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# Correlation and regression, hand calculations

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1st problem

A study is conducted concerning automobile speeds and fuel consumption rates. The following data is collected:

Speed MPG
44 22
51 26
48 21
60 28
66 33
61 32

a. Plot these data in a scatter diagram.

b. Compute the coefficient of correlation.

2nd problem

Tem Rousos, president of Rousos Ford, believes there is a relationship between the number of new cars sold and the number of sales people on duty. To investigate he selects a sample of eight weeks and determines the number of new cars sold and the number of sales people on duty for that week.

Week Salesstaff Carssold
1 5 53
2 5 47
3 7 48
4 4 50
5 10 58
6 12 62
7 3 45
8 11 60

a. Plot these data in a scatter diagram.

b. Determine the coefficient of correlation.

c. Determine the coefficient of determination. Comment on the strength of the association between the two variables.

d. Determine the regression equation.

e. Interpret the regression equation. Where does the equation cross the Y-axis? How many additional cars can the dealer expect to sell for each additional salesperson employed?

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#### Solution Preview

This solution shows details of how to calculate correlation ...

#### Solution Summary

This solution shows details of how to calculate correlation coefficients, and regression coefficients for simple linear regression by hand and gives an interpreation of the slope of the regression equation.

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