A psychologist made a small scale study to examine the nature of the relation between an employee's emotional stability (Y) and the employee's ability to perform in a task group (X). Emotional stability was measured by a written test and ability to perform in a task group (X = 1 if able, X = 0 if unable) was evaluated by the supervisor. The results were as follows:
i: 1 2 3 4 5 6 7 8
Y_i 479 619 584 638 399 481 624 582
X_i 0 1 0 1 0 1 1 1
a) Fit a linear regression and write down the fitted model.
b) Write down separate estimated regression equations for "able" employees and "unable" employees.
c) Is there a linear relationship between X and Y? Test at 5% level.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.