A Regression Was Performed on a Sample of 16 Observations $\beta$

question 97

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 S_b1 = 4.2, S_b2 = 5.6, and S_b3 = 2.8. For this model, SST = 3809.6 and SSR = 3285.4.
a.Compute the appropriate t ratios.
b.Test for the significance of $\beta$ ₁, $\beta$ ₂, and $\beta$ ₃ at 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 R_a². Interpret R².
e.Test the significance of the relationship among the variables at the 5% level of significance.

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Definitions:

Personality Traits

Personality traits are enduring patterns of thoughts, feelings, and behaviors that distinguish individuals from one another.

P Technique

A statistical method used in psychology to analyze the variation of psychological variables within a single individual over time, emphasizing personal patterns of behavior.

Factor-analysis

A statistical method used to identify underlying variables, or factors, that explain the pattern of correlations among multiple variables.

R Technique

A statistical method used in personality research to identify correlations among different personality traits or test items.