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# Statistics: Correlation coefficient, regression analysis

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1) Suppose the following table shows the number of colds 7 different people got during the typical cold season based on the number of times they washed they washed their hands per day during the cold season. Calculate the correlation coefficient and interpret its meaning as applied to this problem. In addition, using a hypothesis test determine if the correlation coefficient is statistically different from 0 (i.e. )

# of Times
Wash Hands # of Colds
0 7
1 4
2 3
3 2
4 2
5 3
6 1

2) The following regression line shows how the monthly return for the mutual fund TWCUX (Twentieth Century Ultra Fund) is mathematically related to the S&P500 monthly return.
TWCUX = -2.61 + 1.27 (S&P500)
Explain what both the intercept and slope of the regression line tell you in the context of this problem. Calculate what the estimated monthly return for TWCUX would be if the monthly return for the S&P 500 were 15%.

#### Solution Preview

Please see the attached files for the full calculation

1) Suppose the following table shows the number of colds 7 different people got during the typical cold season based on the number of times they washed they washed their hands per day during the cold season. Calculate the correlation coefficient and interpret its meaning as applied to this problem. In addition, using a hypothesis test determine if the correlation coefficient is statistically different from 0 (i.e. )

# of Times
Wash Hands # of Colds
0 7
1 4
2 3
3 2
4 2
5 3
6 1

Key: See the excel file. For correlation see excel sheet ...

#### Solution Summary

Correlation coefficient is calculated and interpretation of its meaning is also given in the solution.

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