Question: Although outliers should never be deleted without a reason, there are several reasons why it may be legitimate to conduct an analysis without them. Delete the data point for row 17 (click on the cell with the IQ of 114, enter * and then click on any other cell - this "enters" the asterisk in that previous cell.) and re-calculate the regression line for the remainder of the data (see above to recall how to get regression equation) . You should obtain the following output:

Regression Analysis: Math Score versus IQ

The regression equation is

Math Score = - 32.2 + 0.676 IQ

19 cases used, 1 cases contain missing values

Predictor Coef SE Coef T P

Constant -32.18 10.51 -3.06 0.007

IQ 0.67601 0.09718 6.96 0.000

S = 2.56190 R-Sq = 74.0% R-Sq(adj) = 72.5%

Analysis of Variance

Source DF SS MS F P

Regression 1 317.58 317.58 48.39 0.000

Residual Error 17 111.58 6.56

Total 18 429.16

1. Use the regression line with the Student 17 deleted to estimate the math score for an individual who has an eighth grade IQ o114.. Do you think this estimate could be achieved by anybody?
2. What does the value of R ² represent (just use the latest output)? (Explain it using the variables from this data).
3. What is the correlation between Math Score and IQ for both the data sets, including and excluding the outlier?
4. Use software to find the correlation between Math Score and IQ (you can pick whether do include the outlier or not) Does this correlation value agree with the value you found in part c ?
5. How does the fit of the regression line of the original data (i.e. with outlier) compare (visually and statistically) to the fit of the regression line to the data with the outlier removed? Compare the fit of the regression line between the two sets of data. Pay particular attention to the differences in R ² , the slope and how the line fits each set of data. You may want to repeat the residual plot and probability plot!
6. Facts about correlation . Answer the following questions about correlation (r).
   1. What is the strongest the correlation can ever be? _____
   2. If there is no relationship, r is equal to __________.
   3. The correlation coefficient ranges from ________ to _______.
   4. If the points fall in an almost perfect, negative linear pattern, r is close to: _____
   5. If the points fall in an almost perfect, positive linear pattern, r is close to: _____

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