A Regression Was Performed on a Sample of 16 Observations $\hat { Y }$

question 45

Essay

A regression was performed on a sample of 16 observations. The estimated equation is =23.5 - 14.28X1+6.72X2+15.68X3. The standard errors for the coefficients are Sb₁ = 4.2, Sb2 = 5.6, and Sb3 = 2.8. For this model, SST = 3809.6 and SSR = 3285.4.
$\hat { Y }$
a. Compute the appropriate t ratios.
b. Test for the significance of β₁, β2 and β3at the 5% level of significance.
c. Do you think that any of the variables should be dropped from the model? Explain.
d. Compute R² and Ra2 . Interpret R².
e. Test the significance of the relationship among the variables at the 5% level of significance.

---

Definitions:

Calorie Diet

A way of managing food intake by counting and controlling the number of calories consumed, often used for weight management or nutritional purposes.

Smoking

The inhalation of smoke from burning tobacco products, which is a major health risk factor for various diseases, including lung cancer and heart disease.

Pillows

Soft supports used for comfort, decoration, or support in various settings, including medical facilities to aid in patient comfort and positioning.

Tracheostomy Tube

A tube inserted through a surgical opening in the neck into the trachea to maintain an airway and facilitate breathing.