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.

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Definitions:

Effective

The degree to which something is successful in producing a desired or intended result.

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Relative Worth

The value or importance of a job, task, or item compared to others, often assessed in the context of job evaluations or market value.