Regression tests seek to determine one variable's ability to predict another variable.  In this analysis, one variable is dependent (the one predicted), and the other is independent (the variable that predicts).  Therefore, the dependent variable is the y-variable and the independent variable is the x-variable.

The key here is to utilize

.

"Perfect negative linear correlation" means , while the rest of the problem indicates  and . This enables us to solve for .

Use the formula .

Plug in the given values for and and this becomes an algebra problem.

An observation is an outlier if it falls more than  above the upper quartile or more than  below the lower quartile.

. The minimum value is  so there are no outliers in the low end of the distribution.

. The maximum value is  so there are no outliers in the high end of the distribution.

Use the  criteria:

This states that anything less than  or greater than  will be an outlier.

Thus, we want to find

  where .

Therefore, any new observation greater than 115 can be considered an outlier.

In order to find the outliers, we can use the  and  formulas.

Only two numbers are outside of the calculated range and therefore are outliers:  and .

Using the  and  formulas, we can determine that both the minimum and maximum values of the data set are outliers.

This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.

Step 1: Recall the definition of an outlier as any value in a data set that is greater than  or less than .

Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or . To find  and , first write the data in ascending order.

. Then, find the median, which is  . Next, Find the median of data below , which is  . Do the same for the data above  to get . By finding the medians of the lower and upper halves of the data, you are able to find the value,  that is greater than 25% of the data and , the value greater than 75% of the data. 

Step 3: . No values less than 64.

. In the data set, 105 > 104, so it is an outlier.  

An outlier is any data point that falls  above the 3rd quartile and below the first quartile.  The inter-quartile range is  and .  The lower bound would be  and the upper bound would be .  The only possible answer outside of this range is .

A residual plot shows the difference between the actual and expected value, or residual. This goes on the y-axis. The plot shows these residuals in relation to the independent variable.