# Correlation and Regression

The coach of the Ottawa football team wants to determine if there is a relationship between how fast players can run 60 m and how far they can throw the football. The results for the Ottawa players were as follows:

Player Spring Time (s) Throwing Distances (m)

Jon H. 7.92 32

Tom M. 8.66 29

Sarjay P. 6.58 35

Brandon F. 8.9 32

Tyler C. 7.12 34

Steve K. 8.76 29

Matt H. 7.55 40

Robin L. 7.37 33

Alex H. 7.96 30

Mike N. 8.45 31

Ankit K. 7.75 26

Scott R. 8.05 32

a.Using technology, create a scatter plot of sprint times versus throwing distances.

b.Perform a linear-regression analysis of the data to find the line of best fit and the correlation coefficient.

c.Describe the relationship between these sprint times and throwing distances.

d.State which data points could be identified as outliers, and explain why you chose them.

e.Remove the outliers and repeat the regression analysis. Determine the lines of best fit and the correlation coefficient for this smaller sample.

f.What might the coach conclude from this analysis? What limits the predictions he could make?

g.Use the two regression equations from parts b) and e) to estimate the throwing distance for a player whose sprint time is 6.50s.

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#### Solution Summary

The solution is comprised of detailed step-by-step calculations and explanation of the given problems related to Correlation and Regression Analysis. This solution provides students with a clear perspective of the underlying statistical aspects.

Linear Correlation, Regression Lines and Measures of Variation

1) Testing for a Linear Correlation

Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from the table below using a=0.05. Determine whether the is sufficient evidence to support a claim of a linear correlation between the two variables.

Airline Fares Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.05 significance level to test the claim that there is no difference in cost between flights scheduled one day in advance and those scheduled 30 days in advance. What appears to be a wise scheduling strategy?

Flight scheduled 30 days advance 244 260 264 264 278 318 280

Fight scheduled one day in advance 456 614 567 943 628 1088 536

Create scatter plot

2) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

CPI and Subway Fare ; Find the best predicted cost of a slice of pizza when the consumer price index is 182.5 in the year 2000

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.35 1.50 2.00

3) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

Commuters and Parking Space The Metro-North Station of Greenwich, CT has 2804 commuters . Find the best predicted number of parking spots at that station. Is the predicted value close to the actual value of 127?

Commuters 3453 1350 1126 3120 2641 277 579 2532

Parking Spots 1653 676 294 950 1216 179 466 1454

4) Finding Measures of Variation

Find (a) explained variation, (b) unexplained variation,(c) total variation, (d) coefficient of determination,and (e) standard error of estimate Se, In each case, there is sufficient evidence to support a claim of a linear correlation so that it is reasonable to use the regression equation when making predictions

CPI and Subway Fare The consumer price index and the cost of a slice of pizza from table 10-1

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.25 1.75 2.00