A counselor working with teenagers is interested in the relationship between anxiety and depression. The counselor administers a depression and anxiety test to each teenager. The scores obtained from the administration of the two inventories are given in the following table.

Teenager Anxiety (ANX) Depression (DEP) 

• 1 22 16 
• 2 12 8 
• 3 68 33
•  4 10 6 
• 5 5 5 
• 6 53 24 
• 7 44 1
• 8 8 37 17 
• 9 0 2 
• 10 21 14 
• 11 64 31 
• 12 33 17 
• 13 55 30 
• 14 18 13 
• 15 3 3 
• 
  
• 1. Estimate the equation (DEP) ̂_i=β ̂_0+β ̂_1 〖ANX〗_i+ε_i using OLS. (8M) 
• 2. Calculate their variance and standard error. (5M) 
• 3. Comment on the direction of the relationship.(2M) 
• 4. Does the intercept have a useful interpretation here? Explain. (3M) 
• 5. Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum is zero. (6M) 
• 6. What is the predicted value of DEP when ANX=20? (2M) 
• 7. How much the variation in DEP for every eight students is explained by ANX? (4M)