

19. Please use excel !!

See attachment Cars

^

The estimated regression equation for these data is y = 40,639 â?" 1301.2x What percentage of the total sum of squares can be accounted for by the estimated regression equation? Comment on the goodness of fit. What is the sample correlation coefficient?

21. Please use the calculator for this problem.

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on production volume (units) and cost and using the least squares method to develop an estimated regression equation relating production volume and cost, an accountant can estimate the cost associated with a particular production volume. Consider the following sample of production volume and total cost data for a manufacturing operation.

Production Volume (units) Total Cost ($)

400 4000

450 5000

550 5400

600 5900

700 6400

750 7000

a. Use the data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.

b. What is the variable cost per unit produced?

c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume?

d. The companyâ??s production schedule shows 500 units must be produced next month.

What is the estimated total cost for this operation?

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#### Solution Summary

The solution gives the details of correlation and regression analysis in a step by step manner. Scatter diagram, regression coefficients, interpretation of regression coefficients are also given.