Integer Components

Question

find the eigenvalues  of the following matrix A. For each eigenvalue, give an eigenvector with integer components.
 

A = (11/4 -3/4)
(-1/4 9/4)

Question

For the following scores X Y     3 0       8 10       7 8       5 3       7 7       6 8       

a. Find the   regression equation for predicting Y from X.   

b. Calculate   the predicted Y value for each X.  

Question

It is well known that similarity in attitude, beliefs, and   interests plays an important role in interpersonal attraction. Thus,   correlation for attitudes between married couples should be strong. Suppose a   researcher developed a questionnaire that measures how liberal or   conservative one’s attitudes are. Low scores indicate that the person has   liberal attitudes, whereas high scores indicate conservation. The following   hypothetical data are scores for married couples.       Couple wife   husband   A 11 14    B 6 7    C 16 15    D 4 7    E 1 3    F 10 9    G 5 9    H 3 8     

     Calculate person   correlation and determine whether there is a significant correlation between   attitudes for husbands and wives. Set alpha at .05 two tailed.