Sta 210 Homework 6: 1) What effect did the extreme value have on the correlation

Question

Sta 210 Homework 6:
1) What effect did the extreme value have on the correlation coefficient, r for this data set?
2) Is it justified to use the regression model to predict murder rate based on debt?
simple linear regression results: Dependent Variable: Murder Independent Variable: Debt Murder- -6.4265359 +0.00022383944 Debt Sample size: 19 R (correlation coefficient) 0.77992651 R-sq 0.60828536 Estimate of error standard deviation: 3.2298575 Murder 25 20 Legend Fitted line 15 10t 100000 120000 80000 Debt 40000 60000 The above simple linear regression results are based on the same data as the previous output except a very extreme value (debt 120000, murder rate 25) was added to the data. Use this output to answer questions 17-18. 17) What effect did the extreme value have on the correlation coefficient, r for this data set? 18) Is it justified to use the regression model to predict murder rate based on debt?

Explanation / Answer

1)

Outliers can easily deflate or inflate the sample correlation coefficient. Usually, an outlier that is consistent with the trend of the majority of the data will inflate the correlation and an outlier that is not consistent with the rest of the data can substantially decrease the correlation.

Here in this data we see that, if debt is more then number of merders are also more. And the oulier observation also possess similar trend. So outlier will inflate the correlation coefficient r.

2)

From above result we see that R2 is 0.608. It means that debt variable explain only 60.8% variavtion in murder. It is failed to explain remaing 40% variation. Estimate of error standard deviation is also more. It means that there is much variation in the values of murder predicted from this model. So it is not justified to use the regression model to predict murder rate based on debt.  

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